In exploring certain independent variables and their composite or relative relationship to the dependent variables, it makes sense to use multiple regression. Now if the researcher has a prior Knowledge based on theory or evidence, and wishes to explore some latent variables using the observed variables, is it statistically right to perform a multiple regression and a CFA on the study?
Yes it is okay. Confirmatory factor analysis identifies different factors of the dependent variation,while linear regression tells us the impact of such factors on the dependent variable. Hetroscedasticity test can be applied before multiple regression analysis. Glejser test can also help to find the impact of variables.
Dear Owan,
In multiple regression you are testing the combine effects of your IVs on DV. However, CFA is used to confirm the underlining structure of items used in your study. In the context of SEM, CFA is use to test the construct validity of measurement model(s).
To test the hypothesized relationships you have to test structural model.
Note: If you know the underlying structure that makes each variable scales go for CFA otherwise, to explore such you have to do EFA first.
See the link for detail:
Article An Easy Approach to Exploratory Factor Analysis: Marketing P...
Hi Valentine,
if you are already in a latent variable framework, why leaving it and going for manifest variable analysis? When you apply regression analysis, you need to calculate a composite of the indicators. Even if the CFA showed a clean fit and supported the measurement structure and validity, composites have again incorporated measurement error (in contrast to the latent variable). This biases the regression effects. Two solutions would be
a) stay in the latent variable framework and conduct the regression analysis with latent variables in a SEM (or better specify a bit more complex structure with some restrictions (i.e., zero effects) and testable implications (see Thoemmes et al., 2018), OR
b) use composites but correct for attenuation (with the composite reliability measure gained from the CFA, see Fornell & Larcker, 1981). Likewise you could switch to either factor score regression (Devlieger & Rosseel, 2017) or create a single-indicator latent variable with fixed measurement errror (and using either the reliability or a theoretically-based guess (which has the advantage to incorporate some non-random errors beyond mere reliability) (see Savalei, in press).
HTH
Holger
Devlieger, I., & Rosseel, Y. (2017). Factor score path analysis: An alternative for SEM. Methodology, 13, 31-38. doi:10.1027/1614-2241/a000130
Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18, 39-50.
Thoemmes, F., Rosseel, Y., & Textor, J. (2018). Local fit evaluation of structural equation models using graphical criteria. Psychological Methods, 23(1), 27-41. doi:10.1037/met0000147
Savalei, V. (in press). A comparison of several approaches for controlling measurement error in small samples. Psychological Methods. doi:10.1037/met0000181
Confirmatory factor analysis will help in dealing with the issues related to validity of measurement scales. Whereas, Multiple regression analysis helps in assessing relative impact of predictors on response variable. So we can have both analyses in one study.
Experts in statistics are talking, i am just reading comments
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