Overall fit in covariance structure models: Two types of sample size effects.

A controversial area in covariance structure models is the assessment of overall model fit. Researchers have expressed concern over the influence of sample size on measures of fit. Many contradictory claims have been made regarding which fit statistics are affected by N. Part of the confusion is due to there being two types of sample size effects that are confounded. The first is whether N directly enters the calculation of a fit measure. The second is whether the means of the sampling distributions of a fit index are associated with sample size. I explain these types of sample size effects and illustrate them with the major structural equation fit indices. In addition, I examine the current debate on sample size influences in light of this distinction. Structural equation models, including confirmatory factor analyses, are becoming increasingly popular in psychology. Key to these procedures is the hypothesis that the population covariance matrix of observed variables is a function of the unknown free parameters of a model. Many measures of overall model fit have been proposed to assess the degree to which this hypothesis holds (e.g., Rentier B Bollen, 1986;Hoelter, 1983; Joreskog Tucker & Lewis, 1973).