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SAS/STAT Topics

SAS/STAT Software

Psychometric Analysis

Psychometric methods are well suited for analyzing data on human judgment and perception, such as market research data, but can be used for many other types of data.

The SAS/STAT psychometric analysis procedures include the following:

CORRESP Procedure


The CORRESP procedure performs simple correspondence analysis and multiple correspondence analysis (MCA). You can use correspondence analysis to find a low-dimensional 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 two-way 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 user-specified gamma
    • Crawford-Ferguson family with user-specified weights on variable parsimony and factor parsimony
    • generalized Crawford-Ferguson family with user-specified weights
    • direct oblimin with user-specified tau
    • Crawford-Ferguson family with user-specified weights on variable parsimony and factor parsimony
    • generalized Crawford-Ferguson family with user-specified weights
    • promax with user-specified exponent
    • Harris-Kaiser case II with user-specified exponent
    • Procrustes with a user-specified 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

IRT Procedure


The IRT procedure fits item response theory models. The following are highlights of the IRT procedure's features:

  • fits the following types of models:
    • Rasch model
    • one-, two-, three-, and four-parameter models
    • graded response model with logistic or probit link
    • generalized partial credit models for ordinal items
  • enables different items to have different response models
  • performs multidimensional exploratory and confirmatory analysis
  • performs multiple-group analysis, with fixed values and equality constraints within and between groups
  • estimates factor scores by using maximum likelihood, maximum a posteriori, and expected a posteriori methods
  • displays the polychoric correlation matrix and a heat map for the polychoric correlation matrix
  • displays item characteristic curves and test information curve plots
  • create a SAS data set that corresponds to any output table
  • automatically creates graphs by using ODS Graphics
For further details, see IRT Procedure

MDS Procedure


The MDS procedure fits two- and three-way, 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 sum-of-squares-and-crossproducts (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

TRANSREG Procedure


The TRANSREG (transformation regression) procedure fits linear models, optionally with smooth, spline, Box-Cox, and other nonlinear transformations of the variables. The following are highlights of the TRANSREG procedure's features:

  • enables you to fit linear models including:
    • ordinary regression and ANOVA
    • metric and nonmetric conjoint analysis (Green and Wind 1975; de Leeuw, Young, and Takane 1976)
    • linear models with Box-Cox (1964) transformations of the dependent variables
    • regression with a smooth (Reinsch 1967), spline (de Boor 1978; van Rijckevorsel 1982), monotone spline (Winsberg and Ramsay 1980), or penalized B-spline (Eilers and Marx 1996) fit function
    • metric and nonmetric vector and ideal point preference mapping (Carroll 1972)
    • simple, multiple, and multivariate regression with variable transformations (Young, de Leeuw, and Takane 1976; Winsberg and Ramsay 1980; Breiman and Friedman 1985)
    • redundancy analysis (Stewart and Love 1968) with variable transformations (Israels 1984)
    • canonical correlation analysis with variable transformations (van der Burg and de Leeuw 1983)
    • response surface regression (Meyers 1976; Khuri and Cornell 1987) with variable transformations
  • enables you to use a data set that can contain variables measured on nominal, ordinal, interval, and ratio scales; you can specify any mix of these variable types for the dependent and independent variables
  • transform nominal variables by scoring the categories to minimize squared error (Fisher 1938), or treat nominal variables as classification variables
  • enables you to transform ordinal variables by monotonically scoring the ordered categories so that order is weakly preserved (adjacent categories can be merged) and squared error is minimized. Ties can be optimally untied or left tied (Kruskal 1964). Ordinal variables can also be transformed to ranks.
  • enables you to transform interval and ratio scale of measurement variables linearly or nonlinearly with spline (de Boor 1978; van Rijckevorsel 1982), monotone spline (Winsberg and Ramsay 1980), penalized B-spline (Eilers and Marx 1996), smooth (Reinsch 1967), or Box-Cox (Box and Cox 1964) transformations. In addition, logarithmic, exponential, power, logit, and inverse trigonometric sine transformations are available.
  • fits a curve through a scatter plot or fit multiple curves, one for each level of a classification variable
  • enables you to constrain the functions to be parallel or monotone or have the same intercept
  • enables you to code experimental designs and classification variables prior to their use in other analyses
  • perform sweighted estimation
  • generates output data sets including
    • ANOVA results
    • regression tables
    • conjoint analysis part-worth utilities
    • coefficients
    • marginal means
    • original and transformed variables, predicted values, residuals, scores, and more
  • performs BY group processing, which enables you to obtain separate analyses on grouped observations
  • automatically creates graphs by using ODS Graphics
For further details, see TRANSREG Procedure