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Clio Berry posted on Wednesday, August 01, 2012  10:15 am



Hello, I just wanted to check if I am understanding measurement invariance correctly as I haven't been able to find the answer to my question. I have a 3 factor model with 4 predictors/covariates. I have tested the model with 2 groups (older vs. younger) for invariance. The chisquare change is not significant when comparing the 4 stages of invariance (equal factor means, equal loadings, equal intercepts, equal residuals). This would suggest full invariance. However I have just noticed that when I check the configural invariance of the measurement model (the CFA part only) in the two groups, the loading/coefficient of 1 indicator for 1 factor is not significant in one group. Does this mean that there is partial invariance and I can still therefore, compare means, compare models etc.? The model is: (MEASUREMENT MODEL) Act by sim_sc sim_ci lei_m f2f spo_resp; Belong by sim_p sim_b occ_hrs; Rel by srs_no srs_rec; sim_ci wit sim_b; (STRUCTURAL MODEL) belong rel on act; Act belong rel on das_dp das_na soc_hope occ_hope; *It is the occ_hrs indicator which becomes nonsignificant for the Belong factor in one group. Thank you, Clio. 


The significance of a factor loading is not related to measurement invariance. It tests whether the factor loading is different from zero. Even if it is different in one group and not in the other, the test of equality may still be fulfilled. This is what tests measurement invariance. 

Clio Berry posted on Wednesday, August 01, 2012  5:15 pm



Thank you for your fast response Linda. I'm afraid I still don't understand completely. If the factor loading is nonsignificant then doesn't this imply configural/pattern noninvariance between groups (i.e. as this indicator loading could be fixed to zero in one group but not in the other)? And if configural invariance cannot be established, does this then not mean that one is not supposed to proceed with testing measurement invariance? Apologies if this is unclear... 

Clio Berry posted on Wednesday, August 01, 2012  5:57 pm



In addition to the above: the size of the factor loading coefficient is also quite different across groups. For group 0, the coefficient is 2.5 and significant and for group 1, the coefficient is .88 and nonsignificant. 


I don't think significance is an issue here. When testing for measurement invariance, the issue is the equality of the factor loadings across groups. Some loadings may be significant and some may not be. The lack of significance may be due to a lack of power to detect that the value is significantly different from zero. 

Clio Berry posted on Wednesday, August 08, 2012  7:52 am



Thanks Linda. 

Clio Berry posted on Thursday, August 09, 2012  7:27 am



Apologies, another question regarding this issue in some cases, presumably the nonsignificance may reflect the size of the coefficient/loading, e.g. .664 in one group, .164 (ns) in another group. Is this a problem for configural invariance? Many thanks, Clio. 


Questions not specific to Mplus are best posted on a general discussion forum like SEMNET. 

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