A simulation study to investigate the use of cutoff values for assessing model fit in covariance structure models Subhash Sharma a, * , Soumen Mukherjee b , Ajith Kumar c , William R. Dillon d a Moore School of Business, University of South Carolina, Columbia, SC 29208, USA b MAPS Inc., Waltham, MA, USA c Arizona State University, Tempe, AZ, USA d Southern Methodist University, Dallas, TX, USA Received 3 January 2002; accepted 14 October 2003 Abstract In this paper, we used simulations to investigate the effect of sample size, number of indicators, factor loadings, and factor correlations on frequencies of the acceptance/rejection of models (true and misspecified) when selected goodness-of-fit indices were compared with prespecified cutoff values. We found the percent of true models accepted when a goodness-of-fit index was compared with a prespecified cutoff value was affected by the interaction of the sample size and the total number of indicators. In addition, for the Tucker-Lewis index (TLI) and the relative noncentrality index (RNI), model acceptance percentages were affected by the interaction of sample size and size of factor loadings. For misspecified models, model acceptance percentages were affected by the interaction of the number of indicators and the degree of model misspecification. This suggests that researchers should use caution in using cutoff values for evaluating model fit. However, the study suggests that researchers who prefer to use prespecified cutoff values should use TLI, RNI, NNCP, and root-mean-square-error-of- approximation (RMSEA) to assess model fit. The use of GFI should be discouraged. D 2004 Elsevier Inc. All rights reserved. Keywords: Structural equation modeling; Confirmatory factor analysis; Goodness-of-fit-indices; Simulation 1. Introduction The evaluation of covariance structure models is typical- ly carried out in two stages: (1) an evaluation of overall model fit and (2) evaluations of specific parts/aspects of the model such as the measurement properties of indicators and/ or strength of structural relationships. The chi-square test statistic was among the first set of indices proposed to evaluate overall model fit to the data in a statistical sense. As is the case with most statistical tests, the power of the chi-square test increases with sample size. Since in covari- ance structure analysis, the nonrejection of the model subsumed under the null hypothesis is typically the desired outcome, the rejection of the model through the chi-square test in large samples, even for trivial differences between the sample and the estimated covariance matrices, soon came to be perceived as problematic (Bentler and Bonett, 1980; Tucker and Lewis, 1973). In response to this ‘‘sample-size’’ problem of the chi-square test statistic, several alternative goodness-of-fit indices were proposed for evaluating overall model fit. In turn, a number of simulation studies evaluated the sensitivity of these indices to sample-size variations (e.g., Anderson and Gerbing, 1984; Bearden et al., 1982; Bentler, 1990; Marsh et al., 1988). In their comprehensive, integrative review of various goodness-of-fit indices, McDonald and Marsh (1990) con- cluded that only four indices were relatively insensitive to sample size: the noncentrality parameter (NCP) of McDo- nald (1989) and a normed version thereof (NNCP), the relative noncentrality index (RNI), and the Tucker-Lewis index (TLI). An index is defined to be insensitive to sample size if the expected value of its sampling distribution is not affected by sample size. However, researchers typically evaluate model fit by comparing the value of some good- ness-of-fit index with some prespecified cutoff value. Based on the results of a recent simulation study, Hu and Bentler (1998, 1999) suggest that a cutoff value close to 0.95 for TLI or RNI, a cutoff value close to 0.90 for NNCP or a 0148-2963/$ – see front matter D 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jbusres.2003.10.007 * Corresponding author. Tel.: +1-803-777-4912; fax: +1-803-777-6876. E-mail address: sharma@moore.sc.edu (S. Sharma). Journal of Business Research 58 (2005) 935 – 943