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Temporal Measurement Invariance


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Temporal Measurement Invariance 
Based on the CFA results, measurement invariance of the 15-factor model over time was 
then examined by comparing the model with free loadings against the model with loadings of 
each indicator constrained to equality over time. If the constrained model does not fit worse than 
the unconstrained model, then metric invariance is empirically justified and indicates that the 
latent constructs maintain the same meanings across time (Schmitt & Kuljanin, 2008). Fit indices 
of the 15-factor model with longitudinal constraints on factor loadings across all three times are 
shown in Table 3 and were compared with those of the unconstrained model with free loadings. 
The chi-square difference test was significant between the unconstrained model and the model in 
which loadings were constrained to equality across all three times (Δχ
2
(28) = 74.90, p < .01). 
Previous research has argued against the heavy reliance on the significance of chi-square tests 
when comparing different models (Schmitt & Kuljanin, 2008); instead, CFI has been suggested 
as the best index for change in model fit and that a difference in CFI smaller than or equal to .01 
was considered as the criterion to indicate invariance (Cheung & Rensvold, 2002). Chen (2007) 
suggested pairing the criterion of a .01 difference in CFI with differences in RMSEA of .015 and 
SRMR of .03, and the null hypothesis of invariance rejected when differences in fit exceeded 
these criteria. As shown in Table 3, the parsimonious constrained model did not fit worse than 
the unconstrained model. Thus, metric invariance was suggested for the 15-factor model. Given 
this, we chose to move forward with the more parsimonious constrained model. 
Structural Models and Tests of the Hypotheses
Latent cross-lagged panel models were then built to test for longitudinal bi-directional 
relationships between JI and work behaviors. Autoregressive paths were included in order to 


JOB INSECURITY AND JOB PRESERVATION 15
control for baseline levels for each factor. Since reversed causality should be considered within 
full longitudinal panel designs (Zapf et al., 1996), causal effects and potential reversed effects 
were tested simultaneously in the bi-directional model. In line with previous research (e.g., 
Meier & Spector, 2013), to test a more parsimonious and conservative model, we constrained the 
path coefficients (autoregressive and cross-lagged coefficients) to be equal across all time points. 
Synchronous correlations were specified between constructs measured at the same time point. 
This latent cross-lagged panel model had a reasonable fit (χ
2
(1439) = 3148.15, BIC = 53910.79, 
CFI = .90, RMSEA = .057, SRMR = .072). Estimates of path coefficients are in Figure 1.
-------------------------- 
Insert Figure 1 about here 
-------------------------- 
Most of the cross-lagged paths of causal effects and reversed effects were significant, 
except for the bi-directional relationships between job performance and JI. The lagged 
relationships between JI and subsequent self-presentation ingratiatory behavior (
! = 0.09, SE = 
0.03, p < .01) and knowledge hiding (
! = 0.40, SE = 0.05, p < .01) were significant, supporting 
Hypotheses 1c and 1d. JI was positively associated with subsequent counterproductive work 
behavior (b = 0.39, SE = 0.03, p < .01), counter to our prediction in Hypothesis 1b. Regarding 
the reversed effects described in Hypothesis 2, knowledge hiding behavior was negatively 
related to subsequent JI (
! = -0.19, SE = 0.04, p < .01), while counterproductive work behavior 
was positively related to subsequent JI (
! = 0.47, SE = 0.07, p < .01). This supports Hypotheses 
2c and 2d. Although self-presentation ingratiatory behavior also predicted subsequent JI, this 
relationship was positive (
! = 0.36, SE = 0.09, p < .01), counter to Hypothesis 2b.

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