Abstract
Orientation: The rigid application of conventional confirmatory factor analysis (CFA) techniques, the overreliance on global model fit indices and the dismissal of the chi-square statistic appear to have an adverse impact on the research of psychological ownership measures.Research purpose: The purpose of this study was to explicate the South African Psychological Ownership Questionnaire’s (SAPOS’s) CFA model fit using the Bayesian structural equation modelling (BSEM) technique.Motivation for the study: The need to conduct this study derived from a renewed awareness of the incorrect use of the chi-square statistic and global fit indices of CFA in social sciences research.Research approach/design and method: The SAPOS measurement model fit was explicated on two study samples consisting, respectively, of 712 and 254 respondents who worked in various organisations in South Africa. A Bayesian approach to CFA was used to evaluate if local model misspecifications were substantive and justified the rejection of the SAPOS model.Main findings: The findings suggested that a rejection of the SAPOS measurement model based on the results of the chi-square statistic and global fit indices would be unrealistic and unfounded in terms of substantive test theory.Practical/managerial implications: BSEM appeared to be a valuable diagnostic tool to pinpoint and evaluate local CFA model misspecifications and their effect on a measurement model.Contribution/value-add: This study showed the importance of considering local misspecifications rather than only relying the chi-square statistic and global fit indices when evaluating model fit.
Highlights
OrientationThe motivation for conducting this study was the realisation that many latent variable measurement models of theoretical constructs published in social sciences journals might be flawed because of deficient model testing (Greiff & Heene, 2017; Hayduk, 2014; Hayduk, Cummings, Boadu, Pazderka-Robinson, & Boulianne, 2007; Ropovik, 2015)
There were no convergence problems, and all estimated parameters, standard errors, collinearity and residual variances that could have influenced the model fit statistics were checked for signs of abnormality
The results of the current study show that the SAPOS measurement model is supported by the data obtained, and that the significant maximum likelihood (ML) chi-square obtained for both samples can to a large extent be ascribed to the effect of random noise on the correlated residuals and small cross-loadings
Summary
The motivation for conducting this study was the realisation that many latent variable measurement models of theoretical constructs published in social sciences journals might be flawed because of deficient model testing (Greiff & Heene, 2017; Hayduk, 2014; Hayduk, Cummings, Boadu, Pazderka-Robinson, & Boulianne, 2007; Ropovik, 2015). Ropovik (2015) reports that 80% of accepted models may be statistically flawed and that only 3% of researchers inspected the residual matrix for local misspecification. Greiff and Heene (2017) reported that in many studies (more than 60%) the chi-square and global goodness of fit (GoF) indices (e.g. comparative fit index [CFI], Tucker–Lewis index [TLI], root mean square error of approximation [RMSEA] and standardised root mean squared residual [SRMR]) are applied mindlessly without considering the effect of local misspecifications on model fit. Hayduk’s (2014) statement may be considered radical, ignoring a statistical significant chi-square and accepting the GoF index results in confirmatory factor analysis (CFA) analyses without doing local indicator http://www.sajip.co.za
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