Explicit Estimates for Cell Counts and Modeling The Missing Data Indicators in Three-Way Contingency Table by Log-Linear Models

Missing observations in cross-classified data are an extremely common problem in the process of research in public health, clinical sciences and social sciences. Ignorance of missing values in the analysis can produce biased results and low statistical power. The focus of this study is to expand Baker, Rosenberger and Dersimonian (BRD) model approach to compute the explicit maximum likelihood estimates for cell counts for three-way cross-classified data. Derivation of explicit cell counts for three-way table with supplementary margins can be obtained by controlling the missingness in third variable and by modeling the missing-data indicators using homogeneous log-linear models. Model based approach for contingency tables has the advantage of providing the information of missing data mechanisms. Previous methods for contingency tables with supplementary margins required an iterative algorithm, however, expected cell counts for complete cells as well as missing cells can be obtained by simple algebraic formula. Simulation study with Source of knowledge of cancer data illustrate that how well the explicit maximum likelihood estimates can produce consistent results in idyllic circumstances. Application of the BRD model approach to Slovenian public opinion survey data reveals the effect of smaller sample size to the validity of the method for three-way table