The data were collected from 512 respondents on their self-reports of job engagement, which is defined as the extent to which an employee feels passionate about their jobs and put discretionary efforts into their work. The measure consists of 18 items with three theoretical factors (physical engagement, emotional engagement, and cognitive engagement). Although job engagement is theorized to include three different factors, many psychologists also argue that there is only one factor underlying all the items.

Model 1. The Single Factor Model

Figure 1 describes the notation for the CFA model for a single factor model. A Confirmatory Factor Analysis was conducted to verify the 1-latent factor structure using full-information data.

Figure 1. Confirmatory Factor Analysis. Model 1 Notation Single Factor Model

Table 1, presents the standardized loading factors \(\lambda_{i}\) that varies from 0.615 (JE6_p6) to 0.864 (JE18_c6), while Figure 2 shows the estimation of loading factors and variances for each item in the single factor.

Table 1. Standardized Loading Factor Model 1
95% CI
Item Loading SE LL UL
JE1_p1 0.770 0.019 0.733 0.807
JE2_p2 0.776 0.018 0.740 0.812
JE3_p3 0.763 0.019 0.725 0.801
JE4_p4 0.733 0.021 0.692 0.775
JE5_p5 0.724 0.022 0.681 0.767
JE6_p6 0.615 0.028 0.560 0.671
JE7_e1 0.745 0.021 0.705 0.786
JE8_e2 0.684 0.024 0.636 0.732
JE9_e3 0.633 0.027 0.580 0.687
JE10_e4 0.635 0.027 0.581 0.688
JE11_e5 0.663 0.026 0.613 0.713
JE12_e6 0.693 0.024 0.647 0.740
JE13_c1 0.815 0.016 0.784 0.846
JE14_c2 0.861 0.012 0.837 0.885
JE15_c3 0.875 0.011 0.853 0.897
JE16_c4 0.777 0.018 0.741 0.813
JE17_c5 0.812 0.016 0.781 0.843
JE18_c6 0.864 0.012 0.840 0.888

Model 2. Multidimensional Correlate Factor

Figure 3 presents the notation the 3-latent factor structure model theorized for the self-reports of job engagement construct. Specifically, the single factor JE1 in previous model is replaced for with LV representing physical engagement, emotional engagement, and cognitive engagement. Thus, three measurement models are included in this SEM, where \(\lambda\) coefficients link the observed variables with latent variables, \(\epsilon\) represents the measurement error of each observed exogenous variables, and \(\Phi\) the correlation between latent variables. Additionally, \(\theta_{i}\) indicates the residual variance for each latent variables, which will be a free parameter in estimation (equal to 1) for allowing model identification.

Figure 3. Confirmatory Factor Analysis. Model 2 Notation Three-Factor Structure Model

Table 2, presents the standardized loading factors \(\lambda_{i}\) that varies from 0.656 (JE6_p6) to 0.841 (JE2_p2) in the psychical engagement factor, from 0.775 (JE8_e2) to 0.922 (JE12_e6) in emotional engagement, and 0.783 (JE16_c4) to 0.932 (JE15_c3) in cognitive engagement.

Table 2. Standardized Loading Factor Model 2
95% CI
Item Loading SE LL UL
Factor 1. Physical Engagement
JE1_p1 0.788 0.019 0.751 0.824
JE2_p2 0.841 0.015 0.811 0.871
JE3_p3 0.806 0.018 0.771 0.840
JE4_p4 0.818 0.017 0.785 0.851
JE5_p5 0.804 0.018 0.770 0.839
JE6_p6 0.656 0.027 0.603 0.709
Factor 2. Emotional Engagement
JE7_e1 0.871 0.012 0.847 0.895
JE8_e2 0.775 0.019 0.738 0.812
JE9_e3 0.825 0.015 0.794 0.855
JE10_e4 0.816 0.016 0.785 0.848
JE11_e5 0.899 0.010 0.880 0.919
JE12_e6 0.922 0.008 0.905 0.938
Factor 3. Cognitive Engagement
JE13_c1 0.836 0.014 0.808 0.864
JE14_c2 0.924 0.008 0.908 0.939
JE15_c3 0.932 0.007 0.918 0.946
JE16_c4 0.783 0.018 0.748 0.819
JE17_c5 0.840 0.014 0.812 0.867
JE18_c6 0.887 0.011 0.866 0.908

Furthermore, Figure 4 presents the pattern of coefficients, error variances, and correlations among factors. The correlation between scales in Model 2 ranged from 0.63 < r < 0.85.

The goodness of model fit for measurement models conducted above was evaluated using overall and individual fit indices: (1) overall fit assessed using the \(\chi^{2}\) statistic that evaluates the magnitude of discrepancy between the sample and the model-estimated, largest values of \(\chi^{2}\) indicate a bad fit; (2) the Comparative Fit Index (CFI), Tucker-Lewis index (TLI), and Normed Fit Index (NFI) with values >.90 indicating an acceptable fit and values >.95 indicating a good fit; (3) the Standardized Root Mean Square Residual (SRMR) <.08 being indicative of good fit; and (4) the Root Mean Square Error of Approximation (RMSEA) with values <.08 being indicative of reasonable fit, values <.05 indicating a good fit and >.10 unacceptable.

Table 3. Comparison Model Fit Statistics
RMSEA 90% CI
Model Model.Specif DVs Chisq df p-value CFI TLI NFI SRMR RMSEA LL UL
Model 1 1 Factor 36 2679.429 135 0 0.712 0.674 0.702 0.102 0.192 0.186 0.198
Model 2 3 Factors 39 849.307 132 0 0.919 0.906 0.906 0.049 0.103 0.096 0.110

Model 1 included all 18 items distributed in a unique factor. Based on comparative indices (CFI = .712, TLI = .674, and NFI = .702) the model showed an inadequate fit, additionally the absolute indices (SRMR = .102 and RMSEA = .192) take values above the cut-off criteria for reasonable fit (<.08). Model 2 includes the 18 items distributed in the original 3-factor model (physical, emotional, and cognitive engagement). According to comparative indices (CFI = .919, TLI = .906, and NFI = .906) the model with 3-latent factor showed an acceptable fit, also the absolute indices (SRMR = 0.049) indicative of reasonable fit. However, the RMSEA and their 90% confidence interval exceed the cut-off criterion (RMSEA < .08). In sum, the original theorized model with 3-factors presents a better fit. Furthermore, \(\chi^{2}\) statistics is lower, suggesting that the magnitude of discrepancy between the sample and the model-estimated variance/covariance matrices is lower in the multidimensional model than in the single-factor model.