The multivariate analysis procedures are used to investigate relationships among variables without designating some as independent and others as dependent.
Below are highlights of the capabilities of the SAS/STAT procedures that perform
multivariate analysis:
 CANCORR Procedure — Canonical correlation, partial canonical correlation, and canonical redundancy analysis
 CORR Procedure — Computes correlation coefficients, nonparametric measures of association, and the probabilities associated with these statistics
 CORRESP Procedure — Simple and multiple correspondence analysis
 FACTOR Procedure — Factor and component analyses and rotations
 MDS Procedure — Fits two and threeway, metric and nonmetric multidimensional scaling models
 PRINCOMP Procedure — Principal component analysis
 PRINQUAL Procedure — Principal component analysis of qualitative, quantitative, or mixed data
CANCORR Procedure
The CANCORR procedure performs canonical correlation, partial canonical correlation, and canonical redundancy analysis.
The procedure enables you to do the following:
 test a series of hypotheses that each canonical correlation and all smaller canonical correlations are zero in the population.
 use multiple regression analysis options to aid in interpreting the canonical correlation analysis
 compute standardized and unstandardized canonical coefficients
 compute canonical structure matrices
 base the canonical analysis on partial correlations
 create a data set that contains the scores of each observation on each canonical variable

 create a data set that contains the canonical correlations, coefficients, and most other statistics computed by the procedure
 create a data set that corresponds to any output table
 compute weighted productmoment correlation coefficients
 perform BY group processing, which enables you to obtain separate analyses on grouped observations

For further details, see
CANCORR Procedure
CORR Procedure
The CORR procedure computes Pearson correlation coefficients, three nonparametric measures of association, and the probabilities
associated with these statistics.
The following are highlights of the CORR procedure's features:
 produces the following correlation statistics:
 Pearson productmoment correlation
 Spearman rankorder correlation
 Kendall's taub coefficient
 Hoeffding's measure of dependence, D
 Pearson, Spearman, and Kendall partial correlation
 polychoric correlation
 polyserial correlation
 computes Cronbach's coefficient alpha for estimating reliability
 saves the correlation statistics in a SAS data set for use with other statistical and reporting procedures

 enables you to use Fisher's z transformation to derive confidence limits and pvalues under a specified
null hypothesis for a Pearson or Spearman correlation
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
CORR Procedure
CORRESP Procedure
The CORRESP procedure performs simple correspondence analysis and multiple correspondence analysis (MCA).
You can use correspondence analysis to find a lowdimensional graphical representation of the rows and columns
of a crosstabulation or contingency table. Each row and column is represented by a point in a plot determined
from the cell frequencies. PROC CORRESP can also compute coordinates for supplementary rows and columns.
The procedure enables you to do the following:
 use two kinds of input: raw categorical responses on two or more classification variables or a twoway contingency table
 specify the number of dimensions or axes
 specify the standardization for the row and column coordinates
 create a data set that contains coordinates and the results of the correspondence analysis

 create a data set that contains frequencies and percentages
 create a data set that corresponds to any output table
 perform BY group processing, which enebales you to obtain separate analyses on grouped observations
 automatically display the correspondence analysis plot by using ODS Graphics

For further details, see
CORRESP Procedure
FACTOR Procedure
The FACTOR procedure performs a variety of common factor and component analyses and rotations.
The following are highlights of the procedure's features:
 supports the following factor extraction methods:
 principal component analysis
 principal factor analysis
 iterated principal factor analysis
 unweighted least squares factor analysis
 maximum likelihood (canonical) factor analysis
 alpha factor analysis
 image component analysis
 Harris component analysis
 supports the following rotation methods:
 varimax
 quartimax
 biquartimax
 equamax
 parsimax
 factor parsimax
 quartimin
 biquartimin
 covarimin
 orthomax with userspecified gamma
 CrawfordFerguson family with userspecified weights on variable parsimony and factor parsimony
 generalized CrawfordFerguson family with userspecified weights
 direct oblimin with userspecified tau
 CrawfordFerguson family with userspecified weights on variable parsimony and factor parsimony
 generalized CrawfordFerguson family with userspecified weights
 promax with userspecified exponent
 HarrisKaiser case II with userspecified exponent
 Procrustes with a userspecified target pattern
 provides a variety of methods for prior communality estimation
 input can be multivariate data, a correlation matrix, a covariance matrix, a factor pattern,
or a matrix of scoring coefficients

 enables you to factor either the correlation or covariance matrix
 processes output from other procedures
 produces the following output:
 means
 standard deviations
 correlations
 Kaiser's measure of sampling adequacy
 eigenvalues
 a scree plot
 path diagrams
 eigenvectors
 prior and final communality estimates
 the unrotated factor pattern
 residual and partial correlations
 the rotated primary factor pattern
 the primary factor structure
 interfactor correlations
 the reference structure
 reference axis correlations
 the variance explained by each factor both ignoring and eliminating other factors
 plots of both rotated and unrotated factors
 squared multiple correlation of each factor with the variables
 standard error estimates
 confidence limits
 coverage displays
 scoring coefficients
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 enables you to use relative weights for each observation in the input data set
 creates a SAS data set that corresponds to any table
 automatically creates graphs by using ODS Graphics

