# Regression analysis or Structural Equation Modelling

I have a 26 items questionnaire refined by running Common Factor Analysis. As a result, I got 4 factors (f1, f2, f3, f4). Each factor is measured by 6-7 items in the questionnaire. These four extracted factors would be my Independent Variables. I also have two Dependent Variables. What I want to know is the relationship between the 4 IVs and the 2 DVs.

If I use regression analysis, how can I calculate the extracted factor datasets based on the raw data of 6-7 items?

If I use SEM, how can I change 26 items dataset to 4 factors dataset?

I believe you have 3 questions. 1) how to calculate the extracted factor datasets based on the raw data of 6-7 items: you can save factor scores, also known as 'Regression score' in SPSS and R Check this quick SPSS tutorial

2) If you use SEM, how to change 26 items dataset to 4 factors dataset: SEM requires a theoritical support before you can build model. Lets say you come to know that from a previous study. You can however build models based on factor structure found in factor analysis. Check this detailed SEM tutorial

3) Whether to use SEM or regression analysis: Depends on what you want to measure. If you want to measure effects of factors and underlying 6-7 items on both the dependent variable simultaneously, SEM will be ideal. Regression can however measure only one dependent variable at at time. So one model for dependent 1 with 4 factors, another separate model for dependent 2 with 4 factors.

All the best!

• Thanks for you answer. I think I would go with SEM as you suggested. – Ava XU Apr 16 '15 at 13:45

First of all, especially considering that your model is not that simple, I suggest you to switch for this study from using term regression analysis to using term latent variable modeling (LVM) or, more commonly, structural equation modeling (SEM). The main reason is not the terminology, but emphasizing the fact that SEM encompasses a comprehensive analysis of both measurement model and structural model. In SEM terminology, to analyze a measurement model, you need to perform confirmatory factor analysis (CFA), after you've done EFA, while to analyze a structural model, you need to perform path analysis, also referred to as path modeling (PM) or simply SEM.

In terms of the SEM process, as I said earlier, it is quite a challenge to grasp all concepts and, especially, tie them all into one neat framework. So, I would suggest you to start with this excellent tutorial, after that - this paper (theoretical parts) to understand better SEM in general as well as two major approaches to SEM (CB-SEM and PLS-SEM) and then, perhaps, take a quick look at this paper to get a sense (don't try to understand everything right away) how the full SEM analysis (EFA $\rightarrow$ CFA $\rightarrow$ PM/SEM) should be performed and reported. Then you can return to this question to post small clarifying questions or post them as separate questions. Hope this helps.

Note. Two important aspects: 1) your full SEM model (both measurement and structural models) should be hypothesized by you, based on theory or, if theory doesn't exist for that knowledge domain, literature review as well as your assumptions and arguments; 2) the mapping between 26 items and 4 latent factors is exactly that hypothesized measurement model I was talking about.

• Also note that you don't have "26 items dataset and 4 factors dataset" - you have two models - measurement (26 to 4 mapping) ans structural (paths between those 4 latent factors) and a single data set. – Aleksandr Blekh Apr 16 '15 at 10:27
• If I understand correctly, the structural model you talked about is between my 4 IVs and 2 DVs. Right? (I do not really understand as you said "the structural (paths between those 4 latent factors) and a single data set".) Another question is about confirmatory factor analysis. Does it require new data to run? Thanks Thanks Thanks....HUG HUG HUG – Ava XU Apr 16 '15 at 13:41
• @AvaXU: In addition to hugs (or instead, to not make other people here uncomfortable), you could upvote the answer :-). You understood correctly what constitutes the structural model. Any data set is a separate from models subject. It is preferable to use different data for CFA (vs the EFA's one). Either use different data set, or, if you have a single data set only, you can randomly split it into two parts - one for EFA, another - for CFA/PM. See this for the relevant discussion. – Aleksandr Blekh Apr 16 '15 at 21:27
• @AvaXU: (cont'd) If you plan to perform your analysis in R, you might want to read this JSS paper on lavaan package, which can be used to perform both CFA and PM. – Aleksandr Blekh Apr 16 '15 at 21:28
• @Alekandr Blekh I will upvote your well explained answer once I get 15 reputation. :-) Thanks again! – Ava XU Apr 17 '15 at 2:01