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Accuracy

Adaptive designs for clinical studies

Not available.

Additive smoothing

This is a method for smoothing categorical data and is available in PROC HPBNET in SAS^® Enterprise Miner^™. The method is discussed and an example is shown in SAS Note 60922.

Adjacent categories logit model

This is one type of logistic model described in SAS Note 22871. Available in SAS/STAT^® PROC LOGISTIC.

Adjusted means

See Means, adjusted.

Agreement, interrater

See Kappa and Gwet's agreement coefficients AC₁ and AC₂.

Agresti-Coull confidence interval for binomial probability

BINOMIAL(AGRESTICOULL) option in TABLE statement of Base SAS^® PROC FREQ.

Aliasing structure

When creating a factorial design, use the ALIASING option in the EXAMINE statement of SAS/QC^® PROC FACTEX. For an existing, orthogonally-coded design, use the ALIASING and E options in the MODEL statement of SAS/STAT^® PROC GLM.

Alpha (Cronbach's)

ALPHA option in Base SAS PROC CORR and SAS^® Viya^® PROC CORRELATION.

Alternating Logistic Regression (ALR)

Use the LOGOR= option in the REPEATED statement in the SAS/STAT PROC GENMOD, or (beginning in SAS^® 9.4M3 [TS1M3]) in PROC GEE. See "Generalized Estimating Equations" in SAS Note 22871.

Analysis of means

SAS/QC^® PROC ANOM. Also, in many modeling procedures in SAS/STAT, the DIFF=ANOM option in the LSMEANS statement. Beginning in SAS^® Studio 3.6, the Analysis of Means task.

ANOVA on summary statistics

For comparing two group means, use SAS/STAT PROC TTEST. See the example in the TTEST documentation. For comparing more than two group means, see this sample program (SAS Note 25020).

Area under a curve, estimation of

Area under ROC curve (AUC)

See ROC curve.

Association analysis

Answers questions like "If item A is purchased, what is the probability that item B is also purchased?" Can be done using the Association or Market Basket node in SAS^® Enterprise Miner™.

Attributable (and Population attributable) rate or fraction

INDIRECT(AF) or MH(AF) option in SAS/STAT PROC STDRATE (beginning in SAS^® 9.3M2 [TS1M2]). See the example in SAS Note 24170, which discusses estimating these in a 2×2 table, and SAS Note 63471, which discusses adjusting for covariates using a modeling approach.

Automatic Interaction Detector (AID)

See CHAID below.

Autoregressive Conditional Heteroscedasticity (ARCH)

SAS/ETS^® PROC AUTOREG.

Average treatment effect (ATE)

Beginning in SAS^® 9.4M4 (TS1M4), SAS/STAT PROC CAUSALTRT.

Average treatment effect for the treated (ATT)

Beginning in SAS 9.4M4, SAS/STAT PROC CAUSALTRT.

Bagging (bootstrap aggregation), Boosting, Ensemble models

SAS Enterprise Miner and, beginning in SAS 9.4, PROC HPFOREST in SAS High-Performance Data Mining. See Gradient boosting.

Balanced Incomplete Block Designs (BIBDs)

In the BLOCKS statement in SAS/QC^® PROC OPTEX, use the structure=(b)k block specification to construct block designs with b blocks of size k. See the Balanced incomplete block design example in the OPTEX chapter of the SAS/QC User's Guide (SAS Note 22930).

Balanced Repeated Replication (BRR) and Jackknife variance estimation

These replication methods are available via the VARMETHOD= option in the survey procedures in SAS/STAT software — SURVEYFREQ, SURVEYLOGISTIC, SURVEYMEANS, SURVEYPHREG, and SURVEYREG.

Barnard's unconditional exact test for 2×2 tables

BARNARD option in EXACT statement of SAS/STAT PROC FREQ.

Bartholomew test of ordering of proportions

Not available. But the Cochran-Armitage test of linear trend, which tests a stricter alternative hypothesis, is available.

Bartlett test for variance homogeneity (homoscedasticity), sphericity

See SAS Note 22526 for testing homoscedasticity in PROC ANOVA and PROC GLM. See SAS Note 33323 for testing sphericity in PROC FACTOR. Also, see Covariance matrices, testing the equality of.

Bayesian Methods

Berkson estimation

See Minimum chi-square estimation (Berkson)

Beta-binomial model

Specify DIST=BETABIN in the MODEL statement in SAS/STAT PROC FMM. See the example titled Modeling Mixing Probabilities: All Mice Are Created Equal, but Some Are More Equal in the FMM documentation and this example (SAS Note 52285).

Bhapkar's test

Use the REPEATED statement in the SAS/STAT procedure CATMOD to test marginal homogeneity as in the test of SIDE in the example Repeated Measures, 4 Response Levels, 1 Population in the CATMOD chapter of the SAS/STAT User's Guide (SAS Note 22930). See Agresti (1990), Categorical Data Analysis, pp. 359, 499. Bhapkar's test is asymptotically equivalent to the Stuart-Maxwell test.

Binning (bucket, Winsorized, or quantile)

Beginning in SAS 9.4, Base SAS PROC HPBIN can bin (categorize) interval variables using equal-length (bucket), Winsorized, or pseudo-quantile methods. Also, the GROUPS= option in Base SAS PROC RANK can bin numeric variables into the specified number of quantile-based bins such as quartiles (GROUPS=4), quintiles (GROUPS=5), or percentiles (GROUPS=100).

Binomial cluster model

Specify DIST=BINOMCLUS in the MODEL statement in SAS/STAT PROC FMM. The MODEL statement models the mean and the PROBMODEL statement models the mixing proportions. See the example Modeling Mixing Probabilities: All Mice Are Created Equal, but Some Are More Equal in the FMM documentation.

Binomial probability, test of or confidence interval for

Binomial probabilities, comparing each to overall

Binomial probabilities, comparing two

Biplot

Biserial correlation

BISERIAL macro (SAS Note 24991). See also point biserial correlation.

Bivariate data, generating

See Multivariate data, generating.

Bivariate Logit model

See Multivariate logit model.

Bivariate Probit model

SAS/ETS PROC QLIM beginning in SAS 9.

Bivariate Tobit model

SAS/ETS PROC QLIM beginning in SAS 9.

Bonferroni t-test

SAS/STAT procedures ANOVA, GLM, LIFETEST, MULTTEST, and procedures supporting the LSMEANS, ESTIMATE, or LSMESTIMATE statements with the ADJUST= option.

Bootstrapping (SAS Note 22220)

Boschloo's unconditional exact test for 2×2 tables

Not available.

Box plot (or box-and-whisker plot)

High-resolution: SAS/STAT PROC BOXPLOT, SAS/IML^® Studio, SAS/GRAPH^® PROC GPLOT (I=BOXxxx option in SYMBOL statement). Also SAS Viya PROC SPC.

High- or low-resolution: SAS/QC PROC SHEWHART.

Low-resolution: PLOTS option in Base SAS PROC UNIVARIATE.

Box-Behnken Designs

SAS/QC ADX Interface.

Box-Cox Transformation

Use the BOXCOX transformation in the MODEL statement in SAS/STAT PROC TRANSREG to transform the response variable in a model on independent observations (fit by procedures such as SAS/STAT procedures REG or GLM). For example:

   model BoxCox(y) = identity(x1-x5);

You can also use the BOXCOX option in the MODEL statement of SAS/ETS PROC QLIM. This option allows transformation of both dependent and independent variables. The SAS/QC ADX Interface also provides the Box-Cox transformation. For an autoregressive model, use the BOXCOXAR macro in SAS/ETS.

Box-Tidwell power transformation for independent variables

Not available. See Linearity in the logit (or link), testing.

Bradley-Terry model

SAS/STAT PROC LOGISTIC. See this example (SAS Note 24992).

Breslow-Day test (of homogeneity of odds ratios)

Base SAS PROC FREQ, CMH option.

Brier score or reliability

This is a version of the average squared error when the response is discrete. Beginning in SAS 9.3, the Brier statistic can be obtained from the FITSTAT option in SCORE statement of SAS/STAT PROC LOGISTIC. Also produced by SAS/STAT PROC HPLOGISTIC when the PARTITION statement is specified. Otherwise, Logistic Regression Examples Using the SAS System gives a formula, and it could be computed easily using predicted values from LOGISTIC, PROBIT, or GENMOD.

Calibration

Also known as inverse regression, the goal is to estimate the value of a predictor in the model that produces a specified response mean. See SAS Note 69873, which discusses and illustrates this for generalized linear models. Also see Fiducial (inverse confidence) limits.

Calibration plot

Used in logistic and other categorical response models, this is a smoothed plot of the observed probabilities against the predicted probabilities. Available beginning in SAS^® 9.4M6 (TS1M6) with PLOTS=CALIBRATION or GOF option in PROC LOGISTIC. See example "Goodness-of-Fit Tests and Calibration" in the LOGISTIC documentation (SAS Note 22930) and this blog post.

Causal analysis

Beginning in SAS 9.4M4, SAS/STAT PROC CAUSALTRT estimates the average causal effect of a binary treatment variable on a continuous or discrete outcome. It can adjust for confounding by modeling the treatment assignment or the outcome or both. Beginning in SAS^® 9.4M5 (TS1M5), SAS/STAT PROC CAUSALMED estimates causal mediation effects from observational data. Beginning in SAS Studio 3.6, the Causal Models task. Beginning in SAS Viya 2023.09, PROC CAEFFECT implements model-agnostic estimation methods to adjust for confounding variables when studying the causal effect of a treatment variable on an outcome.

Censored regression

For censored survival models, see Survival analysis and modeling and Interval censored data, analysis and modeling. Models for censored or truncated responses can be fit in SAS/ETS PROC QLIM, PROC HPQLIM (beginning in SAS 9.4), and SAS Viya PROC CQLIM.

CHAID (Chi-square Automatic Interaction Detector)

See the GROW statement in SAS/STAT PROC HPSPLIT for the CHAID and FASTCHAID splitting criterion. In SAS Viya, CHAID can be selected using the GROW statement in the TREESPLIT and FOREST procedures. Also available in SAS Enterprise Miner.

Chi-square goodness-of-fit test for One-way tables (SAS Note 48914)

Chi-square (2-way tables)

CHISQ option in Base SAS PROC FREQ.

Chi-square (corrected)

CHISQ option in Base SAS PROC FREQ.

Chow test

Use the CHOW= or PCHOW= options in the MODEL statement in SAS/ETS PROC AUTOREG or in the FIT statement in SAS/ETS PROC MODEL. The PCHOW= option produces the predictive Chow test. See Example 11 of the book Forecasting Examples for Business and Economics Using the SAS System for information about testing forecasting models for break points using a Chow Test.

Circular (directional, spherical) statistics

Not available.

Clarke test to compare nonnested models (SAS Note 42514)

Classification and Regression Trees

Beginning in SAS 9.4, SAS/STAT PROC HPSPLIT. Classification and regression tree modeling is available in SAS Enterprise Miner and in SAS Viya PROC TREESPLIT. Also, see Decision trees and CHAID.

Clopper-Pearson confidence interval for binomial probability

This is the exact confidence interval provided by the BINOMIAL option in the TABLES or EXACT statement of Base SAS PROC FREQ.

Cluster analysis

Of observations: SAS/STAT procedures CLUSTER, FASTCLUS, MODECLUS. Beginning in SAS Studio 3.6, the Cluster Observations and K-Means Clustering tasks.

Of variables: SAS/STAT procedures VARCLUS. Beginning in SAS Studio 3.6, the Cluster Variables task.

K-means clustering: SAS/STAT PROC FASTCLUS. Beginning in SAS Studio 3.6, the K-Means Clustering task.

Of observations with categorical data: Use SAS/STAT PROC DISTANCE to compute a distance matrix using a selected metric and then analyze the matrix with the CLUSTER or MODECLUS procedure in SAS/STAT. See Distances. Also, you can select a metric and do an analysis using SAS Viya PROC KCLUS.

Tree diagram of: SAS/STAT PROC TREE produces a tree diagram, or dendrogram, summarizing a cluster analysis. See also Classification and regression trees.

Cochran-Armitage trend test

See Trend test for ordered alternatives

Cochran's Q

Create a 2x2x...x2 table and use the AGREE option in Base SAS PROC FREQ. See the example titled Testing Marginal Homogeneity with Cochran's Q in the FREQ chapter of the SAS/STAT User's Guide (SAS Note 22930). Alternatively, create a three-way table with a stratum variable identifying each subject (or matched group), a variable indicating each occasion (condition or individual within matched group), and a binary response variable. Then use the CMH option. For example, if each subject gives a binary response to each of several drugs, use the statement:

  tables subject*drug*response/cmh2 noprint;

Cohen's kappa

See Kappa.

Combinations and Permutations

To compute the number of combinations or permutations use COMB or PERM function in the DATA step. To produce a list enumerating the combinations or permutations, use the ALLCOMB and ALLPERM options (or the LEXCOMB and LEXPERM options) described in the SAS Language Reference: Dictionary (SAS Note 22930). See also the COMB and PERM options in SAS/STAT PROC PLAN. Permuting the observations in a data set (SAS Note 23977) can be done using PROC PLAN or PROC MULTTEST.

Competing-risks data

Beginning in SAS 9.4M1 (TS1M1), use the EVENTCODE= option in the MODEL statement of PROC PHREG. Also, beginning in SAS 9.4M3, use the EVENTCODE= option in the TIME statement of PROC LIFETEST. Beginning in SAS 9.4M5 in PROC PHREG, specify the EVENTCODE(COX)= option in the MODEL statement to fit the Cox model to the cause-specific hazard for each event type separately, or specify EVENTCODE(FG) to fit the proportional subdistribution hazard regression or the Fine and Gray model.

