Evaluating and Modifying Covariance Structure Models: A Review and Recommendation

The purpose of this article is to present a strategy for the evaluation and modification of covariance structure models. The approach makes use of recent developments in estimation under non-standard conditions and unified asymptotic theory related to hypothesis testing. Factors affecting the evaluation and modification of these models are reviewed in terms of nonnormality, missing data, specification error, and sensitivity to large sample size. Alternative model evaluation and specification error search strategies are also reviewed. The approach to covariance structure modeling advocated in this article utilizes the LISREL modification index for assessing statistical power, and the expected parameter change statistic for guiding specification error searches. It is argued that the common approach of utilizing alternative fit indices does not allow the investigator to rule out plausible explanations for model misfit. The approach advocated in this article allows one to determine the extent of sample size sensitivity and the effects of specification error by relying on existing statistical theory underlying covariance structure models.