# Categorical Data Analysis

### Categorical Data Analysis

Categorical data classifies an observation as belonging to one or more categories. The analysis of this type of data is called categorical data analysis. For example, we can judge an item as either bad or good. Also, a response to a survey might include categories like agree, disagree, or no opinion. In SAS, two approaches can be used to perform categorical data analysis.

1. Computing statistics based on tables defined by categorical variables perform hypothesis tests which is related to the association between these variables and require the assumptions of a randomized process. These methods can be called randomization procedures. Categorical variables assume only a limited number of discrete values.
2. Investigating the association by modeling a categorical response variable. This second approach doesn’t care if the explanatory variables are continuous or categorical. These methods can be referred to as modeling procedures.

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Categorical data analysis procedures in SAS/STAT

• CATMOD Procedure

Categorical data modeling (CATMOD) procedure performs categorical data modeling of data that can be represented by a contingency table. We can use PROC CATMOD to fit linear models to functions of response frequencies. Also, it can be used for linear modeling, logistic regression, log-linear modeling, and repeated measurement analysis.

The CATMOD procedure will enable you to do the following:

• Model parameters estimation using Weighted Least Squares (for a full range of general linear models) or Maximum Likelihood (for log-linear models and the analysis of generalized logits.
• Supplying raw materials where each observation is a subject.
• Constructing linear functions of the model parameters or log-linear effects. Also, we can test the hypothesis that the linear combination equals zero.
• Performing a constrained estimation
• Creating a data set that corresponds to any output table, etc.
• FREQ Procedure

This procedure produces one-way to n-way frequency and contingency (cross-tabulation) tables. PROC FREQ measures associations and computes tests for two-way tables. On the other hand, It provides stratified analysis by computing statistical values across and within strata for n-way tables.

The features of FREQ include:

• Computing goodness-of-fit tests for equal or specified null proportions. For one-way frequency tables
• It provides tests for binomial proportions and confidence limits. The tests include equivalence and tests for non-inferiority for one-way frequency tables.
• Examining the relationships between two-classification variables through the computation of various statistics. Some of the statistics for contingency tables include Chi-Square measures and tests, odds ratios, and relative risks for 2×2 tables.
• Measurements and tests of agreement.
• Computing score confidence limits for odds ratios, etc.
• Finite Mixture Models (FMM) Procedure

The Finite Mixture Models model suits statistical models to data for which the distribution of the response is a finite mixture of univariate distributions. This means that each response comes from one of the several random univariate distributions with unknown probabilities.

Listed below are some of the features of the FMM procedure

• Modeling of over-dispersed data
• Weighted estimation
• Using ODS Graphics to automatically create graphs
• Analyses on observations in groups can be obtained separately
• Homogenous mixtures automated model selection
• Linear inequality and equality constraints on model parameters, etc.
• GENMOD Procedure

This procedure is used for generalized linear models. This class of models is an extension of traditional linear models that allows the mean of a population to depend on a linear predictor through a non-linear link function. Generalized linear models also allow the response probability distribution to be any member of an exponential family of distributions. The examples of generalized linear models include classical linear models with normal errors, probit, and logistic models for binary data, and log-linear models for multinomial data.

The features of the GENMOD Procedure are:

• It provides built-in link functions like logit, probit, log, power, complementary log-log, and identity
• It allows users to define their link functions or distributions through data step programming statements used in the procedure
• It can create SAS data sets that correspond to most output tables
• Can produce an over-dispersion diagnostic plot for zero-inflated models
• LOGISTIC Procedure

The LOGISTIC procedure is used for discrete response data by the method of likelihood in linear logistic regression models. Also, it performs conditional logistic regression for binary response data and exact logistic regression for binary and nominal response data

With LOGISTIC Procedure you can do the following:

• Fitting of partial proportional odds logistic regression models
• Specifying contrasts to compare many receivers operating characteristic curves
• Creating any output table corresponding data set
• Carrying out weighted estimation
• Using a previously fitted model to score a data set

The other procedure in categorical data analysis that is not discussed here is the PROBIT procedure. You can contact our categorical data analysis online experts for immediate help with your assignment.