Concordance index

This is the area under the receiver operating characteristic (ROC) curve (AUC).

Collinearity (multicollinearity) diagnostics

Diagnostics for assessing the condition of the information matrix when fitting a model using ordinary least squares are available from the COLLIN (or COLLINOINT), TOL, and VIF options in the MODEL statement in SAS/STAT PROC REG. See SAS Note 32471 for assessing collinearity in generalized linear models fit using maximum likelihood estimation.

Compound distribution model

Estimates aggregate loss over time by modeling the severity (magnitude) of loss and the frequency (count) of loss separately. PROC HPCDM in SAS/ETS and PROC CCDM in SAS Viya. The Tweedie model can be used to model continuous nonnegative data such as loss data, as discussed in SAS Note 68202.

Concordance, Kendall's Coefficient

See Kendall's Coefficient of Concordance.

Conditional logistic model

Conditional Poisson model

See Fixed effects Poisson regression.

Conditional power in a sequential trial

As a means of stochastic curtailment to stop a trial, the CONDPOWER option in SAS/STAT PROC SEQTEST computes the conditional power at an interim stage of rejecting the null hypothesis.

Confidence ellipse for mean or for prediction

Confidence ellipse plots about the mean or individual values are available in Base SAS PROC CORR using the PLOTS=SCATTER(ELLIPSE=MEAN) or PLOTS=SCATTER(ELLIPSE=PREDICTED) option.

Confidence interval

On a mean: CLM, LCLM or UCLM options in Base SAS PROC MEANS. CIBASIC option in Base SAS PROC UNIVARIATE.

On a correlation: FISHER option in PROC CORR.

On a variance or standard deviation: CIBASIC option in Base SAS PROC UNIVARIATE.

On a variance ratio: See SAS Note 70062.

On a percentile (for example, the median): CIPCTLDF or the CIPCTLNORMAL option in Base SAS PROC UNIVARIATE.

On a binomial probability

On a difference between two binomial probabilities: Arrange the proportions as the two rows of a 2x2 table for analysis by PROC FREQ and specify the RISKDIFF option in the TABLES statement.

On a relative potency

On odds ratios

On a rate (SAS Note 24188)

On the area under an ROC curve (AUC): See ROC (Receiver Operating Characteristic) curve.

On hazard (or risk) ratios: Use the RISKLIMITS option in the MODEL statement of SAS/STAT PROC PHREG. To save these to a data set, use the global ODS OUTPUT statement.

On normal regression parameters: CLB option in the MODEL statement of SAS/STAT PROC REG or the CLPARM= option in the MODEL statement of SAS/STAT PROC GLM.

On logistic and probit regression parameters: CLPARM= option in the MODEL statement of SAS/STAT PROC LOGISTIC. Use the LINK=PROBIT option to request a probit model. To save these to a data set, use the global ODS OUTPUT statement.

On the predictor value that produces a specified response probability: Known as inverse (or fiducial) confidence limits in a logistic or probit model. Use the INVERSECL option in SAS/STAT PROC PROBIT.

Conjoint Analysis

SAS/STAT PROC TRANSREG. See SAS Technical Report R-109: Conjoint Analysis Examples. Also see the examples titled Nonmetric Conjoint Analysis of Tire Data and Metric Conjoint Analysis of Tire Data in the TRANSREG chapter of the SAS/STAT User's Guide (SAS Note 22930).

Constraint programming

SAS/OR PROC CLP or the Constraint Programming Solver within PROC OPTMODEL (SOLVE WITH CLP). Also SAS Viya PROC CLP.

Continuation ratio logit model

This is one type of logistic model described in SAS Note 22871.

Control Charts

SAS/QC procedures SHEWHART, MACONTROL, CUSUM, and (beginning in SAS 9.4M3) RAREEVENTS. Beginning in SAS Studio 3.6, the Control Charts task. Also, SAS Viya PROC SPC.

Cook's D

SAS/STAT procedures REG and GLM (COOKD= options in the OUTPUT statement), RSREG (D option in the MODEL statement), and LOGISTIC (C= option in the OUTPUT statement, but this value must be divided by the number of parameters in the model). A similar statistic can be computed for generalized linear models. Specify the COOKD= option in the OUTPUT statement of SAS/STAT PROC GENMOD. Also, see SAS Note 25005.

Copulas

Beginning in SAS 9.3, you can simulate realizations or estimate parameters of multivariate distributions using copulas in SAS/ETS PROC COPULA and HPCOPULA. Also, SAS Viya PROC CCOPULA. Normal, normal mixture, and t copulas are supported in SAS/ETS PROC MODEL with the COPULA= option in the SOLVE statement. For more information and examples, see this paper.

Correlations

Confidence interval using Fisher Z transformation: FISHER option in PROC CORR.
Compare two populations using Fisher Z transformation: FISHER option in PROC CORR. See the example title "Applications of Fisher's z Transformation" in the CORR procedure documentation.

Biserial: BISERIAL macro (SAS Note 24991)
Canonical: SAS/STAT PROC CANCORR and beginning in SAS Studio 3.6, the Canonical Correlation task.
Hoeffding's D: Base SAS PROC CORR (HOEFFDING option)
Intraclass: See Intraclass correlation
Kendall's tau-a: SAS/STAT PROC LOGISTIC for assessing the correlation between observed responses and predicted probabilities
Kendall's tau-b: Base SAS procedures CORR (KENDALL option) and FREQ (MEASURES option)
Matthews correlation coefficient (MCC)
Partial: Base SAS PROC CORR (PARTIAL statement), SAS/STAT PROC REG (PCORR1 and PCORR2 options), SAS/STAT PROC LOGISTIC (PCORR option), SAS/STAT PROC CANCORR (SQPCORR option). Also, for partial correlations for predictors in linear, generalized linear, and other models, see the RsquareV macro (SAS Note 60162) and the discussion and example in SAS Note 22605. For GEE models, a partial R² can be computed as shown in SAS Note 67880.
Pearson: Base SAS procedures CORR, HPCORR (beginning in SAS 9.4), and FREQ (MEASURES option). SAS Viya PROC CORRELATION.
Point biserial: Base SAS PROC CORR (The point biserial correlation is equivalent to the Pearson product moment correlation between two variables where the dichotomous variable is given any two numeric values.); BISERIAL macro (SAS Note 24991)
Polychoric: Base SAS PROC FREQ (PLCORR option). POLYCHORIC option in Base SAS PROC CORR and in SAS/STAT PROC IRT. Beginning in SAS 9.4, the OUTPLC= option in Base SAS PROC CORR saves a matrix of polychoric correlations.
Polyserial: Beginning in SAS 9.3, the POLYSERIAL option in Base SAS PROC CORR. Beginning in SAS 9.4, the OUTPLS= option in Base SAS PROC CORR saves a matrix of polyserial correlations.
Rank Biserial: BISERIAL macro (SAS Note 24991)
Semipartial: SAS/STAT PROC REG (SCORR1, SCORR2 options), CANCORR (SPCORR and SQSPCORR options)
Spearman: Base SAS procedures CORR (SPEARMAN option) and FREQ (MEASURES option)
Stuart's tau-c: Base SAS PROC FREQ (MEASURES option)
Tetrachoric: Same as Polychoric above.

Correspondence Analysis

SAS/STAT PROC CORRESP performs simple and multiple correspondence analysis. Beginning in SAS Studio 3.6, see the Correspondence Analysis task.

Correspondence Analysis, canonical

Not available.

Correspondence Analysis, detrended

Not available.

Count data

Modeling counts: See Poisson regression and Negative binomial regression.

Modeling and estimating rates (counts per exposure amount): See Rates and rate ratios, estimating and comparing.

Distribution analysis of count time series: Beginning in SAS 9.4M3, COUNT statement in SAS/ETS PROC TIMESERIES.

Forecasting count time series: See Leonard & Elsheimer (2015).

Covariance matrices, testing the equality of

SAS/STAT PROC DISCRIM with the POOL=TEST option provides Bartlett's test of the equality of two or more independent covariance matrices. You can input the raw data, or the covariance, correlation, or sums of squares and crossproducts (SSCP) matrices. The test assumes that the variables are normally distributed. See SAS Note 24987.

Cox Regression

SAS/STAT PROC PHREG and SAS Viya PROC PHSELECT. For survey data, SAS/STAT PROC SURVEYREG.

CPK (process capability indices)

SAS/QC PROC CAPABILITY.

CPM (Critical Path Method)

SAS/OR^® PROC CPM.

Crossover analysis

Analysis of data from AB/BA crossover designs with the CROSSOVER= option in the VAR statement of SAS/STAT PROC TTEST.

Crossvalidation

d (Somer's)

See Somer's d.

D-Optimal designs

SAS/QC PROC OPTEX.

Deciles

See Quantiles

Decision trees

Beginning in SAS 9.4, PROC HPSPLIT in SAS/STAT and PROC HPFOREST in SAS High-Performance Data Mining. Also, SAS Enterprise Miner and PROC FOREST in SAS^® Visual Data Mining and Machine Learning. SAS/OR PROC DTREE for decision analysis. Also, see Classification and Regression Trees.

Deming regression

See Errors-in-variables regression.

Dendrogram

SAS/STAT PROC TREE.

Density estimation, Parametric and Nonparametric

Both Parametric density estimation (fitting theoretical distributions to data) and nonparametric, kernel density estimation are available.

Derivatives

The DERIVS sample program (SAS Note 25001) uses SAS/ETS PROC EXPAND to fit a cubic smoothing spline to paired (X,Y) data. The first and second derivatives of the spline are computed and output to a SAS data set. Finally, the first and second derivatives are plotted against X.

Descriptive statistics

Many descriptive, or summary, statistics are available in Base SAS procedures MEANS, SUMMARY, and UNIVARIATE, including such statistics as the number of observations (N), mean, median, mode, total (sum), minimum, maximum, mode, extreme values, range, standard deviation, variance, standard error, skewness, kurtosis, percentiles, and others. Many other procedures provide various subsets of these accompanying their primary analytical results.

Design of experiments

SAS/QC procedures FACTEX, OPTEX and the ADX Interface. See the SAS/QC User's Guide (SAS Note 22930) and Getting Started with the SAS ADX Interface for Design of Experiments

Design matrix, create in a data set

The SAS/STAT procedures GLMMOD, LOGISTIC, and TRANSREG can all create a design matrix and write it to a data set as shown in SAS Note 23217.

DETMAX

SAS/QC PROC OPTEX.

Dickey-Fuller test for unit root

SAS/ETS DFTEST macro or STATIONARITY=ADF option in the IDENTIFY statement of SAS/ETS PROC ARIMA or the White Noise and Stationarity Tests window of the SAS/ETS Time Series Forecasting System. If the test statistic has been computed but the p-value associated with the statistic is needed, use either the SAS/ETS DFPVALUE macro or the SAS/ETS PROBDF function.

Diebold-Mariano Test

Not available. This test compares the forecast accuracy of two competing time series models fit to a given set of data.

Difference in differences of means (SAS Note 61830)

Differential equations

See ODE (Ordinary Differential Equations)

Discrete Choice model

Discriminant analysis

SAS/STAT PROC DISCRIM and beginning in SAS Studio 3.6, the Discriminant Analysis task.

Distances

SAS/STAT PROC DISTANCE and beginning in SAS Studio 3.6, the Compute Similarities and Distances task.

Distribution Fitting

See Density estimation

Distributions, Comparing

Use the EDF option in SAS/STAT PROC NPAR1WAY to compare the distributions of two or more samples.

Duncan multiple range test

SAS/STAT procedures GLM and ANOVA.

Dunnett's test

SAS/STAT procedures GLM and ANOVA.

Durbin-Watson statistic

SAS/STAT PROC GLM (CLI or CLM options), SAS/STAT PROC REG (DW option), SAS/ETS PROC AUTOREG (DW= option), SAS/ETS PROC MODEL (DW option in FIT statement).

ED50

See LD50.

Effect selection

Effect size

See eta-squared and omega-squared below. Use the EFFECTSIZE option in the MODEL statement in SAS/STAT PROC GLM.

Efficiency

The efficiency is a value obtained for each cutpoint on the ROC curve associated with a binary response model. It is a weighted average of sensitivity and specificity. The cutpoint with the maximum efficiency is one choice for an optimal cutpoint. While not directly provided in any modeling procedure, the efficiency is easily computed as p×sensitivity + (1-p)×specificity. It is also available, along with other optimality criteria, in the ROCPLOT macro (SAS Note 25018) and, beginning in SAS Viya 2022.10, using options in ROCOPTIONS in the PROC LOGISTIC statement.

Elastic net selection

Beginning in SAS 9.4M1, SAS/STAT PROC GLMSELECT with option SELECTION=ELASTICNET in the MODEL statement. Also, using SAS/STAT PROC NLMIXED as described in SAS Note 60240

EM (Expectation Maximization) algorithm

Used in SAS/STAT PROC MI (see the EM statement) to compute the maximum likelihood estimate (MLE) of the data with missing values, assuming a multivariate normal distribution for the data. Available in SAS/STAT PROC IRT for estimating item response models. 

E_max or Hill model  SAS Note 22871

Empirical distribution functions, comparison of

EDF option in SAS/STAT PROC NPAR1WAY.

Equality of Means

SAS/QC PROC ANOM, SAS/STAT procedures ANOVA, GLM, MULTTEST, and TTEST.

Equality of Variances

Equivalence (and noninferiority, superiority) tests

For binomial proportion and difference in proportions:  EQUIV, NONINF, and SUP suboptions of BINOMIAL and RISKDIFF options in Base SAS PROC FREQ.

For mean, mean ratio, or mean difference:  TOST option in SAS/STAT PROC TTEST provides Schuirman's two one-sided test (TOST) for normal or lognormal data.

