Cai Li, Maydeu-Olivares Albert, Coffman Donna L, Thissen David
University of North Carolina, Chapel Hill, NC 27599, USA.
Br J Math Stat Psychol. 2006 May;59(Pt 1):173-94. doi: 10.1348/000711005X66419.
Bartholomew and Leung proposed a limited-information goodness-of-fit test statistic (Y) for models fitted to sparse 2(P ) contingency tables. The null distribution of Y was approximated using a chi-squared distribution by matching moments. The moments were derived under the assumption that the model parameters were known in advance and it was conjectured that the approximation would also be appropriate when the parameters were to be estimated. Using maximum likelihood estimation of the two-parameter logistic item response theory model, we show that the effect of parameter estimation on the distribution of Y is too large to be ignored. Consequently, we derive the asymptotic moments of Y for maximum likelihood estimation. We show using a simulation study that when the null distribution of Y is approximated using moments that take into account the effect of estimation, Y becomes a very useful statistic to assess the overall goodness of fit of models fitted to sparse 2(P) tables.
巴塞洛缪和梁针对拟合稀疏2(P)列联表的模型提出了一种有限信息拟合优度检验统计量(Y)。Y的零分布通过矩匹配用卡方分布近似。这些矩是在模型参数预先已知的假设下推导出来的，并且推测当参数需要估计时，这种近似也将是合适的。使用两参数逻辑斯蒂项目反应理论模型的最大似然估计，我们表明参数估计对Y分布的影响太大而不能忽略。因此，我们推导了最大似然估计下Y的渐近矩。我们通过模拟研究表明，当使用考虑估计效应的矩来近似Y的零分布时，Y成为评估拟合稀疏2(P)表模型整体拟合优度的非常有用的统计量。
