## Types of Statistical Analyses

This section illustrates, by example, the wide variety of
categorical data analyses that PROC CATMOD provides. For
each type of analysis, a brief description of the
statistical problem and the SAS statements to provide the
analysis are given. For each analysis, assume that the
input data set consists of a set of cell counts from a
contingency table. The variable specified in the WEIGHT
statement contains these counts. In all these analyses, both
the dependent and independent variables are categorical.
*Linear Model Analysis*

Suppose you want to analyze the relationship between the
dependent variables (r1, r2) and the
independent variables (a, b). Analyze the
marginal probabilities of the dependent variables, and use a
main-effects model.
proc catmod;
weight wt;
response marginals;
model r1*r2=a b;
quit;

*Log-Linear Model Analysis*

Suppose you want to analyze the nominal dependent variables (r1, r2,
r3) with a log-linear model. Use maximum likelihood
analysis, and include the main effects and the
r1*r2 interaction in the model. Obtain the
predicted cell frequencies.
proc catmod;
weight wt;
model r1*r2*r3=_response_ / pred=freq;
loglin r1|r2 r3;
quit;

*Logistic Regression*

Suppose you want to analyze the relationship between the nominal dependent
variable (r) and the independent variables (x1,
x2) with a logistic regression analysis. Use
maximum likelihood estimation.
proc catmod;
weight wt;
direct x1 x2;
model r=x1 x2;
quit;

If x1 and x2 are continuous so that each
observation has a unique value of these two variables, then
it may be more appropriate to use the LOGISTIC, GENMOD, or PROBIT
procedure. See the "Logistic Regression" section.

*Repeated Measures Analysis*

Suppose the dependent variables (r1, r2,
r3) represent the same type of measurement taken at three
different times. Analyze the relationship among the
dependent variables, the repeated measurement factor
(time), and the independent variable (a).
proc catmod;
weight wt;
response marginals;
model r1*r2*r3=_response_|a;
repeated time 3 / _response_=time;
quit;

*Analysis of Variance*

Suppose you want to investigate the relationship between the
dependent variable (r) and the independent variables (a, b).
Analyze the mean of the dependent variable, and include
all main effects and interactions in the model.
proc catmod;
weight wt;
response mean;
model r=a|b;
quit;

*Linear Regression*

PROC CATMOD can analyze the relationship between the dependent
variables (r1, r2) and the independent variables
(x1, x2).
Use a linear regression analysis to analyze the marginal
probabilities of the dependent variables.
proc catmod;
weight wt;
direct x1 x2;
response marginals;
model r1*r2=x1 x2;
quit;

*Logistic Analysis of Ordinal Data*

Suppose you want to analyze the relationship
between the ordinally scaled dependent variable
(r) and the independent variable (a).
Use cumulative logits to take into account
the ordinal nature of the dependent variable.
Use weighted least-squares estimation.
proc catmod;
weight wt;
response clogits;
model r=_response_ a;
quit;

*Sample Survey Analysis*

Suppose the data set contains estimates of a vector of four
functions and their covariance matrix, estimated in such a
way as to correspond to the sampling process that is used.
Analyze the functions with respect to the independent
variables (a, b), and use a main-effects model.
proc catmod;
response read b1-b10;
model _f_=_response_;
factors a 2 , b 5 / _response_=a b;
quit;

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.