Power and sample size:  SAS/STAT PROC POWER for test of binomial proportion or difference of proportions in one-, two-, or paired-sample situations. Also for one-sample test of mean for normal or lognormal data, and for two- or paired-sample tests for mean difference of normal data or for mean ratio of lognormal data.

Errors-in-variables regression

This is a regression model that minimizes the perpendicular distances from the data points to the fitted line. A SAS/IML solution is described in this blog entry. Or use SAS/OR PROC OPTMODEL. Alternatively, see this paper for a macro implementing Deming regression, or use SAS/STAT PROC CALIS (see Specifying Structural Equation Models in the Introduction to Structural Equations with Latent Variables chapter of the SAS/STAT User's Guide).

Eta-squared

EFFECTSIZE option in the MODEL statement in SAS/STAT PROC GLM.

Exact and Monte Carlo methods

Exact confidence interval for binomial probability, p

See Confidence interval for binomial probability, p

Exact logistic regression

EXACT statement in SAS/STAT PROC LOGISTIC. See also the EXACTOPTIONS option in the PROC LOGISTIC statement. Also the EXACT statement in PROC GENMOD with the DIST=BINOMIAL option in the MODEL statement. See also the EXACTOPTIONS statement. A stratified exact analysis is provided if the STRATA statement is also specified in either procedure.

Exact Poisson regression

EXACT statement in PROC GENMOD along with the DIST=POISSON option in the MODEL statement. A stratified exact analysis is provided if the STRATA statement is also specified.

Experimental Design

See Design of Experiments.

Exponentially weighted moving average (EWMA) models

EWMA models can be fit for forecasting purposes. For information about using EWMA models in quality control, see SAS/QC PROC MACONTROL.

F1

The F1 statistic is the harmonic mean of precision (PPV) and recall (sensitivity). See SAS Note 24170. Used by the PRcurve macro (SAS Note 68077) as criterion to find an optimal threshold on the precision-recall curve.

Factor analysis

SAS/STAT FACTOR and CALIS procedures, and beginning in SAS Studio 3.6, the Factor Analysis task.

Factor analysis, confirmatory

SAS/STAT PROC CALIS. See the examples in the Examples section of the CALIS documentation (SAS Note 22930).

Factor analysis, Q-mode

Factorial

Use the Base SAS FACT function. For example, FACT(7) computes 7! ("seven factorial"). The Base SAS GAMMA function can also be used. The factorial of an integer, x, is returned by GAMMA(x+1).

Factorization machines

PROC FACTMAC in SAS^® Visual Data Mining and Machine Learning.

False discovery rate, FDR

In a 2x2 table, see SAS Note 24170. As a p-value adjustment for multiple testing, see the FDR option, and other FDR-related options, in SAS/STAT PROC MULTTEST.

False positive or negative probability

Fiducial (inverse confidence) limits

INVERSECL option in SAS/STAT PROC PROBIT. Also see Calibration.

Fieller's theorem

The INVERSECL option in SAS/STAT PROC PROBIT uses Fieller's theorem to provide confidence intervals for response rates in a binary response model. SAS Note 56476 discusses using Fieller's theorem and the delta method to provide confidence intervals for a ratio of linear combinations of model parameters in generalized linear models.

Fine and Gray model

See Competing-risks data

Finite Mixture Models

SAS/STAT PROC FMM.

Firth's penalized maximum likelihood estimation method

FIRTH option in the MODEL statement of SAS/STAT PROC LOGISTIC (for logit-linked models only) or PROC PHREG. Beginning in SAS 9.4M5, the FIRTH option is available with all links in PROC LOGISTIC. Firth's method is useful in cases of nonconvergence due to separation in logistic regression (SAS Note 22599) or monotone likelihood in the Cox model. Firth's method reduces bias in the parameter estimates. In logistic regression, such bias can occur when modeling a rare event resulting in underestimation of the event probability.

Fishbone diagrams

SAS/QC PROC ISHIKAWA.

Fisher's exact test

Base SAS PROC FREQ (FISHER option in the EXACT statement), SAS/STAT PROC MULTTEST (FISHER option in the TEST statement).

Fisher's least significant difference

SAS/STAT procedures ANOVA and GLM.

Fisher's z transformation

See Confidence Interval and Correlations above.

Fixed effects (conditional) logistic regression

SAS/STAT PROC PHREG, PROC LOGISTIC, or PROC GENMOD using the STRATA statement.

Fixed effects Poisson regression

This model conditions out the strata (clusters, panels) parameters. Beginning in SAS 9.4M1, fit this model using the ERRORCOMP=FIXED option in the MODEL statement and the GROUPID= option in the PROC COUNTREG statement of SAS/ETS PROC COUNTREG. Beginning in SAS 9.4M2, it can be fit in the same way in SAS/ETS PROC HPCOUNTREG. Also, SAS Viya PROC CNTSELECT using the same syntax. For small data sets, exact methods can be used by specifying the EXACT and STRATA statements in SAS/STAT PROC GENMOD. It can also be fit using SAS/STAT PROC NLMIXED by specifying the conditional log likelihood function. However, since the conditional and unconditional models yield identical estimates of the non-strata parameters (see Fixed Effects Regression Methods for Longitudinal Data Using SAS), the conditional model parameters can be obtained by fitting the unconditional model in PROC GENMOD by including the strata variable in the model as a CLASS variable. The unconditional model can also be fit in SAS/ETS PROC COUNTREG, SAS Viya PROC GENSELECT or PROC CNTSELECT, or beginning in SAS 9.4, in SAS/STAT PROC HPGENSELECT or SAS/ETS PROC HPCOUNTREG by specifying the strata identifier variable in both the CLASS and MODEL statements.

Fold-over designs

Fold-over Plackett-Burman designs are directly available in the ADX Interface in SAS/QC. Fractional factorial designs, created by ADX or SAS/QC PROC FACTEX, can be folded over using the DATA step. See the example titled Fold-Over Design in SAS/QC User's Guide (SAS Note 22930). These designs reduce the aliasing in the original design.

Forest plot SAS Note 35413

Four- or 5-parameter logistic model SAS Note 22871

Fractional Factorial Designs

SAS/QC PROC FACTEX and the ADX Interface.

Fractional logistic (or logit) model SAS Note 22871

Fractional polynomials

This method of adaptive regression analysis is not available, but see this paper.

Frailty model

Specifying the RANDOM statement in SAS/STAT PROC PHREG allows you to fit a shared frailty model for clustered data resulting in correlated failure times. Beginning in SAS 9.3M2, adding the BAYES statement requests a Bayesian frailty model. See the discussion and example in the PHREG documentation.

Freeman-Halton test

This is the extension of Fisher's exact test to tables larger than 2x2 and is available via the FISHER option in the EXACT statement in Base SAS PROC FREQ.

Friedman's test

Base SAS PROC FREQ, CMH2 option. The Row Mean Scores Differ CMH statistic is Friedman's test if there is only one response per treatment-block combination. See the example titled "Friedman's Chi-Square Statistic" in the FREQ documentation (SAS Note 22930). For more than one response per combination, this statistic is a generalization of Friedman's test. Alternatively, you can obtain an F-approximation to Friedman's test by using Base SAS PROC RANK to rank the data within blocks and then SAS/STAT PROC GLM to fit a two-way ANOVA model. The LSMEANS statement with the PDIFF option provides approximations to the rank-sum multiple comparisons of treatment effects. For example:

  proc rank data=in out=ranked;
    by block; var y; ranks ry; 
    run;
  proc glm data=ranked;
    class block trt;
    model ry = block trt;
    lsmeans trt / pdiff;
    run;

Full-information maximum likelihood (FIML)

SAS/ETS procedures SYSLIN and MODEL. Beginning in SAS 9.3, METHOD=FIML option in SAS/STAT PROC CALIS.

Gauge (or gage) repeatability and reproducibility (R&R)

METHOD=GRR option in SAS/STAT PROC VARCOMP. Two macros are available in SAS/QC. See the Measurement Systems Analysis appendix in the SAS/QC documentation and the examples in the SAS/QC Sample Library. Also, see the paper by LaBarr (1994) in the Proceedings of the Nineteenth Annual SAS Users Group International Conference (SUGI19).

Gail-Simon Test for Qualitative Interaction

For binary response data in stratified 2x2 tables, use the CMH(GAILSIMON) option in the TABLES statement of Base SAS PROC FREQ. For continuous response, see the GAILSIMON macro presented in the book Analysis of Clinical Trials Using SAS: A Practical Guide by Dmitrienko et. al.

Gains chart SAS Note 41683

GAMs (Generalized Additive Models)

SAS/STAT PROC GAM or, beginning in SAS 9.4M3, PROC GAMPL. Also SAS Viya PROC GAMMOD.

GARCH (Generalized Autoregressive Conditional Heteroscedasticity)

SAS/ETS PROC AUTOREG can fit several variations of the GARCH model. The HETERO statement estimates and tests heteroscedasticity models. Also, SAS/ETS PROC MODEL with the H.var specification. See the examples here of estimating GARCH models.

Gatekeeping strategies for multiple endpoints

These multiple testing strategies are not directly available, but gatekeeping procedures and macros implementing them are presented in the book Analysis of Clinical Trials Using SAS: A Practical Guide by Dmitrienko, et. al. (SAS Institute, 2005).

Geary's c

AUTOCORR option in the COMPUTE statement of SAS/STAT PROC VARIOGRAM.

GEE (Generalized Estimating Equations)

First-order GEE (GEE1): Use the REPEATED statement in SAS/STAT PROC GENMOD or (beginning in SAS 9.4M2) PROC GEE. For multinomial responses: use GEE or GENMOD for an ordinal response, use GEE for a nominal response. Also, SAS/STAT PROC GLIMMIX with the EMPIRICAL option and RANDOM _RESIDUAL_ statement with subject variable in the SUBJECT= option. Beginning in 2023.02 in SAS Visual Statistics, use PROC LOGSELECT. Second-order GEE (GEE2): Can be done using GLIMMIX or SAS/STAT NLMIXED by treating the response as normally distributed, regardless of its true distribution. See Vonesh (2012) in SAS Note 22608. See also, Weighted GEE.

Generalized (Non)Linear (Mixed) Models

SAS/STAT procedures GENMOD, GLIMMIX, NLMIXED, and beginning in SAS 9.4 HPGENSELECT and HPNLMOD. Also, SAS Viya procedures GENSELECT, CQLIM, and NLMOD. Beginning in SAS Studio 3.6, the Mixed Models task. Also, beginning in SAS 9.4M4, SAS/ETS PROC QLIM fits logit and probit models, optionally with random effects. Particular models in this class are also fit by other procedures. For example, logistic models (with no random effects) can also be fit with SAS/STAT PROC LOGISTIC and probit models by SAS/STAT PROC PROBIT.

Generalized Poisson regression SAS Note 56549

Genetic algorithms

SAS/OR PROC OPTLSO. See the SAS/OR User's Guide: Local Search Optimization (SAS Note 22930) for discussion and examples. You can use these tools to optimize problems involving integer, continuous, binary, or combinatorial variables, especially for finding optima for problems where the objective function might have discontinuities or might not otherwise be suitable for optimization by traditional calculus-based methods.

Geometric mean

Beginning in SAS 9.4M2, the GEOMEAN option in the OUTPUT statement of Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY provides a point estimate. The DIST=LOGNORMAL option in SAS/STAT PROC TTEST provides the point estimate(s) and confidence interval(s) for one or two groups and can provide the ratio and a test comparing two groups. Beginning in SAS 9.3M2, the ALLGEO option in SAS/STAT PROC SURVEYMEANS provides a standard error estimate as well as a point estimate and confidence interval for survey data. To compute the geometric mean of values across variables within observations, use the Base SAS function GEOMEAN or GEOMEANZ.

Gini index (of diagnostic test performance)

This is a measure of logistic model fit related to the area under the ROC curve (AUC), c, by Gini = 2c-1. The Gini index is provided by SAS/STAT PROC LOGISTIC as Somers' D. For classification trees, the Gini index is computed by SAS/STAT PROC HPSPLIT and SAS Viya procedures BINNING and TREESPLIT.

Gini's mean difference

ROBUSTSCALE option in Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY. This is a robust estimate of the population standard deviation.

Goal Programming

Beginning in SAS 9.4M6 and SAS Optimization 8.3 in SAS Viya 3.4, use the LSO solver in PROC OPTMODEL.

Goodness-of-fit test

For fitting a theoretical distribution to a sample of data, see Distribution Fitting.

Gradient boosting

Gradient boosting node in SAS Enterprise Miner and PROC GRADBOOST in SAS^® Visual Data Mining and Machine Learning.

Granger causality test

CAUSAL statement in PROC VARMAX. Also, see the example here, which uses the autoregressive specification of a bivariate vector autoregression.

Group sequential methods

See Sequential methods, design and testing.

Guttman scaling

There was a procedure, PROC GUTTMAN, in the Version 5 supplemental library that handled up to twelve items. This procedure is not available after Version 5. Guttman recommended correspondence analysis as an alternative (see Measurement and Prediction, Stouffer and Guttman, Wiley 1966). SAS/STAT PROC CORRESP performs correspondence analysis. A similar method is the Rasch model. See Andrich (1988), Rasch Models for Measurement, Sage Publication 07-068.

Gwet's AC₁ and AC₂

Available for measuring or testing agreement between two or more raters. For two raters only: AC₁ is available beginning in SAS 9.4M4 with the AGREE(AC1) option in Base SAS PROC FREQ and beginning in SAS 9.4M5 with the AGREE(AC1) option in SAS/STAT PROC SURVEYFREQ. For two or more raters: AC₁ and AC₂ (for ordinal response) are available with the MAGREE macro (SAS Note 25006).

