# Hypothesis testing of latent factors - CFA or something else?

Summary: I constructed a conceptual model with few factors, affecting on 1 DV. All factors and effects are based on theory; however, most of them are vaguely defined and they seem hard to be quantified. In my try to quantify the factors, I am using observed variables or measures. Some factors are measured by only 1 observed var., whereas others are measured by 2 or 3 variables.

Questions When trying to prove/reject my hypotheses how should I proceed with the factors? E.g. my hypotheses are: * Factor 1 (measured by var.1 and var.2) positively affects DV. * Factor 2 (measured by var.3) positively affects DV.

Should I go for Confirmatory Factor Analysis (SEM) and then use the factor scores to test my hypotheses?

If yes, is it correct to include in the SEM factors constructed by only 1 observed variables?

Thanks for the support

• If by "measures" you mean the obseved variables, then there's a few comments. 1) By definition, a common factor should load (=drive) more than 1 variable. 2) Usually we even assume that it should load more than 2 variables (we then drop from exploratory FA variables showing high partial correlation). 3) It makes difference whether you use in confirmatory FA original loading matrix 'as is' or the pruned matrix with loadings 1 (loads) or 0 (doesn't load). – ttnphns Aug 9 '13 at 10:36
• @ttnphns 1) If I understood correctly I cannot have latent var.with only 1 observed variable. So whenever using CFA I should include only latent variables having more observed variables. Not completely sure about 2) and 3) can you try to further explain. – Delyan Peyankov Aug 9 '13 at 11:12

Your hypotheses would be tested using the p values and regression weights between your variables (latent or not). Below is an example of an SEM including latent and observed variables. The observed variables are in rectangles, the latent variable is the circle (estimated by the 4 observed variables to the right). 