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.
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.
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.
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.
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.
BSEM appeared to be a valuable diagnostic tool to pinpoint and evaluate local CFA model misspecifications and their effect on a measurement model.
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.
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,
In line with recent publications (Guay, Morin, Litalien, Valois, & Vallerand,
The domain of psychological ownership (PO) provided the ideal platform for the current study as secondary data from a previously published research measurement model as well as an independent sample for replication purposes were available. Psychological ownership, a subdiscipline of positive psychology, has received much attention in scholarly literature on psychology and management over the past decade (Olckers & Van Zyl,
Psychological ownership is a unique concept that can be differentiated from other concepts in positive psychology (Pierce, Kostova, & Dirks,
Dawkins, Tian, Newman and Martin (
Given the likely construct validity limitations of Avey et al.’s (
[
The SAPOS consists of 35 items and four subscales, with 5–16 items per scale. Olckers (
In summary, probabilistic issues in the assessment of the plausibility of measurement models in the social sciences, and more specifically PO, include rigidly applying CFA techniques (Asparouhov, Muthén, & Morin,
This study sought to point out the challenges that come with the rigid application of CFA techniques, the problem of overly generalised CFA model fit indices and the impact of imperfect latent factor indicators on measurement models. More specifically, its aim was to gain new insights into the plausibility of a multidimensional SAPOS measurement model through more flexible and meaningful engagement with the data and the factoring in of substantive test theory principles. In this study, I went beyond evaluating global fit indices and target factor loadings to the explicating of CFA model misfit. I demonstrated the value of Bayesian structural equation modelling (BSEM) as a diagnostic tool for CFA model misfit challenges in the assessment of the more lengthy and multidimensional SAPOS measurement model (Asparouhov et al.,
Bayesian structural equation modelling allows for the analysis of simultaneous and cumulative effects of small cross-loadings and correlated residuals in the CFA measurement model for SAPOS, which could lead to a better understanding of the reasons for model misfit and help to evaluate whether misfit could be considered substantive or not. According to Asparouhov and Muthén (
BSEM can be used to parse out meaningful model misspecifications from small model misspecifications that can also be the cause of model rejections when such small misspecifications are in great number, or sample size is so large that even small misspecifications are enough to reject the model.
The research question for this study is whether item cross-loadings and correlated residuals for the SAPOS measurement model signify significant and substantive parameter misspecifications and whether these justify the rejection of the CFA model. The use of BSEM as a diagnostic tool for studying the significance and substantiveness of model misspecification at a local parameter level is demonstrated.
In the following sections, a critical review of CFA model misspecification and misfit is given and the role of BSEM in diagnosing CFA misfit is clarified. Brief overviews of BSEM as a small-sample factor analysis technique and of the SAPOS measurement model are also presented.
Simulation studies have shown that the GoF indices’ cut-off values suggested by Hu and Bentler (
Contrary to the behaviour of GoF indices, the maximum likelihood (ML) ratio chi-square value has been shown to be overly sensitive in detecting minor misspecifications with increases in sample size, indicator reliability, communalities, deviations from multivariate normality, the size of the covariance matrix and model complexity (Heene, Hilbert, Draxler, Ziegler, & Bühner,
Bayesian structural equation modelling is a viable option for inspecting the substantiveness of misspecifications signified by a statistically significant ML chi-square value. It has rightfully been argued that the ML chi-square statistic used in CFA modelling of substantive theory applies unnecessarily strict criteria for model fit. Confirmatory factor analysis models that assume zero item cross-loadings and zero residual correlations in factor analysis are considered unrealistic when testing the theory underlying multidimensional behavioural measurement models (Asparouhov et al.,
The BSEM technique has, however, been criticised by Stromeyer, Miller, Sriramachandramurthy and DeMartino (
According to Muthén and Asparouhov (
Moreover, using BSEM with diffuse priors can be highly problematic when applied to small samples, leading to biased parameter estimates and insufficient statistical power (McNeish,
The theory and the details of the constructs are described by Olckers (
The first version of the SAPOS (Olckers,
The South African Psychological Ownership Questionnaire measurement model: Standardised parameter estimates for latent construct correlates, indicator (Q) and error (E) values.
The present study employed BSEM to explicate the SAPOS CFA measurement model fit using the original total sample from Olckers’ study and to test and explicate the CFA model fit on a new independent sample. More specifically, this study used the BSEM analysis to inspect the substantiveness of the local misspecifications signified by a statistical significant chi-square on the measurement model of the SAPOS for two independent study samples.
