Comparing estimation methods for categorical marginal models

Categorical marginal models are flexible models for modelling dependent or clustered categorical data which do not involve any specific assumptions about the nature of the dependencies. Categorical marginal models are used for different purposes, including hypothesis testing, assessing model fit, and regression problems. Two different estimation methods are used to estimate marginal models: maximum likelihood (ML) and generalized estimating equations (GEE). We explored three different cases to find out to what extent the two types of estimation methods are appropriate for investigating different types of research questions. The results suggest that ML may be preferred for assessing model fit because GEE has limited fit indices, whereas both methods can be used to assess the effect of independent factors in regression. Moreover, ML is asymptotically efficient, while GEE loses efficiency when the working correlation matrix is not correctly specified. However, for parameter estimation in regression GEE is easier to apply from a computational perspective.