Harmonic mean

You can obtain a nonparametric estimate of the harmonic mean of values in an observation using the Base SAS function HARMEAN or HARMEANZ. A maximum likelihood estimate can be obtained using PROC NLMIXED as described in SAS Note 44415.

Hausman specification test

HAUSMAN option in the FIT statement in SAS/ETS PROC MODEL. The Hausman test for the IIA (Independence of Irrelevant Alternatives) assumption can be performed using %IIA macro available in the PROC MDC documentation example Hausman's Specification and Likelihood Ratio Tests.

Hazard ratios

By default, SAS/STAT PROC PHREG produces hazard ratio estimates for predictors not involved in interactions. The RISKLIMITS option in the MODEL statement provides confidence intervals. The HAZARDRATIO statement can be used to obtain estimates and confidence intervals even when predictors are involved in interactions.

Heckman model

See Sample selection models.

Heteroscedasticity or Homoscedasticity tests

Hidden Markov model

SAS Viya PROC HMM fits the Gaussian hidden Markov model.

Hierarchical Linear Models (HLMs)

Use SAS/STAT PROC MIXED or PROC GLIMMIX with RANDOM statements. HLMs are also commonly called multilevel models or random coefficients models. See SAS Note 22882 for more.

Hodrick-Prescott filter

TRANSFORM= option in the CONVERT statement of SAS/ETS PROC EXPAND.

Hoeffding's D

See Correlations:Hoeffding's D

Hollander-Proschan New Better than Used in Expectation (NBUE) test

Not available.

Homogeneity of Variance, tests of

Hosmer-Lemeshow test of fit

LACKFIT or GOF option in SAS/STAT PROC LOGISTIC.

Hotelling's T-square

See SAS System for Linear Models

Huber-White Sandwich Estimator

See White's empirical ("sandwich") variance estimator and robust standard errors

Hurdle models

PROC FMM beginning in SAS 9.3. See SAS Note 48506.

Impute missing values

See Missing value imputation

Independence of Irrelevant Alternatives (IIA)

See Hausman specification test

Independent Component Analysis (ICA)

Not available. This is a multivariate variable reduction method related to principal components analysis, which finds independent, not just uncorrelated, components for possibly nonnormal data.

Information value (IV)

WOE option in Base SAS PROC HPBIN (beginning in SAS 9.4).

Integration

SAS/IML (CALL QUAD). Beginning in SAS 9.4M3, specify CALL QUAD in SAS/STAT PROC MCMC to use a general integration function enabling the procedure to fit models, such as marginal likelihood models, that require integration. See also Area under a curve, estimation of.

Interim analysis

See Sequential methods, design and testing.

Interpolation, linear

Use SAS/ETS PROC EXPAND as shown in SAS Note 24560.

Interquartile range

Base SAS PROC UNIVARIATE and SAS/QC PROC CAPABILITY.

Interrupted time series analysis (SAS Note 70498)

Interval censored data, analysis and modeling

See SAS/STAT procedures ICPHREG (and this example), ICLIFETEST, and LIFEREG.

Intervention analysis

Consists of difference in difference analysis (SAS Note 61830) for single measures before and after the intervention and interrupted time series analysis (SAS Note 70498) when subjects provide multiple measures before and after intervention.

Intraclass correlation

Use the INTRACC macro (SAS Note 25031). SAS/STAT PROC NESTED can also compute an intraclass correlation. Using the second example in the INTRACC macro description, these statements produce the intraclass correlation in the PAIR row and Percent of Total column of the NESTED results:

proc sort data=table1 out=tt; 
  by pair; 
  run;
proc nested data=tt;
  class pair;
  var score;
  run;

For categorical ratings, the kappa statistic has the properties of an intraclass correlation coefficient and can be used for interrater reliability.

Inverse (fiducial) confidence limits

INVERSECL option in SAS/STAT PROC PROBIT.

Inverse Mill's ratio

See Mill's ratio.

Inverse regression

INVERSECL option in SAS/STAT PROC PROBIT. Also see Calibration.

Ishikawa diagrams

SAS/QC PROC ISHIKAWA and SAS/QC SQC Menu System

Item Response Theory

PROC IRT beginning in SAS 9.4M1.

Iterative Proportional Fitting (IPF)

IPF can be used as a maximum likelihood estimating algorithm for fitting loglinear models. It can also adjust (balance) an observed n-way table using a set of tables with known or desired margins. See SAS/IML subroutine CALL IPF. For fitting loglinear models, also see the ML=IPF option in the MODEL statement in SAS/STAT PROC CATMOD.

Jackknifing

Jeffreys confidence interval for binomial probability

BINOMIAL(JEFFREYS) option in TABLE statement of Base SAS PROC FREQ.

Joint modeling

SAS/STAT PROC GLIMMIX can be used for joint modeling of multivariate outcomes. See the example in the GLIMMIX documentation (SAS Note 22930).

Jonckheere-Terpstra test

See Trend test for ordered alternatives.

Kalman filter

SAS/IML functions KALCVF, KALCVS, KALDFF, and KALDFS.

Kappa for agreement of two or more raters

For measuring or testing agreement between two raters on a set of subjects or objects, kappa (simple or weighted) and prevalence-adjusted bias-adjusted kappa are available with the AGREE option in the TABLES or EXACT statement in Base SAS PROC FREQ. Beginning in SAS 9.4M1, kappa (simple or weighted) is also available with the AGREE option in the TABLES statement in SAS/STAT PROC SURVEYFREQ. See also Gwet's AC₁ and AC₂. For measuring or testing agreement among more than two raters, Fleiss' kappa is available in the MAGREE macro (SAS Note 25006). See SAS Note 69654 on estimating and testing functions of kappas.

Kendall's Coefficient of Concordance

MAGREE macro (SAS Note 25006)

Kendall correlation

Base SAS PROC CORR (KENDALL option).

Kendall's Tau

See Correlations.

Kernel Density Estimation

In Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY, use the KERNEL option in the HISTOGRAM statement (or in the COMPHISTOGRAM statement in PROC CAPABILITY). Beginning in SAS 9.3, SAS/ETS PROC SEVERITY can plot the kernel estimate in plots of the PDF or CDF. In SAS/STAT procedures KDE and DISCRIM, use the KERNEL= and R= options.

Kolmogorov-Smirnov (KS) test

In SAS/STAT PROC NPAR1WAY, the EDF option in the PROC NPAR1WAY statement provides an asymptotic test. The EDF or KS option in the EXACT statement provides an exact test. For assessing a binary response model, such as a logistic model, see SAS Note 39109.

Kriging

SAS/STAT PROC KRIGE2D.

Kronecker (or direct) product of matrices

Use the @ operator in SAS/IML.

Kruskal-Wallis test

In SAS/STAT PROC NPAR1WAY, the WILCOXON option in the PROC NPAR1WAY statement provides an asymptotic test. The WILCOXON option in the EXACT statement provides an exact test.

Kuder-Richardson 20 (KR20)

For binary data, this statistic is equivalent to coefficient alpha and can be computed with the ALPHA option in Base SAS PROC CORR.

Kurtosis

Base SAS procedures UNIVARIATE and MEANS.

L₁ and L₂ penalties for regression

These penalties constrain, or regularize, the regression parameters. L₁ regularization is known as LASSO. L₂ regularization is known as ridging. Elastic net uses a combination of L₁ and L₂ penalties. See Penalized regression methods. See also Least absolute value regression.

Latent Analysis

This is a broad class of methods including Latent Trait Analysis (LTA), Latent Profile Analysis, Latent Class Analysis (LCA), and Latent Class Regression. LTA is also called Item Response Theory. One method is factor analysis of binary or ordinal data. See this site regarding user-written procedures for LCA and LTA. These procedures are not supported by SAS Institute.

LD50

INVERSECL option in SAS/STAT PROC PROBIT. See SAS Note 56476, which illustrates estimating the LD50 and obtaining a confidence interval using both Fieller's theorem and the delta method.

LD50, Comparing across groups SAS Note 44931

LASSO (Least Absolute Shrinkage and Selection Operator), group LASSO, and adaptive LASSO selection

The LASSO method is available in SAS/STAT PROC GLMSELECT and (beginning in SAS 9.3M2) in PROC QUANTSELECT with option SELECTION=LASSO in the MODEL statement. Beginning in SAS 9.4, also in PROC HPREG with option METHOD=LASSO in the SELECTION statement. Beginning in SAS 9.4M1, also in SAS/ETS PROC COUNTREG with option SELECT=PEN in the MODEL statement. The adaptive LASSO method is available in PROC GLMSELECT and (beginning in SAS 9.3M2) in PROC QUANTSELECT with option SELECTION=LASSO(ADAPTIVE) in the MODEL statement. Beginning in SAS 9.4M3, the group LASSO method is available in PROC GLMSELECT with option SELECTION=GROUPLASSO in the MODEL statement and in PROC HPGENSELECT with option METHOD=LASSO in the SELECTION statement. LASSO, and other penalty-based methods, can be implemented in SAS/STAT PROC NLMIXED as shown in SAS Note 60240. In SAS Viya, LASSO methods are available in several procedures including LOGSELECT, GENSELECT, REGSELECT, and PHSELECT.

Least Angle Regression (LAR)

Available for normal-response models in SAS/STAT PROC GLMSELECT. Beginning in SAS 9.4, in SAS/STAT HPREG. Also, SAS Viya PROC REGSELECT.

Least Absolute Value (LAV, L₁, or median) regression

LAV regression minimizes the absolute values of the residuals. This is the default model fit by SAS/STAT PROC QUANTREG. Alternatively, use CALL LAV in SAS/IML.

Levene's test of equal variances

Lift, in a 2×2 table

Lift chart SAS Note 41683

Likelihood ratios, LR⁺ and LR^-, in a 2×2 table

Likelihood Ratio test for model comparison

Likelihood ratio chi-square

Base SAS PROC FREQ (CHISQ option).

Linear programming (optimization)

SAS/OR PROC OPTMODEL and PROC OPTMILP.

Linearity in the logit (or link), testing

To test for nonlinearity in the logit (for logistic models) and more generally for finding a suitable functional form for an independent variable in a generalized linear model (GLM), use the spline smoother on the variable in SAS/STAT PROC GAMPL or SAS Viya PROC GAMMOD. See the example titled "Nonparametric Logistic Regression" in the GAMPL documentation. Also see the ASSESS statement in SAS/STAT PROC GENMOD for assessing the covariate or link function in a GLM or Generalized Estimating Equations (GEE) model.

Ljung-Box Q statistic

SAS/ETS PROC ARIMA. The White Noise and Stationarity Tests window of the SAS/ETS Time Series Forecasting System.

Loess curve-fitting

SAS/STAT procedures LOESS, GAM or, beginning in SAS 9.4M3, GAMPL. 

Loglinear models

DIST=POISSON option in SAS/STAT PROC GENMOD, SAS/ETS PROC COUNTREG, or in SAS Viya, in the CNTSELECT or GENSELECT procedures. Beginning in SAS 9.4, DIST=POISSON options in PROC HPGENSELECT or SAS/ETS PROC HPCOUNTREG. Also, using the LOGLIN statement in SAS/STAT PROC CATMOD.

Longitudinal data analysis

See Repeated measures analysis

Loss model

See Compound distribution model.

M estimation

See Robust Regression

MAD (Median Absolute Deviation)

ROBUSTSCALE option in Base SAS PROC UNIVARIATE, SAS/IML function MAD, SAS/STAT procedures DISTANCE, ROBUSTREG, and STDIZE.

Mahalanobis distances

MAHALANOBIS function in SAS/IML. The Mahalanobis distance from each observation to the mean can also be obtained by computing the square root of the uncorrected sum of squared principal component scores within each output observation from SAS/STAT PROC PRINCOMP using the STD option. See SAS Note 30662 for an example, which also shows computing Mahalanobis distances from each of a set of observations to a reference point and distances between each pair of observations. The SAS/IML function MVE can also be used to compute Mahalanobis distances.

Major axis regression

See Errors-in-variables regression

Mann-Whitney U Test

Equivalent to the Wilcoxon rank sum test.

Mantel-Fleiss criterion for Mantel-Haenszel chi-square approximation

CMH(MANTELFLEISS) option in the TABLES statement of Base SAS PROC FREQ.

Mantel-Haenszel chi square

Base SAS PROC FREQ (CHISQ and CMH options).

Marginal homogeneity, test of

For binary responses, use McNemar's test or Cochran's Q, both provided by the AGREE option in Base SAS PROC FREQ. For multilevel responses, use the REPEATED statement in SAS/STAT PROC CATMOD. See Bhapkar's test and Stuart-Maxwell test.

Marginal model plots

These plots, proposed by Cook and Weisberg (1997) and discussed by Fox and Weisberg (2011), display the marginal relationship between the response and each predictor in a model. See this paper for discussion and examples.

Margins, predictive and marginal effects

The MARGINS statement can estimate and test predictive margins and marginal effects for CLASS (categorical) predictors and is available in many SAS Viya procedures. For both categorical and continuous predictors, the Margins macro (SAS Note 63038) can be used once downloaded and included. The Margins macro can estimate and test predictive margins and average marginal effects in generalized linear and GEE models fit using SAS/STAT PROC GENMOD. Predictive margins and average marginal effects can be estimated by the macro at specified values of other model variables or at computed values such as means or medians. For binary or ordinal logit or probit models, point estimates of marginal effects for predictors not involved in interactions can be obtained from the MARGINAL option in the OUTPUT statement of SAS/ETS PROC QLIM. SAS Note 22604 discusses and illustrates the estimation of marginal effects in logit and probit models.

