Displayed Output
PROC CATMOD displays the following information in the
"Data Summary" table:
- the Response effect
- the Weight Variable, if one is specified
- the Data Set name
- the number of Response Levels
- the number of samples or Populations
- the Total Frequency, which is the total sample size
- the number of Observations from the
data set (the number of data records)
- the frequency of missing observations,
labeled as "Frequency Missing"
Except for the analysis of variance table, all of the
following items can be displayed or suppressed, depending
on your specification of statements and options.
- The ONEWAY option produces the "One-Way
Frequencies" table, which displays the frequencies
of each variable value used in the analysis.
- The populations (or samples) are defined
in a table labeled "Population Profiles."
The Sample Size and the values of the defining
variables are displayed for each Sample.
This table is suppressed if the NOPROFILE option is specified.
- The observed responses are defined in
a table labeled "Response Profiles."
The values of the defining variables are displayed for
each Response.
This table is suppressed if the NOPROFILE option is specified.
- If the FREQ option is specified, then the "Response
Frequencies" table is displayed, which shows the
frequency of each response for each population.
- If the PROB option is specified, then the "Response
Probabilities" table is produced. This table displays
the probability of each response for each population.
- If the COV option is specified, the "Response
Functions, Covariance Matrix" table, which shows the
covariance matrix
of the response functions for each Sample, is displayed.
- The Response Functions are displayed in the
"Response Functions, Design Matrix" table,
unless the COV option is specified,
in which case they are displayed in the
"Response Functions, Covariance Matrix" table.
- The design matrix is displayed in the "Response
Functions, Design Matrix" table for weighted least-squares
analyses, unless the NODESIGN option is specified.
If the model type is AVERAGED, then the design matrix
is displayed with q*s rows, assuming q response
functions for each of s populations.
Otherwise, the design matrix is displayed with
only s rows since the model is the same for
each of the q response functions.
- The "X'*Inv(S)*X" matrix is displayed
for weighted least-squares analyses if the
XPX option is specified.
- The "Analysis of Variance" table for the
weighted least-squares analysis reports the results of
significance tests for each of the design-effects
in the right-hand side of the MODEL statement.
If _RESPONSE_ is a design-effect and is defined
explicitly in the LOGLIN, FACTORS, or REPEATED statement,
then the table contains test statistics for the
individual effects constituting the _RESPONSE_ effect.
If the design matrix is input directly, then the
content of the displayed output depends on whether you
specify any subsets of the parameters to be tested.
If you specify one or more subsets, then
the table contains one test for each subset.
Otherwise, the table contains one
test for the effect MODEL | MEAN.
In every case, the table also contains
the Residual goodness-of-fit test.
Produced for each test of significance are the Source
of variation, the number of degrees of freedom (DF),
the Chi-Square value (which is a Wald statistic),
and the significance probability (Pr > ChiSq).
- The "Analysis of Weighted Least-Squares Estimates" table
lists the Effect in the model for which parameters are
formed, the Parameter number, the least-squares Estimate,
the estimated Standard Error of the parameter estimate,
the Chi-Square value (a Wald statistic) for testing that
the parameter is zero, and the significance probability
(Pr > ChiSq) of the test.
The statistic is calculated as
((parameter estimate)/(standard error))2.
- The "Covariance Matrix of the Parameter
Estimates" table for
the weighted least-squares analysis displays the estimated
covariance matrix of the least-squares estimates of the
parameters, provided the COVB option is specified.
- The "Correlation Matrix of the Parameter
Estimates" table for
the weighted least-squares analysis displays the estimated
correlation matrix of the least-squares estimates of the
parameters, provided that the CORRB option is specified.
- The "Maximum Likelihood Analysis" table is produced when
the ML option is specified for the standard
response functions (generalized logits).
It displays the Iteration number, the number of
step-halving Sub-Iterations, -2 Log Likelihood
for that iteration, the Convergence Criterion,
and the Parameter Estimates for each iteration.
- The "Maximum Likelihood Analysis of Variance" table,
displayed when the ML option is specified for the
standard response functions, is similar to the
table produced for the least-squares analysis.
The Chi-Square test for each effect is a Wald test based
on the information matrix from the likelihood calculations.
The Likelihood Ratio statistic compares the specified
model with the unrestricted (saturated) model and is
an appropriate goodness-of-fit test for the model.
- The "Analysis of Maximum Likelihood Estimates" table,
displayed when the ML option is specified for the
standard response functions, is similar to the
one produced for the least-squares analysis.
The table includes the maximum likelihood estimates,
the estimated Standard Errors based on the information
matrix, and the Wald Statistics (Chi-Square) based
on the estimated standard errors.
- The "Covariance Matrix of the Maximum
Likelihood Estimates" table displays
the estimated covariance matrix of the
maximum likelihood estimates of the parameters,
provided that the COVB and ML options are
specified for the standard response functions.
- The "Correlation Matrix of the Maximum
Likelihood Estimates" table displays
the estimated correlation matrix of the
maximum likelihood estimates of the parameters,
provided that the CORRB and ML options are
specified for the standard response functions.
- For each source of variation specified in a CONTRAST
statement, the "Contrasts" table
lists the label for the source (Contrast),
the number of degrees of freedom (DF),
the Chi-Square value (which is a Wald statistic),
and the significance probability (Pr > ChiSq).
If the ESTIMATE= option is specified, the
"Analysis of Contrasts" table displays, for
each row of the contrast, the label (Contrast), the
Type (PARM or EXP), the Row of the contrast, the
Estimate and its Standard Error, a Wald confidence
interval, the Wald Chi-Square,
and the p-value (Pr > ChiSq) for 1 degree of freedom.
- Specification of the PREDICT option in the
MODEL statement has the following effect.
Produced for each response function within
each population are the Observed and Predicted
Function values, their Standard Errors,
and the Residual (Observed - Predicted).
The displayed
output also includes the values of the
variables that define the populations
unless the NOPREDVAR option is specified in the MODEL statement.
If the response functions are the default ones
(generalized logits), additional information displayed
for each response within each population includes
the Observed and Predicted cell probabilities,
their Standard Errors, and the Residual.
The first cell probability is labeled P1,
the second P2, and so forth.
However, specifying PRED=FREQ in the MODEL statement
results in the display of the predicted cell frequencies,
rather than the predicted cell probabilities.
The first cell frequency is labeled F1,
the second F2, and so forth.
- When there are multiple RESPONSE statements,
the output for each statement starts on a new page.
For each RESPONSE statement, the corresponding title, if
specified, is displayed at the top of each page.
- If the ADDCELL= option is specified in the MODEL statement,
and if there is a weighted least-squares analysis specified,
the adjusted sample size for each population (with number
added to each cell) is labeled Adjusted Sample Size in
the "Population Profiles" table.
Similarly, the adjusted response frequencies and probabilities
are displayed in the "Adjusted Response
Frequencies" and "Adjusted Response
Probabilities" tables, respectively.
- If _RESPONSE_ is defined explicitly in the LOGLIN,
FACTORS, or REPEATED statement, then the definition
is displayed as a NOTE whenever _RESPONSE_ appears
in the output.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
