Estimating the Simultaneous Association-Marginal Model for Longitudinal Data with Missingness: A Simulation Study

Document Type : Original Article

Authors

1 Statistics,Mathematics and Insurance department Faculty of Commerce Alexandria University Alexandria Egypt

2 Statistics, Sports and Insurance department Faculty of Commerce Alexandria University Alexandria Egypt

3 Department of Statistics, Sports and Insurance Commerce College Alexandria University Alexandria Egypt

Abstract

This paper introduces and applies a new model that describes simultaneously the association structure (A) with the marginal distributions (M) of the responses for longitudinal data in the presence of missing data (MS) through a composite link. This new model (AM-MS) is of great importance where it is applicable for large and sparse tables. In addition it can also be used for fitting log linear models to contingency tables with missing data (MS), fitting log linear models with some variables more finely categorized for some units than other units (sparse tables) and fitting models with various assumptions about the missing data mechanisms either MCAR, MAR or NMAR. A simulation study is conducted to apply this new idea, under various situations including (missing mechanisms, missing rates and five methods for handling missing data). The goodness-of-fit test statistics and the number of adjusted residuals greater than 2 are used as evaluation criteria. The results showed that after analyzing and estimating the AM model with MS for MCAR with low missing rate, the best method for handling MS to estimate the AM model is LOCF while with high missing the best method for handling MS to estimate the AM model is the mode imputation method. For MAR the best method for handling MS is MI. But for NMAR with low missing rate, the best method for handling MS is also the LOCF method while for NMAR with high missing the best method for handling MS is the mode imputation method.

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