“数通古今，学贯中外”学术讲座第二十五期预告【袁克海教授】
作者：高冰 来源：数学学院 华体会体育（中国）：2012-06-26
报告人：袁克海（University of Notre Dame）
题目：Empirical correction to the likelihood ratio statistic for structural equation modeling with many variables
报告时间：2012年6月28日（星期四）15：00—17：00
地点：中心教学楼620
Title：Empirical correction to the likelihood ratio statistic for structural equation modeling with many variables
Abstract: Survey data typically contain many variables. Structural equation modeling (SEM) is one of the most widely used methods in analyzing such data. The most widely used statistic for testing the adequacy of a SEM model is the likelihood ratio statistic $T_{ML}$. Under normality assumption, $T_{ML}$ approximately follows a chi-square distribution when the number of observations ($n$) is large and the number of items or variables ($p$) is small. However, in practice, $p$ can be very large while $n$ is always limited due to not having enough participants in surveys. Even with a relatively large $n$, empirical results show that $T_{ML}$ rejects the correct model too often when $p$ is large. Various analytical corrections to $T_{ML}$ were proposed whereas an exact Bartlett correction is hard to obtain. This paper proposes empirical corrections so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that two empirically corrected statistics follow the nominal chi-square distribution much more closely than previously proposed statistics. The formulations of the two statistics are further used to predict type I errors of $T_{ML}$ as reported in the literature, and they perform well.
题目：Empirical correction to the likelihood ratio statistic for structural equation modeling with many variables
报告时间：2012年6月28日（星期四）15：00—17：00
地点：中心教学楼620
Title：Empirical correction to the likelihood ratio statistic for structural equation modeling with many variables
Abstract: Survey data typically contain many variables. Structural equation modeling (SEM) is one of the most widely used methods in analyzing such data. The most widely used statistic for testing the adequacy of a SEM model is the likelihood ratio statistic $T_{ML}$. Under normality assumption, $T_{ML}$ approximately follows a chi-square distribution when the number of observations ($n$) is large and the number of items or variables ($p$) is small. However, in practice, $p$ can be very large while $n$ is always limited due to not having enough participants in surveys. Even with a relatively large $n$, empirical results show that $T_{ML}$ rejects the correct model too often when $p$ is large. Various analytical corrections to $T_{ML}$ were proposed whereas an exact Bartlett correction is hard to obtain. This paper proposes empirical corrections so that the mean of the resulting statistic approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that two empirically corrected statistics follow the nominal chi-square distribution much more closely than previously proposed statistics. The formulations of the two statistics are further used to predict type I errors of $T_{ML}$ as reported in the literature, and they perform well.