Comparison of Model Fit Indices Used in Structural Equation Modeling Under Multivariate Normality

Abstract

The purpose of this study is to investigate the impact of estimation techniques and sample sizes on model fit indices in structural equation models constructed according to the number of exogenous latent variables under multivariate normality. The performances of fit indices are compared by considering effects of related factors. The Ratio Chi-square Test Statistic to Degree of Freedom, Root Mean Square Error of Approximation, and Comparative Fit Index are the least affected indices by estimation technique and sample size under multivariate normality, especially with large sample size.

The Power of One: Benford’s Law

“…The graphical evidence of conformance provided by Figure 5 might be significant, compelling, and even dominating. However, several statistical tests known as the goodness-of-fit or lack-of-fit tests [14], and techniques based on so-called fit indexes [14][15][16][17], are available for supporting the graphical evidence. Apart from the graphical evidence, only three such techniques will be used in this paper.…”

“…The root mean square error (RMSE) fit index [14][15][16][17] is considered as one of the best indexes of its kind [16] and is easier to understand and evaluate than the chi-square test. Furthermore, it may be used to evaluate the strength of the fit and is useful for comparing different data sets.…”

“…However, rejecting a hypothesis based on a level of significance of 0.05 might be unnecessarily conservative in the case of Benford's law. Based on several references from the literature [14][15][16][17], the cut-off criterion for the value of the RSME-fit index that will be used in this paper is shown in Table 3.…”

“…Fit is acceptable RMSE > 0. 10 Fit is poor Table 4 shows a set of possible guidelines for deciding whether or not a data set might be expected to conform to Benford's law [14][15][16][17]. The results obtained from applying a Benford test on a data set should be interpreted with care and insight.…”

A Review of the Tripartite Model Linking Associations between TQM, Organizational Learning, and Performance

“…It is worthy to mention that the various fit indices validity and their thresholds remain controversial. Cangur and Ercan (2015) found that χ2/df, RMSEA, and CFI are the least affected indices regardless of the estimation technique and sample size. This evidence suggests the significance of these indicators as critical indices for the construct validity.…”