I have a couple of concerns regarding the purpose of CFA. Of course, when we are conducting the confirmatory factor analysis we assume that the scales are developed and we have to confirm its reliability and validity. While on the other side we have goodness of fit indices that checks the appropriateness of a model.
My question is while checking for the appropriateness of a model, I should look the standardised factor loadings or the goodness of fit indices, because some of the factor loadings are around .5 yet the model shows a perfect goodness of fit indices.
Hi Pallavi,
the CFA model is a causal model that makes some bold claims. These claims are that there is a common underlying entity that is responsible for the items to be correlated, namely, because its their underlying cause. The reflects the fundamental principle, that common causes create artificial correlations among their descentents.
Even if this model is correct (and the model fits), you don't know what this latent entity is (may be "your" intended factor or anything else). Hence the factor loadings which connect the observed variables with the latent variable can inform you what it is or if it comes sufficiently close to the thing you want to measure. Hence, rules of thumb are nonsense. Rather YOUR thoretical imagination of the factor and its proposed relation to the items should be the basis for checking factor loadings. I tend to select/create items that are conceptually as close as possible to the supposed factor. Hence, anything below .8 would make me wonder what I have really measured.
HTH
Holger
Hi Pallavi,
CFA aims to test if the data fit the a priori hypothesized model. The hypotheses are based on the previous theory and empirical studies. Therefore, the researcher should have a specific hypothesis about the factorial structure; otherwise exploratory factor analysis is a more suitable method. To test different hypotheses the researcher may impose different constraints to the covariance matrix.
In CFA there are several tests to determine if the hypothesized model fits the data. Take into account that if a model shows a good fit does not mean in no way that your model is “the correct model” or the better. You can never prove that your model is the “true model” (for mathematical reasons), but a good fit only indicates that your model is tenable.
About factor loadings, I suggest a standardized coefficient of at least 0.7. In this way you will not have problems with the convergent validity computing the Average variance extracted and composite reliability (CR). But this is just a rule of thumb. Each model is a particular case and a researcher should evaluate models according to this rule accounting for his every single choice
If the model does not fit the data, it means that there is a discrepancy between the sample covariance matrix and the reproduced (fitted) covariance matrix. Thus, it does not make sense to check other parameters.
Best,
Gianmaria
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