Measures of fit impacts: Application to the causal model of consumer involvement

Abstract

Using the Monte Carlo simulation method, this study analyzes the impacts on fit indices by the degree of nonnormality of variables, the sample size, and the choice of estimation method. To address these issues, we use the causal model of consumer involvement as elaborated by Mittal and Lee. Results of this study show that adjusted goodness of fit index (AGFI) and goodness of fit index (GFI) are subject to variation in sample size, and their use requires a sample size of at least 300 observations to be reliable. Comparative fit index (CFI) and root mean square error of approximation (RSMEA) are more reliable with the generalized least squares (GLS) compared with maximum likelihood estimation (MLE) method under different settings of sample size and degree of nonnormality. Finally, for the standardized root mean square residual (SRMR), it is recommended that it is used with the MLE method. This study provides prescriptions for the choice of fit indices and the requirements of sample size and estimation method to test the causal model of consumer involvement. The method used here can be extended to any model before fitting it to real data. It helps researchers to prevent conflictual results regarding the choice of fit indices.