Tests of Independence with Incomplete Contingency Tables Using Likelihood Functions

Kang (2006) used the log-likelihood function with Lagrangian multipliers for estimation of cell probabilities in two-way incomplete contingency tables. The constraints on cell probabilities can be incorporated through Lagrangian multipliers for the likelihood function. The method can be readily extended to multidimensional tables. Variances of the MLEs are derived from the matrix of second derivatives of the log likelihood with respect to cell probabilities and the Lagrange multiplier. Wald and likelihood ratio tests of independence are derived using the estimates and estimated variances. Simulation results, when data are missing at random, reveal that maximum likelihood estimation (MLE) produces more efficient estimates of population proportions than either multiple imputation (MI) based on data augmentation or complete case (CC) analysis. Neither MLE nor MI, however, leads to an improvement over CC analysis with respect to power of tests for independence in 2×2 tables. Thus, the partially classified marginal information increases precision about proportions, but is not helpful for judging independence.

• Publication year

  2021

• Venue

  Journal of data science

• Publication date

  2021-04-05

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.6339/JDS.201110_09(4).0001
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

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• No concepts are published for this paper.

• Missing data

  2019cited by this paper
• Imputation Methods for Missing Categorical Questionnaire Data: A Comparison of Approaches

  2010cited by this paper
• MLE for Incomplete Contingency Tables with Lagrangian Multiplier

  2006cited by this paper
• Generalized Linear Models

  2001cited by this paper
• Obtaining the Maximum Likelihood Estimates in Incomplete R C Contingency Tables Using a Poisson Generalized Linear Model

  1998cited by this paper
• Analysis of Incomplete Multivariate Data

  1997cited by this paper
• Generalized linear models. 2nd ed.

  1993cited by this paper
• Performing likelihood ratio tests with multiply-imputed data sets

  1992influential reference
• Large-sample significance levels from multiply imputed data using moment-based statistics and an F reference distribution

  1991cited by this paper
• Multiple Imputation for Nonresponse in Surveys

  1988cited by this paper
• Models for Nonresponse in Sample Surveys

  1982cited by this paper
• Maximum Likelihood Estimation and Model Selection in Contingency Tables with Missing Data

  1982influential reference
• Multiple imputations in sample surveys

  1978cited by this paper
• Two-Dimensional Contingency Tables with Both Completely and Partially Cross-Classified Data

  1974influential reference

• No citing papers are available for this paper.