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The CATMOD Procedure |

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"

- 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.

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