A cross-sectional survey research design was followed in this study. Participants were recruited through non-probability purposive samples of mostly professional-level employees from various organisations in both the private and public sectors in South Africa. Sample 1 was the data set that Olckers (
Sample 1 consisted of the data used for the initial development of the SAPOS (Olckers,
Sample 2 was newly acquired and consisted of 254 respondents of which 66% were men and 34% were women. Of the sample, 54% were white respondents and 36% were Africans. The average age of the respondents was 39 years. Approximately 53% of the sample had obtained a tertiary education. Of the respondents, 82% functioned on a managerial level. In terms of employment tenure, 24% had been working in their current organisation for a period of less than 5 years and the remainder (76%) had been employed for more than 5 years.
The SAPOS consists of 35 items and represents four factors: self-identity, responsibility, autonomy and territoriality. The original item numbering reported in the study conducted by Olckers (
Participants from several organisations completed the questionnaire in their personal capacity and they gave their informed consent. The purpose of the research was explained to the respondents, and participation in the survey was voluntary. Data were collected by means of an electronic self-administered questionnaire or hard copies of the questionnaire that were distributed. The confidentiality and anonymity of the respondents were respected at all times.
A CFA factor analysis was used to test for the SAPOS measurement model for each of the samples, followed by BSEM to investigate the parameters that might have been misspecified, contributing to a significant chi-square value and consequently model rejection (Asparouhov et al.,
The BSEM analysis allows for models to be modified progressively from a CFA model using a Bayes estimator to a full BSEM model that includes parameters with cross-loadings and correlated residuals (Asparouhov et al.,
The first model (Model 1) consisted of a CFA model that did not specify cross-loading or correlated residuals: by implication all the parameters were fixed to zero. The second model (Model 2) consisted of a CFA model specifying small variance priors, resulting in normally distributed non-zero cross-loadings which could vary between being important (λ < 0.30) and being near zero. The third model (Model 3) consisted of the cross-loading priors specified in Model 2 and additional potentially misspecified correlated residual parameters with small variances priors around zero.
Model 1 was obtained by running a CFA with a Bayes estimator with a diffuse or non-restricted variance prior setting that would equate the analyses with those of an ML CFA model.
Model 2 was obtained by using sensitivity analyses of at least five runs, starting with normal distribution zero (0) priors with extremely small variances (0.001), depicted in MPlus as N (0, 0.001). The priors’ variances systematically increased with each run as follows: N (0, 0.005), N (0, 0.01), N (0, 0.015), N (0, 0.02) and N (0, 0.025). The effect of the varying small variance priors for the factor cross-loadings on the measurement model fit was tested using posterior predictive
Model 3 was obtained using the diagonal residual covariance matrix (θ) of the CFA model. The prior for the θ matrix is set as an inverse Wishart prior θ~IW(
The BSEM estimations were done with four independent MCMC chains using the Gibbs sampler. Model convergence was assessed using the potential scale reduction (PSR) factor diagnostic as well as the Kolmogorov–Smirnov test (K–S test) and a visual inspection of the parameter trace and density plots. Convergence was assumed when the PSR value was below or close to 1.05 and the quality and density of the trace plots suggested sufficient coverage and mixing of the chains. All model tests were started with 50 000 iterations, and, if satisfactory convergence was not obtained, the iterations were increased twofold until satisfactory convergence was obtained. Model fit was evaluated using PPP. The PPP value is defined as the proportion of the chi-square values of the simulated or replicated data that exceeds that of the observed data. A low PPP (< 0.05) indicates poor model fit, whereas PPP values of around 0.50 indicate very good fit (Muthén & Asparouhov,
In accordance with the recommendations of Dunn, Baguley and Brunsden (
The SAPOS variables were standardised to form a uniform metric with a standard deviation of 1 and a mean of 0 to ensure that the scale does not interfere with the prior settings.
Ethical clearance for the research was obtained from the Ethics Committee of the Faculty of Economics and Management Sciences at the relevant university. Individuals from several organisations took part in the research in their personal capacity and they gave their informed consent for participation. The purpose of the research was explained to the respondents and participation in the survey was voluntary. Data were collected by through electronic self-administered questionnaire or hard copies of the questionnaire that were distributed. The confidentiality and anonymity of the respondents were respected at all times.
