Sample Size Effects on Chi Square and Other Statistics Used in Evaluating Causal Models

Abstract

A simulation study of the effects of sample size on the overall fit statistic provided by the LISREL program indicates the statistic is well behaved over a wide range of sample sizes for simple models. However, this statistic is apparently not chi square distributed for more complex models when samples are relatively small, and will reject the hypothesized model too often. A set of additional measures suggested by various researchers for evaluating causal models also is examined. These statistics are well behaved for both models tested as they converge to the true value and their variance approaches zero as sample size increases.

My life has become a major distraction from my cell phone: Partner phubbing and relationship satisfaction among romantic partners

“…The chi-squared statistic was significant (p < .01) in each CFA, but this was not unexpected since it is known to be sensitive to large sample sizes (Bearden, Sharma, & Teel, 1982;Marsh, Balla, & McDonald, 1988). The construct reliability estimates for the Pphubbing scale (.93), the involvement scale (.96), the attitude scale (.92), the cell phone addiction (.81), and the cell phone conflict scale (.94) were acceptable.…”

Switching intention model development: Role of service performances, customer satisfaction, and switching barriers in the hotel industry

“…Specifically, the 2 /df value of 3.202 falls within a range of acceptable values from 2 to 5 as suggested by Marsh and Hocevar (1988). Other practical fit indices demonstrated that the measurement model fits the data well (RMSEA = 0.079, CFI = 0.917, and NFI = 0.884) (Bearden et al, 1982;Hair et al, 1998;Marsh and Hocevar, 1988). Subsequently, reliability and construct validity were examined.…”

An empirical comparison of the efficacy of covariance-based and variance-based SEM

“…Both start from the same set of theoretical and measurement equations but differ in how they approach the parameter estimation problem. Assume a structural equation model with a set of latent exogenous variables (ξ i ) measured by indicators x i and associated measurement error δ i , and a set of latent endogenous variables (η j ) measured by indicators y j and Note: Does not include simulation studies that are focused on the relative performance of different fit indices (e.g., Bearden, Sharma, & Teel, 1982;Curran, West, & Finch, 1996;Hu & Bentler, 1998) or on the analysis of specific issues, such as the estimation of interaction effects (e.g., Chin et al, 2003), between-group differences (e.g., Qureshi & Compeau, 2009), measurement model misspecification (e.g., Jarvis, MacKenzie, & Podsakoff, 2003) and item parceling (e.g., Bandalos, 2002;Kim & Hagtvet, 2003;Nasser & Wisenbaker, 2003). associated measurement error ε j .…”