|Introduction to Categorical Data Analysis Procedures
There are some differences in the way that models are
parameterized, which means that you might get different
parameter estimates if you were to perform logistic
regression in each of these procedures.
Parameter estimates from the procedures may differ in sign,
depending on the ordering of response levels, which you
can change if you want.
The parameter estimates associated with a categorical
independent variable may differ among the procedures
since the estimates depend on the coding of the indicator
variables in the design matrix. By default, the design
matrix column produced by PROC CATMOD for a binary independent
variable is coded using the values 1 and -1 .
The same column produced by the CLASS statement of PROC GENMOD
and PROC PROBIT is
coded 1 and 0. PROC CATMOD uses fullrank parameterization
using differential effects. As a result, the parameter
estimate printed by PROC CATMOD is one-half of the estimate
produced by the others. PROC LOGISTIC does not automatically
create indicator variables for categorical independent variables.
So, the parameterization depends on how you code the
indicator variables (1,0 versus -1,1).
"Details" sections in the chapters on the CATMOD, GENMOD,
and PROBIT procedures for more information on the generation
of the design matrices used by these procedures.
The maximum-likelihood algorithm used differs among the procedures.
PROC LOGISTIC uses Fisher's scoring
method while PROC PROBIT, PROC GENMOD, and PROC CATMOD use the Newton-Raphson method
(the PROC PROBIT algorithm is ridge stabilized and is a modified
Newton-Raphson algorithm.) The
parameter estimates should be the same for all three procedures
and the standard errors should
be the same for the logistic model. For the normal and extreme-value
distributions (handled by the PROBIT, GENMOD, and LOGISTIC procedures), the standard errors
In general, tests computed using the standard
errors from the Newton-Raphson method will be more conservative.
The LOGISTIC, GENMOD, and PROBIT procedures can fit logistic
regression models for ordinal response data using maximum-likelihood
estimation. PROC LOGISTIC and PROC GENMOD use a different
parameterization from that of PROC PROBIT, which results in different
intercept parameters. Estimates of the slope parameters,
however, should be the same for both procedures. The estimated
standard errors of the slope estimates are slightly different
between the two procedures because of the different computational
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