Descriptive statistics for Sample 1 showed a mean item skewness of -0.96 and varied between -1.59 and 0.35. The kurtoses mean was 1.49 and varied between -1.19 and 6.24. Sample 2 showed a mean item skewness of -1.34 and varied between -2.58 and 0.16. The kurtoses mean was 2.37 and varied between -1.22 and 10.68. The ML robust and Bayesian estimators used in this study are known to be effective for non-normal distributions.
The CFA fit statistics for Sample 1, using a robust chi-square statistic, were as follows:
The results of the BSEM analysis conducted on Sample 1 are presented in
Trace plot for question 22 parameter loading on the latent variable of territoriality (Sample 1).
Density function for question 22 parameter loading on territoriality (Sample 1).
Bayesian structural equation modelling model fit statistics for Sample 1.
Model | # | pd | PPP | PPPP | Lower 2.5% PP limit | Upper 97.5% PP limit | Difference in PP limit |
---|---|---|---|---|---|---|---|
Bayes CFA model with no informative priors | 111 | 111.29 | 0.00 | n/a | 1291.75 | 1448.15 | - |
BSEM model with cross-loading priors |
216 | 156.33 | 0.00 | 0.00 | 1022.25 | 1192.99 | 170.74 |
BSEM model with cross-loading priors |
216 | 186.52 | 0.00 | 0.00 | 940.49 | 1108.06 | 167.57 |
BSEM model with cross-loading priors |
216 | 193.62 | 0.00 | 0.02 | 935.46 | 1102.17 | 166.71 |
BSEM model with cross-loading priors |
216 | 195.94 | 0.00 | 0.50 | 935.34 | 1102.57 | 167.23 |
BSEM model with cross-loading priors |
216 | 196.77 | 0.00 | 0.90 | 935.75 | 1102.85 | 167.10 |
BSEM model with cross-loading priors |
811 | 460.98 | 0.37 | 1.0 | −86.08 | 116.49 | - |
BSEM model with cross-loading priors |
811 | 434.51 | 0.16 | 1.0 | −49.99 | 154.90 | - |
BSEM model with cross-loading priors |
811 | 422.41 | 0.09 | 1.0 | −32.97 | 171.27 | - |
#, number of free parameters; pd, estimated number of parameters; PPP, posterior predictive
With respect to Sample 1, the BSEM model fit indices for Model 1 showed inadequate fit (PPP < 0.05) in a way that agrees with the ML CFA model fit. Model 2 also showed inadequate fit (PPP < 0.05); however, the lower (PP limit = 2.5%) and upper (PP limit = 97.5%) confidence levels showed that at a 95% confidence interval, the difference between the observed and the replicated chi-square values had improved compared to Model 1. Model 2 also showed inadequate fit (PPP < 0.05), and the relative stable PPP difference values across the models tested suggested that the varying small cross-loading priors were insufficient to obtain an overall acceptable model fit. The PPPP value of 0.49 that was obtained in the sensitivity analysis for small variance priors
Correlated residuals for Sample 1.
Only approximately 2% of correlated residuals were not within the range of 0.10 to -0.10, with the largest value being -0.13. In total, 50 of 595 correlated residuals were significant (95% credibility interval that does not contain zero), none of which can be considered substantive. Values around 0.20 can be considered as substantive and ‘statistically significant’, which means that there is a 95% credibility interval (Asparouhov et al.,
Bayesian structural equation modelling factor loadings for samples 1 and 2 of Model 3.
