Model fit may be improved by the addition of pathways that come from modification indices. I adjusted a model (CFI = .95) and a professor who saw the structural model by accident told me: why are there so many measurement errors correlated? Alas, we couldn't talk afterward but she puzzled me.
Dear Jaime,
The modification Indices represent an estimation of how much the overall model will decrease if the specific parameter is freely estimated. Therefore, a model that shows a good fit should produce small modification indices, otherwise the model is miss-specified. However, take into account that the MI are sensitive to large sample sizes.
A golden rule in model respecification (not anymore confirmatory but exploratory approach) is that a researcher should freely (previous fixed or constrained) estimate a parameter suggested by MI only if there is a theoretical substantive basis for doing it. Parameters should not be freed with the sole intent of improving model fit. Every respecification of the model should be justified on the basis of theory.
If you have many measurement errors correlated it basically means that there is an external latent factor (not considered in the model) that affects the observed variables. So, the model is miss-specified.
Several scholars have highlighted the problems that occur when models are specified exclusively on the basis of modification indices (see MacCallum 1986). Estimating many correlations between residual variances basically means that you are adjusting your model according to the numerous idiosyncratic characteristics of your sample. A model is useful when it can be generalized. In addition that can cause other problems such as biasing other parameters in the model (e.g. factor loadings).
Best,
Gianmaria
Dear Gianmaria,
Your answer was also useful to me. Thank you.
I understand your point, but if there is only one factor to estimate (an unidimensional measure)? In this case, it still is a problem?
Best whishes
Hi Pedro
As long as you can theoretically justify (or also considering previous researches) the correlations, you are allowed to add those parameters.
But if you specify the correlations between residual variances just to improve the model fit, this is not a good way to proceed in the specification of a model.
A feasible way could be to specify the model on one sample, if the model does not fit add the parameters responsible for the miss-specification (now you are changing approach from confirmatory to exploratory), and then test this respecified model on another independent sample or samples from the same population in order to cross-validate the model (obviously this imply a large sample).
You can see my paper “Validation of a social cohesion theoretical framework: a multiple group SEM strategy”.
Best,
Gianmaria
Thank you Gianmaria a Pedro. Your interchange helped me a lot. Best regards.
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Statistics
- Statistical Software
- SPSS