Goodness-of-Fit Tests for Log-Linear Models in Sparse Contingency Tables
研究了稀疏列联表中对数线性模型拟合优度检验的渐近正态性，发现似然比统计量的正态近似比卡方近似更准确，但估计矩的偏差在极稀疏表中可能成为问题。
Abstract The asymptotic normality of the likelihood ratio goodness-of-fit statistic is demonstrated for testing the fit of log-linear models with closed form maximum likelihood estimates in sparse contingency tables. Unlike the traditional chi-squared theory, the number of categories in the table increases as the sample size increases, but not all of the expected frequencies are required to become large. Some results of a small Monte Carlo study are presented. The traditional chi-squared approximation is reasonably accurate for the Pearson statistic for many sparse tables, but cases are presented for which it fails. The normal approximation can be much more accurate than the chi-squared approximation for the likelihood ratio statistic, but the bias of estimated moments is a potential problem for very sparse tables. Key Words: Asymptotic normalityChi-squared testsMaximum likelihood estimationMultinomial distribution