Question number | Question | I |
R |
A |
T |
Residual variances |
|||||
---|---|---|---|---|---|---|---|---|---|---|---|
S1 | S2 | S1 | S2 | S1 | S2 | S1 | S2 | S1 | S2 | ||
Q6 | I feel the need to defend my organisation to outsiders when it is criticised. | 0.008 | 0.087 | −0.067 | −0.086 | 0.139 |
0.092 | 0.748 |
0.730 |
||
Q9 | I feel the need to support my organisation’s goals and policies. | 0.157 |
0.229 |
−0.048 | 0.107 | 0.024 | 0.025 | 0.705 |
0.599 |
||
Q12 | I am proud to say that ‘this is my organisation’ to people whom I meet. | −0.021 | 0.062 | 0.079 | −0.007 | −0.033 | −0.066 | 0.576 |
0.456 |
||
Q24 | I feel a strong linkage between me and my organisation. | −0.098 |
−0.006 | 0.112 |
0.109 | −0.043 | 0.012 | 0.402 |
0.492 |
||
Q27 | I feel as if this organisation is ‘MY’ organisation. | −0.032 | −0.018 | −0.005 | 0.106 | 0.034 | 0.175 |
0.534 |
0.647 |
||
Q31 | I feel that I belong to this organisation. | −0.036 | −0.057 | 0.052 | −0.028 | −0.038 | −0.066 | 0.278 |
0.245 |
||
Q34 | I feel ‘at home’ in this organisation. | −0.05 | −0.02 | 0.107 |
0.018 | −0.094 |
−0.110 | 0.333 |
0.309 |
||
Q40 | I feel totally comfortable being in the organisation. | 0.068 | 0.009 | 0.081 | 0.009 | −0.054 | −0.023 | 0.389 |
0.250 |
||
Q43 | I feel that this organisation is part of me. | −0.058 | −0.085 | −0.004 | 0.014 | −0.012 | 0.078 | 0.273 |
0.218 |
||
Q49 | I feel I have a considerable emotional investment in my organisation. | 0.084 | 0.053 | −0.042 | −0.052 | 0.041 | 0.132 | 0.676 |
0.629 |
||
Q51 | I personally experience the successes and failures of the organisation as my successes and failures. | −0.028 | 0.159 |
−0.096 | −0.009 | 0.054 | 0.100 | 0.570 |
0.614 |
||
Q52 | I feel I have a strong bond with the organisation. | −0.046 | −0.024 | −0.134 |
−0.015 | 0.022 | −0.026 | 0.262 |
0.254 |
||
Q55 | I feel secure in this organisation. | −0.043 | −0.082 | 0.100 | −0.042 | −0.018 | −0.136 | 0.467 |
0.587 |
||
Q56 | I feel that I have common interests with my organisation that are stronger than our differences. | 0.061 | −0.049 | −0.060 | −0.071 | −0.081 | −0.012 | 0.434 |
0.408 |
||
Q61 | I feel the need to be seen as a member of the organisation. | 0.147 |
−0.160 |
0.032 | 0.143 |
0.084 | 0.709 |
0.622 |
|||
Q66 | I feel that my personal values and those of the organisation are aligned. | 0.031 | −0.094 | 0.058 | 0.079 | 0.007 | −0.005 | 0.484 |
0.445 |
||
Q16 | I accept the consequences of my decisions in the organisation | −0.051 | −0.092 | 0.052 | 0.015 | −0.043 | 0.035 | 0.529 |
0.589 |
||
Q28 | I take responsibility for my decisions in the organisation. | −0.025 | −0.013 | 0.102 | 0.03 | −0.010 | 0.022 | 0.624 |
0.598 |
||
Q47 | I accept full responsibility for my actions within the organisation. | −0.005 | 0.024 | −0.032 | −0.085 | 0.038 | −0.020 | 0.355 |
0.501 |
||
Q48 | I feel I should take the consequences of my work in the organisation. | 0.039 | −0.018 | 0.006 | 0.030 | 0.023 | 0.071 | 0.543 |
0.481 |
||
Q54 | I accept ownership for the results of my decisions and actions. | 0.013 | 0.047 | −0.011 | −0.054 | −0.011 | −0.013 | 0.417 |
0.471 |
||
Q59 | If the buck stops with me, I ensure that the task/complaint is resolved successfully every time. | −0.034 | 0.06 | 0.009 | 0.025 | −0.042 | 0.004 | 0.646 |
0.580 |
||
Q62 | If I cannot deliver on a task for whatever reason, I maintain the responsibility to find an alternative resource or solution. | 0.029 | 0.097 | −0.005 | 0.035 | −0.021 | −0.073 | 0.612 |
0.570 |
||
Q63 | I feel personally responsible for the work I do in my organisation. | 0.049 | 0.02 | −0.023 | 0.096 | 0.023 | −0.083 | 0.513 |
0.464 |
||