Market basket analysis

See Association analysis.

Market Research methods

These methods include conjoint analysis, correspondence analysis, discrete choice analysis, multidimensional preference analysis, multidimensional scaling, perceptual mapping methods, and preference mapping. See also these Market Research papers and tools.

Matthews correlation coefficient, MCC

Also known as the phi coefficient, MCC is the geometric mean of precision (PPV) and recall (sensitivity). Used by the PRcurve macro (SAS Note 68077) as criterion to find an optimal threshold on the precision-recall curve.

MARS^Note (Multivariate Adaptive Regression Splines)

Beginning in SAS 9.3M2, SAS/STAT PROC ADAPTIVEREG fits multivariate adaptive regression splines, a nonparametric regression technique.

Maximum likelihood estimation in linear models

McFadden's model

See Conditional Logistic model.

McNemar's test and related confidence interval

AGREE option in Base SAS PROC FREQ. Alternatively, create a three-way table with a stratum variable identifying each subject (or matched group), a binary variable indicating each occasion (or condition or individual within matched group), and a binary response variable. Then use the CMH option. For example, if each subject gives a binary response to each of two drugs, use the statement: tables subject*drug*response/cmh2 noprint;
Using this three-variable form of the data, additional methods can produce a test of the difference between the two occasions/conditions (marginal homogeneity) and a confidence interval of the difference. See SAS Note 46997.

Means, adjusted

See the LSMEANS statement and the Margins macro (SAS Note 63038) for two approaches. The construction of LSMEANS is described in "Construction of Least Squares Means" in the Shared Concepts and Topics chapter of the SAS/STAT User's Guide (SAS Note 22930).

Means, test of equality of

See Equality of Means

Median

See Quantiles

Mediation analysis

Beginning in SAS 9.4M5, SAS/STAT PROC CAUSALMED. Also, see SAS Note 59081.

Meta-analysis

There is no procedure or macro that specifically conducts meta-analyses. However, PROC MIXED has been used for meta-analysis, as discussed in this paper by considering multiple observed studies as a random sample of possible studies in a larger population and employing a random effects model. Also, SAS Note 59221 illustrates a Bayesian meta-analysis to estimate study-specific and pooled odds ratios using a random effects model.

Mills ratio

The inverse Mills ratio can be computed for censored or truncated continuous responses, binary discrete responses, and endogenous selection variables via the MILLS option in the OUTPUT statement of SAS/ETS PROC QLIM and SAS Viya PROC CQLIM.

Minimum aberration designs

SAS/QC PROC FACTEX (MINABS option in the MODEL statement)

Minimum chi-square estimation (Berkson)

This is an alternative method for estimating the parameters of a logistic regression model requiring multiple observations at each setting of the covariates. See Maddala (1983), Limited dependent and qualitative variables in econometrics. It is not directly available in any procedure. SAS/STAT procedures LOGISTIC, PROBIT, and GENMOD estimate the logistic model by maximum likelihood.

Missing value imputation

SAS/STAT procedures MI, MIANALYZE, and (beginning in SAS 9.4M3) SURVEYIMPUTE. Beginning in Base SAS 9.4, PROC HPIMPUTE. Beginning in SAS Studio 3.6, the Replace Missing Values task. SAS/STAT PROC STDIZE (see the MISSING=, REPLACE, and REPONLY options). Base SAS PROC STANDARD (REPLACE option) replaces missing values with the mean or a constant. SAS/STAT PROC PRINQUAL (METHOD=MGV and REPLACE options). For time series data, see SAS/ETS PROC EXPAND.

Mixed logit model

Mixture experiments: Design and analysis

Mixture experiment designs such as simplex-centroid and simplex-lattice designs, possibly with constraints or including process variables, can be produced and analyzed by the SAS/QC ADX Interface. See Getting Started with the ADX Interface for Design of Experiments. SAS/QC PROC OPTEX can also be used for experiment design. See examples titled "Constructing a Mixture-Process Design" and "Adding Space-Filling Points to a Design".

Model selection

Several methods for selecting a final model from among a list of candidate effects are available in many procedures. Methods include forward, backward, stepwise, best subset, R-square-based, least angle regression (LAR), LASSO (including adaptive LASSO and group LASSO), and elastic net selection methods. The procedures offering some of these methods are listed in SAS Note 52362, which also discusses grouping of effects for entry or removal from the model.

Modified Park test

For selecting a suitable response distribution in log-linked generalized linear models, based on the mean-variance relationship. See SAS Note 60335.

Monte Carlo estimation of exact p-values

See Exact and Monte Carlo methods

Monte Carlo Simulation

See Simulation.

Moran's I

AUTOCORR option in the COMPUTE statement of SAS/STAT PROC VARIOGRAM.

Mosaic plots

Available for two- or multi-way tables in Base SAS PROC FREQ and SAS/STAT PROC SURVEYFREQ when specifying the PLOTS=MOSAICPLOT option.

Moving average

MLOGIT or MPROBIT procedures

These are not procedures written or supported by SAS Institute. The last known contact for these procedures is Salford Systems. See Multinomial Logit model, Conditional logistic model, Multinomial Probit model, or Mill's ratio.

Multidimensional preference analysis

SAS/STAT PROC PRINQUAL and, beginning in SAS Studio 3.6, the Multidimensional Preference Analysis task.

Multidimensional scaling

SAS/STAT PROC MDS.

Multinomial cluster model

Beginning in SAS 9.4M2, specify DIST=MCLUS in the MODEL statement in SAS/STAT PROC FMM. The MODEL statement models the mean and the PROBMODEL statement models the mixing proportions. See the example Modeling Multinomial Overdispersion: Town and Country in the FMM documentation.

Multinomial Logit model

Multinomial Probit model

SAS/ETS PROC MDC

Multiple comparisons of means

See Student's t-test. In the context of generalized linear models, the NLMeans macro (SAS Note 62362).

Multiple comparisons (repeated measures)

In SAS/STAT PROC MIXED, use the PDIFF option in the LSMEANS statement to generate multiple comparisons on repeated measures.

Multiple testing, p-value or confidence interval adjustment for

Many adjustment methods are available in SAS/STAT PROC MULTTEST (Bonferroni, Sidak, Holm, Hochberg, Hommel, Stouffer-Liptak, false discovery rate (FDR), Fisher combination, adaptive methods, step-up and step-down methods, and resampling methods using bootstrap or permutation). MULTTEST does not provide adjusted confidence intervals. Adjustment of p-values and confidence intervals is available via the ADJUST= option in the LSMEANS or LSMESTIMATE statement in many SAS/STAT procedures (STRATA statement in PROC LIFETEST). 

Multivariate GARCH models

GARCH statement in SAS/ETS PROC VARMAX.

Multivariate logit model SAS Note 22871

Multivariate data, generating

Use the RANDxxx function modules in SAS/IML to generate samples from multivariate normal, multivariate t, Wishart (generalization of gamma), Dirichlet (generalization of beta), multinomial (generalization of binomial) distributions. SAS/STAT PROC SIMNORMAL can perform conditional and unconditional simulation for a set of correlated normal random variables. To generate multivariate binary data from variables with specified means and correlation matrix, see the RanMBin macro (SAS Note 66969).

Multivariate normality, Test of

See Normality, test of.

Multivariate probit models

SAS/ETS PROC QLIM

Negative binomial regression

SAS/STAT procedures GENMOD, GLIMMIX, NLMIXED, or beginning in SAS 9.4, HPGENSELECT, HPNLMOD. Also, SAS Viya procedures GENSELECT, CNTSELECT, and NLMOD. SAS/ETS PROC COUNTREG, or beginning in SAS 9.4, PROC HPCOUNTREG. A version of the negative binomial with linear variance function is also available with the DIST=NEGBIN(P=1) option in COUNTREG, HPCOUNTREG, or CNTSELECT.

Negative predictive value, NPV

Nested Logit models

Network optimization

For graph theory, combinatorial, or network analysis optimization, use SAS/OR PROC OPTNET or the NETWORK solver in SAS/OR PROC OPTMODEL. Beginning in SAS Studio 3.6, see the Network Optimization task. In SAS Viya, see the NETWORK and OPTNETWORK procedures and the Network Optimization action set.

Neural Networks

Neural node in SAS Enterprise Miner or PROC HPNEURAL beginning in SAS 9.4 of SAS High-Performance Data Mining. Also, PROC NNET in SAS^® Visual Data Mining and Machine Learning.

Newey-West standard error correction

SAS/ETS PROC MODEL with KERNEL= option in the FIT statement with GMM estimator. See SAS Note 40098 for discussion and examples. Beginning in SAS 9.3M2, SAS/ETS PROC AUTOREG with COVEST=NEWEYWEST option in the MODEL statement (see available suboptions). Not available in SAS/STAT PROC REG.

Noncentrality parameter for F, t, or chi-square

Base SAS functions FNONCT, TNONCT, and CNONCT respectively

Noninferiority test for binomial proportion or difference in proportions

See Equivalence tests.

Nonparametric methods

See the Introduction to Nonparametric Analysis chapter in the SAS/STAT User's Guide (SAS Note 22930).

One sample: Base SAS PROC UNIVARIATE provides tests for location (median).

Two or more independent samples: SAS/STAT PROC NPAR1WAY provides tests for location and scale differences.

Multiple comparisons for more than two independent samples: Beginning with SAS 9.3M2, specify the DSCF option in PROC NPAR1WAY.

Two dependent samples: Base SAS PROC UNIVARIATE provides tests for location (median). Base SAS PROC FREQ provides McNemar's test.

More than two dependent samples: Friedman's test in Base SAS PROC FREQ

Regression: See Nonparametric, Robust (or Resistant) Regression

Correlation: Base SAS procedures CORR and FREQ. See Correlations.

Trend: The Jonckheere-Terpstra test is a nonparametric test of trend.

Density estimation: See Kernel Density Estimation

Discriminant Analysis: SAS/STAT PROC DISCRIM with METHOD=NPAR option and either the K= (nearest neighbor) or the R= (kernel density estimation) option.

Nonparametric, Robust (or Resistant) Regression

Includes such methods as median or quantile regression, kernel regression, adaptive regression, thin-plate splines, loess, radial smoothing, wavelets, least absolute value (LAV) or L₁ regression, Least Median of Squares (LMS), Least Trimmed Squares (LTS), Minimum Covariance Determinant (MCD), and Minimum Volume Ellipsoid (MVE). SAS/STAT PROC ADAPTIVEREG fits multivariate adaptive regression splines. SAS/STAT PROC ROBUSTREG (see the METHOD= option) provides Huber M estimation, high breakdown value estimation (LTS and S methods), and combinations of the two (MM method), and employs a generalized MCD algorithm in leverage point analysis. See also the SAS/IML functions LAV, LMS, LTS, MCD, and MVE.

Normality, test of

Univariate tests of normality are provided by Base SAS PROC UNIVARIATE, and SAS/QC PROC CAPABILITY. Tests of univariate and four tests of multivariate normality (Royston, Mardia, Henze-Zirkler, and Doornik-Hansen) can be obtained using the MultNorm macro (SAS Note 24983). The Mardia and Henze-Zirkler tests are available with the NORMAL option in the FIT statement of SAS/ETS PROC MODEL.

Number needed to treat SAS Note 24170

Odds Ratios

Model-based methods: By default, SAS/STAT PROC LOGISTIC produces odds ratio point estimates and confidence intervals (CLODDS= to select Wald or profile likelihood intervals) for predictors not involved in interactions. The ODDSRATIO statement provides estimates and confidence intervals even when predictors are involved in interactions. If associated p-values are desired, include the ORPVALUE option in the MODEL statement. The ODDSRATIO option (SAS Note 24455), along with the DIFF= or SLICEDIFF= option, in the LSMEANS statement of PROC GLIMMIX provides point estimates (add CL option for confidence intervals). Custom odds ratios can be computed in the SAS/STAT procedures CATMOD, LOGISTIC, GENMOD, GLIMMIX, or SURVEYLOGISTIC by determining the contrast of logistic model parameters that represents the desired difference in log odds for two groups and then using the CONTRAST or ESTIMATE statement with the ESTIMATE=EXP or EXP option. When GLM parameterization of CLASS variables is used in the LOGISTIC, GENMOD, GLIMMIX, or SURVEYLOGISTIC procedures, you can also use the EXP option in the LSMESTIMATE statement, or the DIFF and EXP options in the LSMEANS and SLICE statements.

Nonmodeling methods: The RELRISK or MEASURES option in Base SAS PROC FREQ for 2x2 tables and the CMH option for stratified 2x2 tables provide point estimates and confidence intervals. The OR and COMOR options in the EXACT statement provide exact confidence intervals and tests. 

ODE (Ordinary Differential Equations), solving

SAS/ETS PROC MODEL. SAS/IML CALL ODE. Beginning in SAS 9.4M3, specify CALL ODE in SAS/STAT PROC MCMC to use an ordinary differential equation (ODE) solver enabling the procedure to fit models that contain differential equations such as pharmacokinetic models.

Omega-squared

EFFECTSIZE option in the MODEL statement in SAS/STAT PROC GLM.

One-sided test

See Test model parameter(s) equal to a constant (one- or two-sided).

Optimization

SAS/OR procedures OPTMODEL, OPTLP, OPTQP, OPTMILP, and OPTNET. These procedures and PROC OPTNETWORK are also available in SAS Viya along with the Optimization and Network Optimization action sets. Also see SAS/ETS PROC MODEL. In SAS/IML, see the linear and nonlinear optimization subroutines. See also Network optimization.

