# Using Factor Analysis as a Data-Reduction Tool

I’m working with a really messy dataset. My dependent variables consist of Likert-scale responses that are judging a person’s speech (how annoying it sounds, how intelligent it sounds, etc). My independent variables mostly consist of the demographic/social data of the participants.

It has been suggested that a lot of the Likert-scale options that the participants responded to might be measuring a smaller set of latent variables. It’s been suggested that I use factor analysis to find these latent variables and thus reduce the number of dependent variables. My question is how to do this. I’ve been coached through the basics of FA using R, and I have the factor loadings for the different items. But I don’t know where to go from here.

For instance, my analysis seems to indicate that annoying, rude, being a know-it-all, and being unfriendly all load onto the same factor. This seems to make sense, thematically. But if I want to regress my (many) independent variables into this, how do I go about reducing the data set? Is there a way to combine those four dependent variables into a single dependent variable? Is there another way of reducing the dataset?

Am I totally off base here? I don’t want to continue with my analysis if this is a totally illogical way to go about handling this data. Apologies for how “layman" this is. My experience with stats is limited, but I’m trying to get my hands dirty.

• If you have a bunch of Likert-scale responses which more or less give the same info, it's probably best to do a sequential test to see which (either 1 or more) are significant. Eg. suppose you have variables x1, x2, ... ,xN. You can test if xN is significant given x1, x2...,x(N-1) are in the model. If it's not (so a high p-value in R) remove it from the model. Do the same for x(N-1). Repeat this until you test a variable against a model with all of the remainders, and it still comes up significant. I think you should be very careful if you go about combining them into a single variable though. – Patty Sep 21 '16 at 21:18
• Welcome to our site! I have added a couple of tags that seem to be relevant for you. I have also snipped out the bit about this being a layman question and moved it to the bottom - in search results it's only the first few sentences that show up, so to help future readers I thought it would be better for that to be about the substance of the question itself. Feel free to revert my edit if you prefer. – Silverfish Sep 21 '16 at 22:27
• (Surprisingly, I can only see one other thread which has both the [dimensionality-reduction] and [likert] tags, and that one currently doesn't have an answer. I had expected this to be a more common theme!) – Silverfish Sep 21 '16 at 22:30
• all load onto the same factor... But if I want to regress my (many) independent variables into this, how do I go about reducing the data set? You probably want to compute factor scores variable for that factor (which replaces the many variables) and use it as the DV in your regression. – ttnphns Sep 22 '16 at 6:55
• There is also a question why do you think you need FA at all? A regression can have multiple DVs and it can reduce dimensionality of the DVs. Such regression (supervised) dim. red. is called canonical correlation analysis (CCA). But because some of your IVs might be categorical you might want perhaps to consider Categorical CCA (see). – ttnphns Sep 22 '16 at 7:00