For further details, see
FACTOR Procedure
MDS Procedure
The MDS procedure fits two and threeway, metric and nonmetric multidimensional scaling models.
Multidimensional scaling refers to a class of methods. These methods estimate coordinates for a set of objects in a space of
specified dimensionality. The input data are measurements of distances between pairs of objects. A variety of models can be used that
include different ways of computing distances and various functions relating the distances to the actual data.
The following are highlights of the MDS procedure's features:
 estimates the following parameters by nonlinear least squares:
 configuration — the coordinates of each object in a Euclidean or weighted
Euclidean space of one or more dimensions
 dimension coefficients — for each data matrix, the coefficients that multiply each coordinate
of the common or group weighted Euclidean space to
yield the individual unweighted Euclidean space
 transformation parameters — intercept, slope, or exponent in a linear, affine, or power transformation
relating the distances to the data
 fits either a regression model of the form
fit(datum) = fit(trans(distance)) + error
or a measurement model of the form
fit(trans(datum)) = fit(distance) + error
where
 fit is a predetermined power or logarithmic transformation
 trans is an estimated (`optimal') linear, affine, power, or monotone transformation
 datum is a measure of the similarity or dissimilarity of two objects or stimuli
 distance is a distance computed from the estimated coordinates of the two objects and estimated
dimension coefficients in a space of one or more dimensions
 error is an error term assumed to have an approximately normal distribution and to be
independently and identically distributed for all data
 performs BY group processing, whcih enables you to obtain separate analyses on grouped observations
 performs weighted analysis
creates a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
MDS Procedure
PRINCOMP Procedure
The PRINCOMP procedure performs principal component analysis. The following are highlights of the PRINCOMP procedure's features:
 input can be in the form of raw data, a correlation matrix, a covariance matrix, or a sumofsquaresandcrossproducts (SSCP) matrix
 creates output data sets that contain eigenvalues, eigenvectors, and standardized or unstandardized principal component scores
 automatically creates the scree plot, component pattern plot, component pattern profile plot, matrix plot of component scores, and component score plots
by using ODS Graphics

 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 performs weighted analysis
 creates a SAS data set that corresponds to any output table

For further details, see
PRINCOMP Procedure
PRINQUAL Procedure
The PRINQUAL procedure performs principal component analysis (PCA) of qualitative, quantitative, or mixed data.
PROC PRINQUAL enables you to do the following:
 find linear and nonlinear transformations of variables, using the method of alternating least squares,
that optimize properties of the transformed variables' correlation
or covariance matrix. Nonoptimal transformations such as logarithm and rank are also available.
 fit metric and nonmetric principal component analyses
 perform metric and nonmetric multidimensional preference (MDPREF) analyses
 reduce the number of variables for subsequent use in regression analyses, cluster analyses, and other analyses
 choose between three methods, each of which seeks to optimize a different property of the transformed variables' covariance
or correlation matrix. These methods are as follows:
 maximum total variance, or MTV
 minimum generalized variance, or MGV
 maximum average correlation, or MAC
 transform ordinal variables monotonically by scoring the ordered categories so that order is weakly preserved (adjacent categories can be merged) and the covariance
matrix is optimized. You can undo ties optimally or leave them tied. You can also transform ordinal variables to ranks.

 transform nominal variables by optimally scoring the categories
 transform interval and ratio scale of measurement variables linearly, or transform them nonlinearly with spline transformations or monotone spline transformations.
In addition, nonoptimal transformations for logarithm, rank, exponential, power, logit, and inverse trigonometric sine are available.
 estimate missing data without constraint, with category constraints (missing values within the same group get the same value), and with order constraints (missing
value estimates in adjacent groups can be tied to preserve a specified ordering).
 detect nonlinear relationships
 perform weighted estimation
 perform BY group processing, which enables you to obtain separate analyses on grouped observations
 create a SAS data set that contains the original variables, transformed variables, components, or data approximations
 create a SAS data set that corresponds to any output table
 automatically create graphs by using ODS Graphics

For further details, see
PRINQUAL Procedure