Ordered (or ordinal) logistic or probit models

Several types of ordinal models are available and described in SAS Note 22871. SAS/STAT procedures LOGISTIC, HPLOGISTIC, GLIMMIX, GENMOD, PROBIT, and SAS/ETS PROC QLIM. Also, SAS Viya procedures LOGSELECT, GENSELECT, CQLIM, and NLMOD. For repeated measures data, SAS/STAT PROC GENMOD and PROC GEE.

Orthogonal regression

See Errors-in-variables regression

Outlier detection

In the context of regression, see the DIAGNOSTICS and LEVERAGE options in the MODEL statements of SAS/STAT procedures ROBUSTREG and QUANTREG. MVE function in SAS/IML. See also the example titled Outliers in the FASTCLUS chapter of the SAS/STAT User's Guide (SAS Note 22930).

Overdispersion and Underdispersion

See the general discussion in SAS Note 22630 and the examples in SAS Note 56549 of models available for count data exhibiting over- or underdispersion.

p, test or confidence interval for

See Binomial Probability.

Paired t-test

See Student's t-test

Panel data analysis

Panel data occurs when time series and cross-sectional data are combined. SAS/ETS procedures PANEL, HPPANEL, and TSCSREG fit econometric models to such data. Also, SAS Viya PROC CPANEL and PROC CNTSELECT. For panel data arising from repeated and correlated measures on subjects or objects, see Repeated measures analysis.

Pareto charts

SAS/QC PROC PARETO and SQC Menu System. Beginning in SAS Studio 3.6, the Pareto Analysis task.

Partial correlation

See Correlations

Partial least squares

SAS/STAT PROC PLS, SAS Viya PROC PLSMOD, and beginning in SAS Studio 3.6, the Partial Least Squares task.

Partial Proportional Odds Model

Partial regression leverage plots

PARTIAL option in the MODEL statement of SAS/STAT PROC REG.

Partially Balanced Incomplete Block Designs (PBIBDs)

See Balanced Incomplete Block Designs. No procedure creates these specifically, but SAS/QC PROC OPTEX might find such designs if they are optimal according to the criterion used.

Passing-Bablok regression

Not available, but see Errors-in-variables regression.

Path analysis

SAS/STAT PROC CALIS

Path diagrams

Beginning in SAS 9.4M1, PROC CALIS. Beginning in SAS 9.4M2, PROC FACTOR.

Pearson correlation

See Correlations

Penalized regression methods

Methods include LASSO (including group and adaptive LASSO), ridging, and elastic net and are available in several SAS/STAT and SAS/ETS procedures. The LASSO method is useful for model selection. These penalized regression methods can also be implemented in SAS/STAT PROC NLMIXED by specifying the likelihood function and including the appropriate penalty term as described in SAS Note 60240. See also the Firth method.

Percentiles

See Quantiles

Perceptual mapping methods

This encompasses the following methods: See correspondence analysis, preference mapping, multidimensional preference analysis, and multidimensional scaling.

Permutations

See Combinations and permutations.

PERT

SAS/OR PROC CPM

Peto test

The Peto mortality-prevalence test is available in SAS/STAT PROC MULTTEST. The Peto-Peto and modified Peto-Peto test for comparing survival curves is available in SAS/STAT PROC LIFETEST.

Pharmacokinetics (PK) compartment model

Beginning in SAS 9.4M5, the CMPTMODEL statement in SAS/STAT PROC NLMIXED and PROC MCMC enables you to fit one-, two-, and three-compartment models. Also, see ODE. 

Phi coefficient

Base SAS PROC FREQ (CHISQ option).

Piecewise Regression

PROC NLIN provides a method to estimate segmented models. PROC NLIN requires you to specify the functional form of your equation. See the example, Segmented Model, in the PROC NLIN documentation, which illustrates fitting a continuous, smooth curve in two segments joined at an unknown point. PROC TRANSREG is another procedure that can fit a piecewise regression model via splines. The number and location of knots can be specified. See the example, Using Splines and Knots in the PROC TRANSREG documentation. Other SAS/STAT procedures such as LOESS, TPSLINE, GAM, and GAMPL can fit flexible, nonparametric models to data. Also see Spline effects in models.

Point biserial correlations

See Correlations

Poisson regression

SAS/STAT procedures GENMOD, GLIMMIX, NLMIXED, or beginning in SAS 9.4, HPGENSELECT, HPNLMOD. Also, SAS Viya procedures GENSELECT, CNTSELECT, and NLMOD, SAS/ETS PROC COUNTREG, or beginning in SAS 9.4, PROC HPCOUNTREG. To fit a Poisson model to data collected using survey sampling methods, see this example (SAS Note 59722).

Polychoric correlation

See Correlations

Polychotomous logit model SAS Note 22871

Polyserial correlation

See Correlations

Population attributable rate (PAR) or fraction

INDIRECT(AF) or MH(AF) option in SAS/STAT PROC STDRATE (beginning in SAS 9.3M2). See the example in SAS Note 24170.

Portfolio optimization

SAS/OR PROC OPTQP or SAS/OR PROC OPTMODEL (use SOLVE WITH QP statement).

Positive predictive value, PPV

Power and sample size

In SAS/STAT, the POWER and GLMPOWER procedures, the Power and Sample Size Application, and beginning in SAS Studio 3.6, the Power and Sample Size task all perform prospective power and sample size analyses. Also, see the sample programs for computing sample size or the power of chi-square tests that compare two proportions (SAS Note 25012) or testing independence in RxC tables (SAS Note 25013) and this discussion (SAS Note 24298) on computing power in contingency tables.

Precision

Precision is also known as the Positive Predictive Value (PPV). Can be plotted against precision (positive predictive value, PPV) by PRcurve macro to assess model performance for rare event data.

Precision-recall curve

Often used to assess performance of a binary response model or classifier with rare event data where the ROC curve can be misleading. Beginning in SAS Viya 2022.09, PROC LOGISTIC can plot the curve, compute the area beneath it, and find optimal points using various criteria. Also, the PRcurve macro (SAS Note 68077) plots precision against recall, computes the area beneath it, and can find optimal points on the curve.

Prediction intervals

For normally distributed data, prediction intervals are available via options in the OUTPUT statements of the REG, GLM, NLIN, and HPMIXED procedures, and in the MODEL statement of the TRANSREG procedure in SAS/STAT software. The SCORE statement in SAS/STAT PROC PLM can also produce prediction intervals, but only for regression models on normally distributed data with identity link. For non-normal distributions used in generalized linear models, quantile-based prediction intervals (including uncertainty in the mean estimate or not) are available with the GLMPI macro (SAS Note 69692).

Predictive power in a sequential trial

As a means of stochastic curtailment to stop a trial, the PREDPOWER option in SAS/STAT PROC SEQTEST computes the predictive power at an interim stage of the trial.

Preference mapping

SAS/STAT PROC TRANSREG.

Prevalence Ratio

See Relative Risk.

Principal Components Analysis (PCA)

SAS/STAT PRINCOMP, FACTOR, and (beginning in SAS 9.4M1) HPPRINCOMP. Also, SAS Viya PROC PCA, and beginning in SAS Studio 3.6, the Principal Components Analysis task.

Probability plots

Base SAS PROC UNIVARIATE and SAS/QC PROC CAPABILITY.

Project management

SAS/OR PROC CPM.

Projection pursuit

Not available.

Propensity score analysis

Beginning in SAS 9.4M4, SAS/STAT PROC PSMATCH can compute propensity scores (PSMODEL statement) or import propensity scores (PSDATA statement), and can match observations based on those scores (MATCH statement) using one of three methods. The balance of the resulting matched data can be assessed (ASSESS statement). Creation of strata (STRATA statement) or weights (OUTPUT statement) is also available for use in outcome analysis done in other procedures.

Proportion, test or confidence interval for

See Binomial Probability.

Proportional hazards model

SAS/STAT procedures PHREG, ICPHREG, and SURVEYPHREG.

Q-mode factor analysis

QIC for GEE models

Provided by PROC GEE and PROC GENMOD with the REPEATED statement.

Quantiles

Base SAS procedures UNIVARIATE, MEANS, and SUMMARY can estimate quantiles and weighted quantiles. If the weights are survey weights, use SAS/STAT PROC SURVEYMEANS.

Quantile regression

SAS/STAT procedures QUANTREG, QUANTLIFE, and QUANTSELECT. Also, SAS Viya PROC QTRSELECT. See also Least Absolute Value regression.

Quartiles

See Quantiles

Queuing

Not available.

R-square

An R-square statistic based on sums of squares is provided in several SAS/STAT regression procedures (REG, ORTHOREG, ROBUSTREG, GLM, GLMSELECT, and others) and clustering and multivariate procedures (CLUSTER, DISCRIM, FASTCLUS, VARCLUS). Several likelihood-based R-square measures are available in SAS/STAT procedures that use maximum likelihood estimation such as LOGISTIC, HPLOGISTIC, SURVEYLOGISTIC as well as in several SAS/ETS procedures (AUTOREG, QLIM, TSCSREG, and others). An R-square measure based on the squared length of the variance function for models like generalized linear models and generalized additive models is available using the RsquareV macro (SAS Note 60162). For GEE models, an R² statistic can be computed as shown in SAS Note 67880.

R-square, partial

For models fit in SAS/STAT PROC REG, see SAS Note 22641. For generalized linear models and generalized additive models, a partial R² based on the variance function is available from the RsquareV macro (SAS Note 60162). For GEE models, a partial R² can be computed as shown in SAS Note 67880.

Radial smoothing

SAS/STAT PROC GLIMMIX with TYPE=RSMOOTH and KNOTMETHOD= options in the RANDOM statement.

Random forests

Beginning in SAS 9.4, PROC HPFOREST in SAS High-Performance Data Mining. Also, PROC FOREST in SAS^® Visual Data Mining and Machine Learning.

Random numbers, generating

Use the RAND function in the DATA step to generate random values from any of a wide variety of theoretical univariate distributions. Also, see Multivariate data, generating.

Random sampling

SAS/STAT PROC SURVEYSELECT provides several methods for selecting probability-based random samples. Beginning in SAS 9.4, Base SAS PROC HPSAMPLE performs simple random sampling or stratified sampling. Beginning in SAS Studio 3.6, the Random Sampling task. Random sampling can also be done in the DATA step.

Rank Biserial Correlation

See Correlations

Rasch model

See Item Response Theory

Rates and rate ratios, estimating and comparing

A count of an observed event over a period or amount of exposure is a rate that can exceed 1, such as the number of injuries per person-year. Rates can be modeled, estimated, and compared using Poisson or negative binomial models as shown in SAS Note 24188 and zero-inflated versions of these as in SAS Note 44354. In these models, the log of the rate denominator is specified as an offset. Procedures that can be used include GLIMMIX, GENMOD, HPGENSELECT, and GAMPL in SAS/STAT, COUNTREG and HPCOUNTREG in SAS/ETS as well as others. Comparison of rates can be done in terms of ratios or differences of rates. Proportions, which are bounded between 0 and 1, are typically modeled, estimated, and compared using binomial models such as logistic models that can be fit using SAS/STAT PROC LOGISTIC and others.

Ratio analysis

The RATIO statement in SAS/STAT PROC SURVEYMEANS provides point estimates, confidence intervals, and tests for ratios of continuous or categorical variables. The TEST=RATIO option in SAS/STAT PROC TTEST provides point estimates, confidence intervals, and tests of mean ratios for either normal or lognormal data. In the context of a generalized linear model, which uses a link function involving the log (such as logistic or count models), ratios of means, rates, or log odds can be estimated and tested using the DIFF and EXP option in the LSMEANS, SLICE, or ESTIMATE statement. SAS Note 56476 shows how the Fieller and delta methods can be used to obtain confidence intervals for ratios of functions of model parameters. See also the NLMeans (SAS Note 62362) macro.

Reduced major axis regression

This regression model minimizes the areas of the right triangles formed by the data points' vertical and horizontal deviations from the fitted line and the fitted line. Use SAS/OR PROC NLP with appropriate minimization criterion. For example:

   proc nlp;
      min area;
      parms b1=1, b0=1;
      area=(y - (b0 + b1*x))**2 / abs(b1);
      run;

Recall

Recall is also known as sensitivity. Can be plotted against precision (positive predictive value, PPV) by PRcurve macro to assess model performance for rare event data.

Regression

A wide range of regression models is available in many SAS/STAT and SAS/ETS procedures as well as PROC RELIABILITY in SAS/QC. See the SAS/STAT, SAS/ETS, and SAS/QC User's Guides (SAS Note 22930) for details and examples. See also procedures in SAS Viya.

Regularization methods for regression

Regularization methods constrain the regression parameters by applying a penalty. See Penalized regression methods.

Relative potency estimate and confidence interval

See SAS Note 56476, which illustrates using the delta method in SAS/STAT PROC NLMIXED and using Fieller's theorem in SAS/IML. This is also illustrated in Categorical Data Analysis Using the SAS System.

Relative Risk

Also known as the risk ratio. The RELRISK and MEASURES options in Base SAS PROC FREQ compute the relative risk for a 2x2 table and for each strata in a stratified 2x2 tables. For stratified 2x2 tables, an estimate of the common (across strata) relative risk is provided by the CMH option. SAS/STAT PROC GENMOD can provide a model-based estimate of the relative risk (SAS Note 23003).

Reliability coefficient

Base SAS PROC CORR, ALPHA option. See also, Intraclass correlation.

Repeated measures analysis

For normally distributed responses, use SAS/STAT procedures GLM or MIXED. For other response distributions (and normal distributions), use SAS/STAT procedures GENMOD, GLIMMIX, NLMIXED, or (beginning in SAS 9.4M2) PROC GEE. Beginning in SAS 9.4M1, SAS/ETS PROC COUNTREG can be used for repeated count responses (panel data). Beginning in SAS 9.4M2, SAS/ETS PROC HPCOUNTREG is also available for repeated count responses. In SAS Viya, SAS Econometrics PROC CNTSELECT, and beginning in 2023.02 SAS Visual Statistics PROC LOGSELECT.

