Testing operational research hypothesis 1

Operational research hypothesis 1 represents substantive research hypothesis 1 but without assuming method factors. Substantive research hypothesis 1 postulates that the SD scale of the SAPI provides a construct valid measure of social desirability conceptualised as a two- dimensional construct comprising the two positively correlated latent dimensions of self-

deception enhancement and impression management. A two-factor measurement model was

therefore fitted to the data by having the Social Desirability scale items load on the two factors as they were categorised in Table 5. This model was therefore based on the factor solution implied by the social desirability factors that the items were measuring in the original scales from which they were harvested. A measurement model is a description of the process that is claimed to have brought about the observed covariance matrix. If estimates for the freed model parameters can be found that allows the observed covariance matrix to be accurately reproduced, the measurement model fits the data. The measurement model may then be regarded as a plausible description of the process that brought about the observed covariance matrix. The parameter estimates may then be regarded as credible and worthy of interpretation.

LISREL 8.8 was used to fit the two-factor measurement model without method factors in which each SD-scale item measures one of two positively correlated latent dimensions of self-deception

enhancement and impression management. A visual representation of the measurement model

that was fitted to the reduced dataset (n=1240) is displayed in Figure 8.

Figure 8: Representation of the fitted two-factor social desirability measurement model hypothesised by operational research hypothesis 1 (completely standardised solution)

The fit statistics for the two-factor measurement model are reported below in Table 27. The indices that are to be reported on are presented in bold in Table 27.

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Table 27:

Goodness of Fit Statistics for the two-factor Social Desirability Measurement Model (operational hypothesis 1)

Goodness of Fit Statistics Degrees of Freedom = 53

Minimum Fit Function Chi-Square = 465.062 (P = 0.0)

Normal Theory Weighted Least Squares Chi-Square = 572.396 (P = 0.0) Satorra-Bentler Scaled Chi-Square = 493.919 (P = 0.0) Chi-Square Corrected for Non-Normality = 266.333 (P = 0.0)

Estimated Non-centrality Parameter (NCP) = 440.919 90 Percent Confidence Interval for NCP = (373.485 ; 515.816)

Minimum Fit Function Value = 0.375 Population Discrepancy Function Value (F0) = 0.356 90 Percent Confidence Interval for F0 = (0.301 ; 0.416) Root Mean Square Error of Approximation (RMSEA) = 0.0819

90 Percent Confidence Interval for RMSEA = (0.0754 ; 0.0886) P-Value for Test of Close Fit (RMSEA < 0.05) = 0.000

Expected Cross-Validation Index (ECVI) = 0.439 90 Percent Confidence Interval for ECVI = (0.385 ; 0.499)

ECVI for Saturated Model = 0.126 ECVI for Independence Model = 2.148

Chi-Square for Independence Model with 66 Degrees of Freedom = 2637.792 Independence AIC = 2661.792 Model AIC = 543.919 Saturated AIC = 156.000 Independence CAIC = 2735.266 Model CAIC = 696.991 Saturated CAIC = 633.584 Normed Fit Index (NFI) = 0.813 Non-Normed Fit Index (NNFI) = 0.787 Parsimony Normed Fit Index (PNFI) = 0.653

Comparative Fit Index (CFI) = 0.829 Incremental Fit Index (IFI) = 0.829

Relative Fit Index (RFI) = 0.767 Critical N (CN) = 201.289

Root Mean Square Residual (RMR) = 0.0562 Standardized RMR = 0.0654 Goodness of Fit Index (GFI) = 0.929 Adjusted Goodness of Fit Index (AGFI) = 0.895 Parsimony Goodness of Fit Index (PGFI) = 0.631

The exceedence probability associated with the Satorra-Bentler Scaled chi-square test statistic indicated that the null hypothesis of the exact fit (H011: RMSEA=0) is rejected. This result was

expected as exact fit represents a somewhat unrealistic position in that it states that the single- group measurement model is able to reproduce the observed sample covariance matrix to a degree of accuracy that could be explained solely in terms of sampling error.

The operational hypothesis that is represented by the close fit null hypothesis (H021) assumes that

the measurement model describes an approximation of the process that operated in reality to create the observed covariance matrix (Browne & Cudeck, 1993). The Root Mean Square of Error of Approximation (RMSEA) is a test statistic that is of importance. It is a popular measure of fit that articulates the difference between the observed and the estimated sample covariance matrices. According to Diamantopoulos and Siguaw (2000) it is one of the most informative fit indices as it takes the complexity of the model into consideration.

In Table 27 the RMSEA value is reported as .0819 and this indicates that the measurement model shows only reasonable fit in the sample. The p-value for the test of close fit provides further evidence for the hypothesis ( : RMSEA ≤ .05) and is reported in Table 27 as approximating 0. Therefore, the close fit null hypothesis : RMSEA ≤ .05 was rejected. This

meant that the measurement model does not show close fit in the parameter although it did show reasonable fit in the sample. It therefore had to be concluded that the two-factor measurement model did not offer a plausible description of the process that created the observed covariance matrix in that the model failed to reproduce the observed covariance matrix to a sufficient degree of accuracy. Confidence intervals assess the precision of the RMSEA estimates and the fit statistics in Table 27 reported the upper and lower bounds of the 90% interval to be .0754 to .0886. Interpretation of the confidence interval indicated that the true RMSEA value in the population fell within the relatively narrow bounds of .0754 and .0886, which presents a high degree of precision (Byrne, 2001) but lack of close fit since the confidence interval excluded the critical close fit cut-off value for RMSEA of .05.

The parameter estimates of the two-factor measurement model were consequently not interpreted.

A visual representation of the modification indices calculated for the two-factor measurement model that was fitted to the reduced dataset (N=1240) is displayed in Figure 9. The large number of statistically significant (p<.05) modification index values obtained for the currently fixed measurement error covariances in were noteworthy. Allowing the measurement error terms associated with the SD-scale items to correlate would statistically significantly (p<.05) improve the fit of the two-factor measurement model.

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Figure 9: Representation of the modification indices calculated for the fitted two-factor social desirability measurement model

These large number of statistically significant modification index values for  suggested that

the items of the SD-scale share one or more other common source of variance that the current measurement model ignores. This in turn bolstered confidence in operational research hypotheses 2, 3 and 4.