What Causes the Mean Bias of the Likelihood Ratio Statistic with Many Variables?

Survey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. However, conventional SEM methods are not crafted to handle data with a large number of variables (p). A large p can cause T, the most widely used likelihood ratio statistic, to depart drastically from the assumed chi-square distribution even with normally distributed data and a relatively large sample size N. A key element affecting this behavior of T is its mean bias. The focus of this article is to determine the cause of the bias. To this end, empirical means of T via Monte Carlo simulation are used to obtain the empirical bias. The most effective predictors of the mean bias are subsequently identified and their predictive utility examined. The results are further used to predict type I errors of T. The article also illustrates how to use the obtained results to determine the required sample size for T to behave reasonably well. A real data example is presented to show the effect of the mean bias on model inference as well as how to correct the bias in practice.