Repeated measures multiple comparisons

See Multiple comparisons (repeated measures).

Ridge regression

RIDGE= option in SAS/STAT PROC REG. See also Penalized regression methods.

Risk difference (difference in proportions) for multiway tables

Beginning with SAS 9.4M1, the RISKDIFF(COMMON) option (and beginning with SAS 9.4M5, the COMMONRISKDIFF option) in the TABLES statement of PROC FREQ provides the common (overall) risk difference for multiway 2x2 tables. The risk difference can also be estimated when fitting a categorical response model, as discussed in SAS Note 37228.

Risk ratio

Also known as the Relative Risk. Also see Hazard ratios.

Robust estimators

Of location: Trimmed mean or Winsorized mean.

Of scale (variability): Includes Gini's mean difference, interquartile range and MAD (Median Absolute Deviation).

Of R-square: SAS/STAT PROC ROBUSTREG.

Of AIC and BIC: SAS/STAT PROC ROBUSTREG.

Of model parameter standard errors: See White empirical ("sandwich") variance estimator and robust standard errors.

ROC (Receiver Operating Characteristic) curve

Also see Precision-recall curve.

Plot the ROC curve:   Binary response data is required. For a model fit in SAS/STAT PROC LOGISTIC, use an ROC statement, the PLOTS=ROC option, or the OUTROC= option. See the examples in the Examples section of the LOGISTIC documentation (SAS Note 22930). Given predicted event probabilities from any model or method, use the PRED= option in the ROC statement as shown in SAS Note 41364. Beginning in SAS 9.3M2, use the PLOTS=ROC(ID= ) option to label points in the ROC curve with predictor (requires an ID statement) or statistic values. See the two ROC examples in the Examples section of the LOGISTIC documentation. Beginning in SAS 9.4M2, the OUTROC= option in the MODEL statement in PROC HPLOGISTIC produces a data set that can be used with PROC SGPLOT to plot the ROC curve. See the example titled "Modeling Binomial Data" in the HPLOGISTIC documentation (SAS Note 22930). The ROCPLOT macro (SAS Note 25018) also plots and labels points on the ROC curve with additional capabilities. A bias-adjusted estimate of the ROC curve based on an approximate leave-one-out crossvalidation method can be obtained as discussed in SAS Note 39724. Beginning in SAS 9.4M3: For a decision tree model on binary data, use PLOTS=ROC in SAS/STAT PROC HPSPLIT.

Find optimal cutpoints on the ROC curve:  Optimal cutpoints based on the Youden index, efficiency, and other optimality criteria can be found using the ROCPLOT macro (SAS Note 25018) and, beginning in SAS Viya 2022.10, using options in ROCOPTIONS in the PROC LOGISTIC statement. Binary response data is required.

Area under the ROC curve (AUC):   Estimated by default for binary response models and presented as the c statistic (known as the concordance index) in SAS/STAT PROC LOGISTIC. Also, beginning in SAS 9.4, use the ASSOCIATION option in the MODEL statement in PROC HPLOGISTIC with binary response data. An extension of AUC for multinomial responses is available in the MultAUC macro (SAS Note 64029). Given predicted event probabilities from any model or method, use the PRED= option in the ROC statement in PROC LOGISTIC as shown in SAS Note 41364. Use the ROCCI option in the MODEL statement (beginning in SAS 9.4M3 in PROC LOGISTIC) or specify the ROC and ROCCONTRAST statements in PROC LOGISTIC to obtain point and confidence interval estimates of the AUC as shown in SAS Note 31821, which also shows how to test if the AUC differs from 0.5 indicating a model no better than chance. A bias-adjusted estimate and confidence interval for the area based on either validation data or on an approximate leave-one-out crossvalidation method can be obtained as discussed in SAS Note 39724. For a decision tree model on binary data, use SAS/STAT PROC HPSPLIT beginning in SAS 9.4M3.

Comparing areas under several ROC curves:   For binary response models, use the ROC and ROCCONTRAST statements in SAS/STAT PROC LOGISTIC to perform a nonparametric comparison of areas under correlated ROC curves, such as multiple models fit to the same data. To compare independent ROC curves, see SAS Note 45339.

ROC curve for survival models:   Beginning in SAS 9.4M4, ROC statement in SAS/STAT PROC PHREG. See also the CONCORDANCE, PLOTS=ROC | AUC | AUCDIFF, and ROCOPTIONS options in the PROC PHREG statement.

Runs or Wald-Wolfowitz test SAS Note 33092

Runs test or Western Electric Rules

SAS/QC PROC SHEWHART (TESTS= option). Also SAS Viya PROC SPC.

Sample selection models

SAS/ETS PROC QLIM fits the Heckman selection model via maximum likelihood or the two-step estimation method (HECKIT option).

Scheffe multiple comparisons

SAS/STAT procedures ANOVA, GLM, LIFETEST, and procedures supporting the LSMEANS, ESTIMATE, and LSMESTIMATE statements with the ADJUST= option.

Seasonal Kendall's test

Not available.

Seemingly unrelated regression

SAS/ETS procedures SYSLIN and MODEL.

Semi-partial correlations

See Correlations

Sensitivity, True positive rate or fraction (TPR, TPF)

Can be computed by Base SAS PROC FREQ. See SAS Note 24170 for examples. Beginning in SAS 9.4M6, use TABLES statement option SENSPEC. In the context of binary-response models, SAS/STAT PROC LOGISTIC (CTABLE and OUTROC= options).

Sequential methods, design and testing

SAS/STAT procedures SEQDESIGN and SEQTEST.

Shrinkage methods for regression

The use of a penalty shrinks the regression parameters towards zero. See Penalized regression methods.

Simple effects in an interaction, testing

SLICE statement available in many modeling procedures. Note that GLM parameterization (PARAM=GLM) is required for the specified variables.

Simulated annealing

Not available. 

Simultaneous Equations

For estimation of a linear system of simultaneous equations using either two- or three-stage least squares, use SAS/ETS PROC SYSLIN with the 2SLS or 3SLS option in the PROC SYSLIN statement. For estimation of a nonlinear system of simultaneous equations using either two- or three-stage least squares, use the SAS/ETS PROC MODEL with the 2SLS or 3SLS option in the FIT statement. To solve a system of simultaneous equations involving N equations and N unknowns, use PROC MODEL with a SOLVE statement as illustrated in this example. SAS/STAT PROC CALIS for constrained and unconstrained problems in simultaneous equation models with reciprocal causation.

Simulation

See these Blog entries on simulation. Also see Random numbers, generating and Multivariate data, generating. Also see the SOLVE statement in SAS/ETS PROC MODEL for model-based simulation involving nonlinear system models and includes dynamic and Monte Carlo simulation.

Skewness

Base SAS procedures UNIVARIATE and MEANS, and SAS/QC PROC CAPABILITY.

Social network analysis

SAS^® Social Network Analysis. Also, PROC OPTGRAPH in SAS^® Fraud Framework or SAS^® Customer Link Analytics. Also PROC NETWORK in SAS Viya.

Somer's d

Includes Somer's d_XY and d_YX. See the MEASURES option in Base SAS PROC FREQ.

Spatial prediction or modeling

SAS/STAT procedures KRIGE2D and VARIOGRAM. Spatial error structures in repeated measures model can be used by specifying one of the SP covariance structures in the TYPE= option of the REPEATED statement in SAS/STAT PROC MIXED. Beginning in SAS 9.4M4, SAS/ETS PROC SPATIALREG. Also SAS Viya PROC CSPATIALREG. Beginning in SAS 9.4M3, spatial effects can be added in count response models in SAS/ETS PROC COUNTREG.

Spearman correlation

See Correlations

Spearman-Karber estimate of LD50

Not available. See LD50 for other estimation methods.

Specificity, True negative rate or fraction (TNR, TNF)

Can be computed by Base SAS PROC FREQ. See SAS Note 24170 for examples. Beginning in SAS 9.4M6, use TABLES statement option SENSPEC. In the context of binary-response models, SAS/STAT PROC LOGISTIC (CTABLE and OUTROC= options).

Spline effects in models

The EFFECT statement supports truncated power function, B-spline, and natural cubic spline bases in many SAS/STAT and SAS Viya procedures. For more information, see EFFECT Statement in the Shared Concepts and Topics chapter of the SAS/STAT User's Guide and SAS Note 57975. See also SAS Note 70221 and SAS Note 57682 regarding predicted values and plotting in models with splines. For procedures that don't support the EFFECT statement, use the EFFECT statement and OUTDESIGN= option in the LOGISTIC or GLMSELECT procedure to create the design variables representing the spline effect (see SAS Note 23217). Then specify the saved OUTDESIGN= data set in the desired procedure and use the spline variables in your model. Also see Thin-plate smoothing or regression splines, Piecewise Regression, and GAMs (Generalized Additive Models). SAS/STAT PROC TRANSREG can also fit linear models with splines of various types.

Standard deviation, Test and Confidence Interval of

See Variance (one-sample), Test and Confidence Interval

Standardizing data

Base SAS PROC STANDARD, SAS/STAT PROC STDIZE, SAS/STAT PROC DISTANCE.

Standardized mortality (or morbidity) ratio (SMR)

SAS/STAT PROC STDRATE (beginning in SAS 9.3M2).

Standardized rates and risks

Beginning in SAS 9.3M2, SAS/STAT PROC STDRATE provides direct or indirect standardization methods for rates and risks (proportions). See SAS Note 66731 for methods to compute directly standardized stratum-specific rates or risks and confidence intervals.

Stochastic Frontier Models

FRONTIER option in the ENDOGENOUS statement of SAS/ETS PROC QLIM and (beginning in SAS 9.4) PROC HPQLIM. Also SAS Viya PROC CQLIM.

Structural Equation Modeling

SAS/STAT PROC CALIS.

Stuart-Maxwell test

Bhapkar's test is asymptotically equivalent to the Stuart-Maxwell test for marginal homogeneity.

Student-Newman-Keuls test

SAS/STAT procedures GLM and ANOVA.

Student's t-test

One sample: SAS/STAT PROC TTEST using the VAR statement, or Base SAS procedures UNIVARIATE, MEANS, or SUMMARY.

Two independent samples: SAS/STAT PROC TTEST with CLASS and VAR statements, or SAS/STAT PROC MULTTEST (primarily when adjusting for multiple tests).

Two independent samples using summary statistics: See ANOVA on summary statistics.

Two dependent (paired) samples: SAS/STAT PROC TTEST using the PAIRED statement. Or use Base SAS procedures UNIVARIATE, MEANS, or SUMMARY to test that the mean of the difference of paired values is zero.

More than two independent samples (multiple comparisons): Use the MEANS or LSMEANS statement with DIFF option in most SAS/STAT modeling procedures. See also the STRATA statement in SAS/STAT PROC LIFETEST and the TEST MEAN statement in SAS/STAT PROC MULTTEST.

Sum of squares

Corrected and uncorrected sum of squares are available for single samples in Base SAS procedures UNIVARIATE, MEANS, and SUMMARY, and SAS/QC PROC CAPABILITY. In the context of analysis of variance: SAS/STAT procedures ANOVA and GLM.

Summary statistics, ANOVA on

See ANOVA on summary statistics above.

Superiority test for binomial proportion or difference in proportions

See Equivalence tests.

Support vector machines

PROC SVMACHINE in SAS^® Visual Data Mining and Machine Learning.

Survival analysis and modeling

SAS/STAT procedures PHREG, LIFEREG, LIFETEST, ICPHREG, ICLIFETEST, QUANTLIFE, RMSTREG, SURVEYREG, and SAS/ETS PROC SEVERITY. For information, see Introduction to Survival Analysis Procedures in the SAS/STAT Users's Guide (SAS Note 22930). See also, Cox Regression, Frailty model, Competing risks data, Interval censored data, Quantile regression, and Proportional hazards model.

Symmetry, test of in 2-way table

AGREE option in Base SAS PROC FREQ.

System of logistic equations

Not available.

t-test

See Student's t-test.

Taguchi designs

SAS/QC ADX Interface. See Getting Started with the SAS ADX Interface for Design of Experiments.

Tau-a (Kendall's)

See Correlations

Tau-b (Kendall's)

See Correlations

Tau-c (Stuart's)

See Correlations

Test model parameter(s) equal to a constant (one- or two-sided)

Tests of model parameters, or functions of model parameters, against a zero or nonzero null, including one-sided (one-tailed) and two-sided (two-tailed) tests, can be done as discussed in SAS Note 24094.

Tetrachoric correlation

See Correlations

Tetrachoric correlation matrix

OUTPLC= option in Base SAS PROC CORR. Also, see the POLYCHOR macro (SAS Note 25010). For two binary variables, the polychoric correlation is the tetrachoric correlation.

Thin-plate smoothing or regression splines

SAS/STAT procedures TPSPLINE, GAM, and beginning in SAS 9.4M3, GAMPL. Also, PROC GAMMOD in SAS Viya.

Three-stage least squares (3SLS)

SAS/ETS procedures SYSLIN and MODEL.

Tobit analysis

SAS/STAT PROC LIFEREG. Also SAS/ETS PROC QLIM and (beginning in SAS 9.4) PROC HPQLIM.

Tolerance intervals

SAS/QC PROC CAPABILITY.

Trend test for ordered alternatives

For binary responses: Cochran-Armitage test in Base SAS PROC FREQ (TREND option in TABLES statement); SAS/STAT PROC MULTTEST (CA option in TEST statement); score test in SAS/STAT PROC LOGISTIC (equivalent to the Cochran-Armitage test).