Q11 | I have the freedom to schedule my work and determine how it is done. | −0.052 | −0.041 | 0.028 | 0.063 | 0.015 | 0.067 | 0.569 |
0.583 |
||
Q19 | I have the opportunity for independent thought and action. | 0.011 | 0.038 | 0.067 | 0.007 | −0.102 | −0.093 | 0.478 |
0.568 |
||
Q23 | I take responsibility for my decisions in the organisation. | −0.033 | −0.045 | −0.043 | 0.073 | 0.014 | −0.065 | 0.502 |
0.511 |
||
Q29 | I am allowed to use my personal initiative and judgement in carrying out my work. | 0.001 | 0.085 | 0.013 | 0.019 | −0.024 | −0.098 | 0.407 |
0.369 |
||
Q38 | I have almost complete responsibility for deciding how and when the work is done. | 0.119 | 0.084 | −0.018 | −0.104 | 0.128 |
0.149 |
0.437 |
0.447 |
||
Q42 | I have considerable opportunity for independence and freedom in how I do my work. | 0.046 | −0.008 | 0.042 | −0.026 | 0.048 | 0.054 | 0.318 |
0.398 |
||
Q2 | I feel I need to defend my work environment from others in the organisation. | 0.024 | 0.122 | −0.042 | −0.065 | −0.028 | −0.028 | 0.765 |
0.765 |
||
Q22 | I feel the need to protect my belongings from others in the organisation. | 0.049 | −0.006 | −0.028 | −0.046 | 0.037 | −0.017 | 0.646 |
0.557 |
||
Q26 | I feel that people I work with should not invade my work environment. | −0.085 | −0.033 | 0.009 | 0.083 | 0.048 | 0.024 | 0.545 |
0.728 |
||
Q35 | I feel the need to protect my intellectual property from being used by others in the organisation. | 0.071 | −0.05 | −0.01 | 0.078 | 0.007 | −0.015 | 0.544 |
0.636 |
||
Q39 | I feel the need to discourage others to invade my work space. | −0.047 | 0.025 | 0.028 | −0.096 | 0.039 | 0.053 | 0.368 |
0.525 |
Note: Bold values are substantive loadings.
I, Identity; R, Responsibility; A, Autonomy; T, Territoriality; S1, Sample 1, S2, Sample 2; Q, Question number.
, Significant loadings (95% credibility interval that does not contain zero).
The CFA fit statistics for Sample 2, using a robust chi-square statistic, were as follows:
With respect to Sample 2, the BSEM model fit indices (see
Correlated residuals for Sample 2.
Bayesian structural equation modelling model fit statistics for Sample 2.
Model | # | pd | PPP | PPPP | Lower 2.5% PP limit | Upper 97.5% PP limit | Difference in PP limit |
---|---|---|---|---|---|---|---|
Bayes CFA model with no informative priors | 111 | 110.57 | 0.00 | n/a | 735.52 | 901.73 | - |
BSEM model with cross-loading priors |
216 | 130.81 | 0.00 | 0.00 | 660.00 | 832.45 | 172.45 |
BSEM model with cross-loading priors |
216 | 162.22 | 0.00 | 0.00 | 577.19 | 751.70 | 174.51 |
BSEM model with cross-loading priors |
216 | 175.60 | 0.00 | 0.00 | 560.75 | 734.19 | 173.44 |
BSEM model with cross-loading priors |
216 | 182.00 | 0.00 | 0.00 | 556.55 | 730.70 | 174.15 |
BSEM model with cross-loading priors |
216 | 185.69 | 0.00 | 0.08 | 555.66 | 729.77 | 174.11 |
BSEM model with cross-loading priors |
216 | 188.01 | 0.00 | 0.32 | 555.79 | 729.80 | 174.01 |
BSEM model with cross-loading priors |
216 | 189.51 | 0.00 | 0.63 | 556.35 | 730.47 | 174.12 |
BSEM model with cross-loading priors |
811 | 394.77 | 0.29 | 1.0 | −76.58 | 129.60 | - |
BSEM model with cross-loading priors |
811 | 366.64 | 0.13 | 1.0 | −42.66 | 158.89 | - |
BSEM model with cross-loading priors |
811 | 346.04 | 0.04 | 1.0 | −46.442 | 154.17 | - |
#, number of free parameters; pd, estimated number of parameters; PPP, posterior predictive
Included in
The pattern of inter-correlations between the four latent variables of the SAPOS (see the BSEM model’s values below the diagonal line in
Inter-correlation (covariance) matrix for the latent variables as produced by the confirmatory factor analysis and Bayesian structural equation modelling models.
