Tests of Independence with Incomplete Contingency Tables Using Likelihood Functions

10.6339/JDS.2011.09(4).941

Shin-Soo Kang；Michael D. Larsen

Lagrangian multiplier ； likelihood ratio test ； missing at random ； missing value analysis ； Wald statistic

Journal of Data Science

9卷4期（2011 / 10 / 01）

487 - 500

英文

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.