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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Rochani, Haresh D"],"institution":null,"degree_name":"Doctor of Public Health in Biostatistics (Dr.P.H.)","degree_level":"Dissertation (restricted to Georgia Southern)","degree_discipline":"Department of Biostatistics (COPH)","degree_department":null,"school":null,"contributors":["Hani Samawi","Daniel Linder"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:52Z","subjects":["ETD","Contingency table","Three-way table","Log-linear model","Missing data","Crossclassified data","Maximum likelihood method","Applied Statistics","Biostatistics","Categorical Data Analysis","Statistical Methodology","Statistical Models"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1053","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hani Samawi","Daniel Linder"]},{"key":"dc:creator","label":"Author","values":["Rochani, Haresh D"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-04-10T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Biostatistics (COPH)"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation (restricted to Georgia Southern)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Public Health in Biostatistics (Dr.P.H.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Contingency table","Three-way table","Log-linear model","Missing data","Crossclassified data","Maximum likelihood method","Applied Statistics","Biostatistics","Categorical Data Analysis","Statistical Methodology","Statistical Models"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1053"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:source","label":"Dc Source","values":["Haresh Rochani, Robert L. Vogel, Hani M. Samawi and Daniel F. Linder. \"Estimates for cell counts and common odds ratio in three-way contingency tables by homogeneous log-linear models with missing data\" AStA Advances in Statistical Analysis Vol. 101 Iss. 1 (2016) p. 51 - 65. DOI: https://doi.org/10.1007/s10182-016-0275-y"]},{"key":"dc:title","label":"Title","values":["Explicit Estimates for Cell Counts and Modeling The Missing Data Indicators in Three-Way Contingency Table by Log-Linear Models"]}]}],"canonical_facts":{"dc:contributor":["Hani Samawi","Daniel Linder"],"dc:creator":["Rochani, Haresh D"],"dc:date.available":["2019-04-10T07:00:00Z"],"dc:description.abstract":["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.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1053"],"dc:source":["Haresh Rochani, Robert L. Vogel, Hani M. Samawi and Daniel F. Linder. \"Estimates for cell counts and common odds ratio in three-way contingency tables by homogeneous log-linear models with missing data\" AStA Advances in Statistical Analysis Vol. 101 Iss. 1 (2016) p. 51 - 65. DOI: https://doi.org/10.1007/s10182-016-0275-y"],"dc:subject":["ETD","Contingency table","Three-way table","Log-linear model","Missing data","Crossclassified data","Maximum likelihood method","Applied Statistics","Biostatistics","Categorical Data Analysis","Statistical Methodology","Statistical Models"],"dc:title":["Explicit Estimates for Cell Counts and Modeling The Missing Data Indicators in Three-Way Contingency Table by Log-Linear Models"],"thesis:degree_discipline":["Department of Biostatistics (COPH)"],"thesis:degree_level":["Dissertation (restricted to Georgia Southern)"],"thesis:degree_name":["Doctor of Public Health in Biostatistics (Dr.P.H.)"]},"updated_at":"2026-07-24T02:27:52Z"}