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I have a dataset derived from a questionnaire filled out by high school students, with 7 variables (one continuous and six binary). Three variables(binary) are related to "interest in physics".

Is it possible, after having derived the new variable "Interest in physics" from the three original variables, to then perform a multivariate logistic regression with the new variable "interest in physics" as the response variable?

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If I understand correctly, you are going to use factor analysis on the 3 binary variables that are related to "interest in physics" and then create a binary variable from the factor scores. I don't think that will work. From the factor analysis you will get up to 3 sets of factor loadings for each variable, for which I don't see any way to derive a binary variable, and if you did find a way you would be discarding a lot of information by dichotomising.

An alternative approach would be to use a latent variable method, with one latent variable measured by the 3 related binary variables and then have the other variables predict the latent variable, this would be an example of a "Multiple Indicator, Multiple Cause" (MIMIC) model and would look like this:

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where IntPhys is the latent variable for interest in physics, X1-X3 are the variables that measure interest in physics, and Z1-Z4 are the other variables that predict interest in physics. From this model you could investigate, for example, the strength of the regressions of IntPhys on Z1-Z4, whether these differ between groups (male and female for example), and whether the latent variable scores are different between groups.

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  • $\begingroup$ Thanks; I am thinking of going for 3 models also, one for each response variable for "interest in physics". In the case of three models, I have another question: using the same 7 variables in all three models, would it be ok to use two of the variables as explanatory variables in one model, and then as response variables in the next..? $\endgroup$
    – schvost
    Jun 19 '16 at 20:13
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    $\begingroup$ @schvost I am not suggesting 3 models - I am suggesting 1 model with all your variables. If you want to run 3 separate regressions with each of the 3 variables as the response, you can do that, but I don't think it makes a lot of sense as it won't answer your research question, which is, presumably, something like how do the other 4 variables predict interest in physics. The 3 separate model setup will only predict which variables predict one specific (0/1 variable) component in "interest in physics". As that wasn't mentioned in your question it would be better to write a new one for that. $\endgroup$ Jun 19 '16 at 21:15

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