The Need for Alternative Measures of Fit in Covariance Structure Modeling

Arguments are raised against Kaplan's (1990) view that fit indices other than the likelihood ratio test need not be used in covariance structure modeling except when sample size sensitivity is observed. Kaplan's criterion for the presence of sample size sensitivity is called into question. Furthermore, it is argued that the likelihood ratio test should not be relied on heavily because (a) it is inherently biased when sample size is large; (b) it is dependent on distributional assumptions as well as a large sample size; (c) the hypothesis that it tests, perfect fit of the model in the population, is not of central empirical interest; and (d) it does not provide information about the important issues of close (but imperfect) fit in the population, and cross-validity to other samples. Other measures of fit are available that overcome these problems, though they are likely to be subject to other problems. The general recommendation is that multiple approaches to assessment of fit be used in conjunction with Kaplan's recommended procedures.