SAPOS Factors | Sample 1 ( |
Sample 2 ( |
||||||
---|---|---|---|---|---|---|---|---|
I | R | A | T | I | R | A | T | |
I | 0.438 |
0.647 |
0.005 | 0.574 |
0.721 |
0.194 |
||
R | 0.445 |
0.412 |
−0.012 | 0.564 |
0.566 |
0.113 | ||
A | 0.616 |
0.378 |
−0.037 | 0.710 |
0.556 |
0.243 |
||
T | 0.015 | −0.021 | −0.100 | 0.205 | 0.150 | 0.249 |
Note: Values in bold on the diagonal line are omega reliability coefficients.
Bayesian structural equation modelling model inter-correlation coefficients are located below the diagonal line. The omega reliability coefficients for the BSEM model are located on the diagonal line. The CFA model’s factor inter-correlations are located above the diagonal line.
I, Identity; R, responsibility; A, autonomy; T, territoriality.
, Significant correlations (95% credibility interval that does not contain zero).
The omega reliability coefficients reported in
In summary, the results suggested that the rejection of the ML CFA model might have been partly because of small cross-loadings but particularly because of the accumulated effect of small and random residual correlations, and that the model should, therefore, be considered a good approximation of the data.
The purpose of this study was to explicate the SAPOS’s CFA measurement model fit using BSEM, a methodology that has only recently been adopted by researchers in the field (De Beer & Bianchi,
The results of the current study show that the SAPOS measurement model is supported by the data obtained, and that the significant 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. The fact that the powerful new PPPP statistic for small variance priors has not rejected the assumption that the parameter cross-loadings are non-substantive and near zero further supports the notion that model misfit can be ascribed to the effect of random noise (Asparouhov & Muthén,
The results show that many minor correlated residuals account for most of the model misfits in the ML CFA model of the SAPOS. One noticeable correlated residual on the SAPOS is for Q55 and Q56 (Q55: ‘I feel secure in this organisation’ and Q56: ‘I feel that I have common interests with my organisation that are stronger than our differences’). The existence of isolated correlated residuals that are substantive can be ascribed to methodological artefacts resulting in variance unrelated to the construct, such as negative wording, adjacency effects, question order, parallel wording and similar contexts (De Beer & Bianchi,
The evidence from this study suggested that substantive misspecifications of the factor indicators or item cross-loadings, inflated factor inter-correlations, isolated substantive correlated residuals, the possibility of missing factors, over-factoring, item redundancy in factors and other substantive nuisance factors in the SAPOS CFA measurement model should be of little concern.
With the aim of improving the existing PO theory, this study displayed a very important and relevant shift from the loosely applied CFA global model fit dogma to the detailed examining of local parameter misspecifications or flaws (Greiff & Heene,
In this study, the extent and reasons of parameter misspecifications in the SAPOS measurement model were investigated for the first time using two independent study samples. This study provided important evidence concerning the plausibility of the theoretical deductions that can be made after distinguishing between the substantive and non-substantive misspecifications within the framework of substantive classical test theory (Asparouhov et al.,
As demonstrated by the findings of this study, a parallelism may be drawn between the problem associated with ML CFA chi-square fit indices and the ideas suggested by Cohen (
In this study, the SAPOS measurement model fit was explicated using two independent samples, and the findings suggested that a rejection of the CFA model based on a significant chi-square statistic and the unreliable GoF indices would be unrealistic and unfounded in terms of substantive classical test theory.
Plausible alternative models (e.g. second-order and bifactor models) were not investigated in this study. It is recommended that future studies should focus on alternative models. The sample in the current study was limited to a South African population group, and the SAPOS measurement model may not be generalised to other population groups.
The author wishes to thank Prof. Chantal Olckers, Department of Human Resources Management, University of Pretoria, South Africa, for making the SAPOS data available for the purposes of this study.
The author declares that he has no financial or personal relationship(s) which may have inappropriately influenced him in writing this article.
I declare that I am the sole author of this research article.
This manuscript is based on research partly supported by the National Research Foundation of South Africa (Grant Number 103796).
The Mplus sytax used in the BSEM analysis is available on reasonable request from the corresponding author. The data is the intellectual property of the University of Pretoria and not for sharing.
The views and opinions expressed in this article are the author’s own and do not reflect an official position of the University of Pretoria or the National Research Foundation of South Africa.