For binary or multilevel responses: Jonckheere-Terpstra test in Base SAS PROC FREQ (JT option in the TABLES statement).

For continuous responses: Use Base SAS PROC CORR with KENDALL option. The p-value for the Kendall statistic is equivalent to the two-tailed p-value for the Jonckheere statistic. The one-tailed p-value is half this p-value. If the number of distinct response values is small, Base SAS PROC FREQ with the JT option can also be used. In small sample situations, an exact test is available (use the EXACT JT; statement).

Trimmed mean

TRIMMED= option in Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY. 

Truncated negative binomial model SAS Note 43522

Truncated Poisson model SAS Note 43522

Truncated regression

SAS/ETS PROC QLIM and PROC HPQLIM (beginning in SAS 9.4) fit the truncated normal model. Beginning in SAS 9.3, SAS/STAT PROC FMM and SAS/ETS PROC SEVERITY (and PROC HPSEVERITY beginning in SAS 9.4) can fit truncated models using various distributions. Also SAS Viya PROC CQLIM and SEVSELECT.

Tukey's range test

SAS/STAT procedures ANOVA, GLM, LIFETEST, and procedures supporting the LSMEANS statement with the ADJUST= option.

TURF (Total Unreplicated Reach and Frequency) analysis

Not available.

Tweedie model

In SAS/STAT, DIST=TWEEDIE option in PROC HPGENSELECT, PROC GENMOD (beginning in SAS 9.4M1), and PROC GAMPL (beginning in SAS 9.4M5). Also SAS Viya procedures GENSELECT, GAMMOD, and SEVSELECT. Two parameterizations of the Tweedie distribution are available in SAS/ETS PROC SEVERITY beginning in SAS 9.3, in SAS/ETS PROC HPSEVERITY beginning in SAS 9.4, and in SAS Viya PROC SEVSELECT. The Tweedie model can be used to model continuous nonnegative data such as loss data, as discussed in SAS Note 68202. See also the Ratemaking node in SAS Enterprise Miner 7.1 or later for modeling pure premium.

Two-stage least squares (2SLS)

SAS/ETS procedures SYSLIN and MODEL.

van Elteren test SAS Note 25022

Variable selection

Variance (one-sample), Test and Confidence Interval

Base SAS PROC UNIVARIATE (CIBASIC option) provides one- and two-sided confidence intervals for the standard deviation and variance. SAS/STAT PROC TTEST provides a confidence interval for the standard deviation using either of two methods. Robust estimators of scale are also available.

Variances (k samples), test of equality

Variance inflation factors (VIF)

See Collinearity (multicollinearity) diagnostics.

Vector autoregressive models

SAS/ETS PROC VARMAX

Vuong test to compare nonnested models SAS Note 42514

Wald confidence interval for binomial probability

BINOMIAL(WALD) option in TABLE statement of Base SAS PROC FREQ.

Wald-Wolfowitz or Runs test SAS Note 33092

Wavelets

WAVxxx functions in SAS/IML.

Weight of evidence (WOE)

WOE option in Base SAS PROC HPBIN (SAS 9.4 or later).

Weighted Generalized Estimating Equations (WGEE)

Beginning in SAS 9.4M2, SAS/STAT PROC GEE. The GEE method for longitudinal analysis assumes data missing completely at random (MCAR). WGEE extends this to situations in which data are missing at random (MAR).

Weighted means

Base SAS procedures MEANS, SUMMARY, and UNIVARIATE with WEIGHT statement (for estimates). SAS/STAT PROC GLM with WEIGHT statement (for test comparing weighted means). SAS/STAT PROC SURVEYMEANS (if weights are from a complex survey design).

Weighted quantiles (percentiles, quartiles, deciles)

See Quantiles

Western Electric Rules

See Runs test

Westgard Rules

Use the TESTS=T and TESTS=M chart statement options in SAS/QC PROC SHEWHART to specify custom T-pattern and M-pattern tests.

White's empirical ("sandwich") variance estimator and robust standard errors

In ordinary regression: WHITE option in the MODEL statement of SAS/STAT PROC REG displays White standard errors and tests based on them.

In generalized linear models: This is the default variance estimator used when the REPEATED statement is specified in SAS/STAT PROC GENMOD or (beginning in SAS 9.4M2) PROC GEE, and parameter tests are based on it. Note that repeated measurements are not required in order to use the REPEATED statement.

In mixed models: EMPIRICAL option in the PROC statements of SAS/STAT PROC MIXED, PROC GLIMMIX, and PROC NLMIXED displays White standard errors and tests based on them.

In econometric models: HCCME= option in the FIT statement of SAS/ETS PROC MODEL and in the MODEL statement of SAS/ETS PROC PANEL displays White standard errors and tests based on them.

Wilcoxon Rank Sum Test

SAS/STAT PROC NPAR1WAY, WILCOXON option. Base SAS PROC FREQ, CMH option.

Wilcoxon Signed Rank Test

Base SAS PROC UNIVARIATE

Wilson (score) confidence interval for binomial probability

BINOMIAL(WILSON) option in TABLE statement of Base SAS PROC FREQ.

Winsorized mean

WINSORIZED= option in Base SAS PROC UNIVARIATE or SAS/QC PROC CAPABILITY. 

Youden index

The Youden index is a value obtained for each cutpoint on the ROC curve associated with a binary response model. It is the height of each cutpoint above the diagonal line representing an uninformative model. The cutpoint with the maximum Youden index is one choice for an optimal cutpoint. The Youden index is easily computed as sensitivity+specificity-1. Beginning in SAS Viya 2022.10, it is available using options in ROCOPTIONS in the PROC LOGISTIC statement. It is also available, along with other optimality criteria, in the ROCPLOT macro (SAS Note 25018).

Yule's Q for 2x2 tables

Same as Gamma statistic in Base SAS PROC FREQ (CHISQ option)

Zelen's Exact Test for Equal Odds Ratios

ZELEN option in the EXACT statement of Base SAS PROC FREQ.

Zero-inflated models

The most common are zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models. Zero-inflated models are often used to account for overdispersion (SAS Note 22630). ZIP and ZINB models are available in SAS/STAT PROC GENMOD. SAS/ETS PROC COUNTREG and SAS Viya PROC CNTSELECT also fit ZIP and ZINB models. Beginning in SAS 9.3, SAS/STAT PROC FMM can add zero-inflation to any of the wide range of models it can fit, which include ZIP and ZINB models. Beginning in SAS 9.4, ZIP and ZINB models can be fit in SAS/STAT PROC HPGENSELECT and SAS/ETS PROC HPCOUNTREG. PROC HPGENSELECT allows for selection of effects in both the mean and zero-inflation parts of the model. GEE analysis of zero-inflated models is not available. However, zero-inflated models can also be fit using SAS/STAT PROC NLMIXED, which also allows for inclusion of random effects. See the example in SAS Note 44354 and the example here of zero-inflated count models, and SAS Note 52161 for an example of a zero-inflated binomial model.

 

 

__________

MARS^® is a trademark of Jeril, Inc. and is licensed exclusively to Salford Systems.

 

 

 

Operating System and Release Information

Product Family	Product	System	SAS Release
			Reported	Fixed*
SAS System	SAS/STAT	z/OS
		OpenVMS VAX
		Microsoft® Windows® for 64-Bit Itanium-based Systems
		Microsoft Windows Server 2003 Datacenter 64-bit Edition
		Microsoft Windows Server 2003 Enterprise 64-bit Edition
		Microsoft Windows XP 64-bit Edition
		Microsoft® Windows® for x64
		OS/2
		Windows
		Microsoft Windows 95/98
		Microsoft Windows 2000 Advanced Server
		Microsoft Windows 2000 Datacenter Server
		Microsoft Windows 2000 Server
		Microsoft Windows 2000 Professional
		Microsoft Windows NT Workstation
		Microsoft Windows Server 2003 Datacenter Edition
		Microsoft Windows Server 2003 Enterprise Edition
		Microsoft Windows Server 2003 Standard Edition
		Microsoft Windows XP Professional
		WINDOWS/NTSV
		Windows Millennium Edition (Me)
		Windows Vista
		64-bit Enabled AIX
		64-bit Enabled HP-UX
		64-bit Enabled Solaris
		ABI+ for Intel Architecture
		AIX
		HP-UX
		HP-UX IPF
		IRIX
		Linux
		Linux on Itanium
		OpenVMS Alpha
		Solaris
		Tru64 UNIX
SAS System	SAS/QC	z/OS
		OpenVMS VAX
		Microsoft® Windows® for 64-Bit Itanium-based Systems
		Microsoft Windows Server 2003 Datacenter 64-bit Edition
		Microsoft Windows Server 2003 Enterprise 64-bit Edition
		Microsoft Windows XP 64-bit Edition
		Microsoft® Windows® for x64
		OS/2
		Windows
		Microsoft Windows 95/98
		Microsoft Windows 2000 Advanced Server
		Microsoft Windows 2000 Datacenter Server
		Microsoft Windows 2000 Server
		Microsoft Windows 2000 Professional
		Microsoft Windows NT Workstation
		Microsoft Windows Server 2003 Datacenter Edition
		Microsoft Windows Server 2003 Enterprise Edition
		Microsoft Windows Server 2003 Standard Edition
		Microsoft Windows XP Professional
		WINDOWS/NTSV
		Windows Millennium Edition (Me)
		Windows Vista
		64-bit Enabled AIX
		64-bit Enabled HP-UX
		64-bit Enabled Solaris
		ABI+ for Intel Architecture
		AIX
		HP-UX
		HP-UX IPF
		IRIX
		Linux
		Linux on Itanium
		OpenVMS Alpha
		Solaris
		Tru64 UNIX
SAS System	SAS/ETS	z/OS
		OpenVMS VAX
		Microsoft® Windows® for 64-Bit Itanium-based Systems
		Microsoft Windows Server 2003 Datacenter 64-bit Edition
		Microsoft Windows Server 2003 Enterprise 64-bit Edition
		Microsoft Windows XP 64-bit Edition
		Microsoft® Windows® for x64
		OS/2
		Windows
		Microsoft Windows 95/98
		Microsoft Windows 2000 Advanced Server
		Microsoft Windows 2000 Datacenter Server
		Microsoft Windows 2000 Server
		Microsoft Windows 2000 Professional
		Microsoft Windows NT Workstation
		Microsoft Windows Server 2003 Datacenter Edition
		Microsoft Windows Server 2003 Enterprise Edition
		Microsoft Windows Server 2003 Standard Edition
		Microsoft Windows XP Professional
		WINDOWS/NTSV
		Windows Millennium Edition (Me)
		Windows Vista
		64-bit Enabled AIX
		64-bit Enabled HP-UX
		64-bit Enabled Solaris
		ABI+ for Intel Architecture
		AIX
		HP-UX
		HP-UX IPF
		IRIX
		Linux
		Linux on Itanium
		OpenVMS Alpha
		Solaris
		Tru64 UNIX
SAS System	SAS/IML	z/OS
		OpenVMS VAX
		Microsoft® Windows® for 64-Bit Itanium-based Systems
		Microsoft Windows Server 2003 Datacenter 64-bit Edition
		Microsoft Windows Server 2003 Enterprise 64-bit Edition
		Microsoft Windows XP 64-bit Edition
		Microsoft® Windows® for x64
		OS/2
		Windows
		Microsoft Windows 95/98
		Microsoft Windows 2000 Advanced Server
		Microsoft Windows 2000 Datacenter Server
		Microsoft Windows 2000 Server
		Microsoft Windows 2000 Professional
		Microsoft Windows NT Workstation
		Microsoft Windows Server 2003 Datacenter Edition
		Microsoft Windows Server 2003 Enterprise Edition
		Microsoft Windows Server 2003 Standard Edition
		Microsoft Windows XP Professional
		WINDOWS/NTSV
		Windows Millennium Edition (Me)
		Windows Vista
		64-bit Enabled AIX
		64-bit Enabled HP-UX
		64-bit Enabled Solaris
		ABI+ for Intel Architecture
		AIX
		HP-UX
		HP-UX IPF
		IRIX
		Linux
		Linux on Itanium
		OpenVMS Alpha
		Solaris
		Tru64 UNIX
SAS System	SAS/OR	z/OS
		OpenVMS VAX
		Microsoft® Windows® for 64-Bit Itanium-based Systems
		Microsoft Windows Server 2003 Datacenter 64-bit Edition
		Microsoft Windows Server 2003 Enterprise 64-bit Edition
		Microsoft Windows XP 64-bit Edition
		Microsoft® Windows® for x64
		OS/2
		Windows
		Microsoft Windows 95/98
		Microsoft Windows 2000 Advanced Server
		Microsoft Windows 2000 Datacenter Server
		Microsoft Windows 2000 Server
		Microsoft Windows 2000 Professional
		Microsoft Windows NT Workstation
		Microsoft Windows Server 2003 Datacenter Edition
		Microsoft Windows Server 2003 Enterprise Edition
		Microsoft Windows Server 2003 Standard Edition
		Microsoft Windows XP Professional
		WINDOWS/NTSV
		Windows Millennium Edition (Me)
		Windows Vista
		64-bit Enabled AIX
		64-bit Enabled HP-UX
		64-bit Enabled Solaris
		ABI+ for Intel Architecture
		AIX
		HP-UX
		HP-UX IPF
		IRIX
		Linux
		Linux on Itanium
		OpenVMS Alpha
		Solaris
		Tru64 UNIX

* For software releases that are not yet generally available, the Fixed Release is the software release in which the problem is planned to be fixed.

---

FASTats: Frequently Asked-For Statistics

Type:	Usage Note
Priority:
Topic:	Analytics

Date Modified:	2025-08-11 11:42:34
Date Created:	2007-10-09 17:17:13