The Effect of the Number of Observations per Parameter in Misspecified Confirmatory Factor Analytic Models

Some authors have suggested that sample size in covariance structure modeling should be considered in the context of how many parameters are to be estimated (e.g., Kline, 2005 Kline, R. B., 2005. Principles and practice of structural equation modeling, . New York: Guilford; 2005. Google Scholar). Previous research has examined the effect of varying sample size relative to the number of parameters being estimated (N:q). Although some support has been found for this effect, the effect size appears to be small compared to other influences, such as indicator reliability and sample size (Jackson, 2003 Jackson, D. L., 2003. Revisiting sample size and the number of parameter estimates: Some support for the N:q hypothesis., Structural Equation Modeling: A Multidisciplinary Journal 10 (2003), pp. 128–141.Taylor & Francis Online, Web of Science ® , Google Scholar). Efforts to extend this work to the case where models are intentionally misspecified are described in this article. In addition to varying the number of observations per estimated parameter, several other known influences on model fit were varied such as sample size, the degree of misspecification, number of variables per factor, and the communality of the measured variables. The results suggest that decreasing the number of parameters to be estimated while holding sample size constant can help detect misspecification errors, and some fit indexes were more sensitive to this manipulation than others. In general, the effects of N:q were small relative to other experimental effects.