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I have about 5,000 responses to a survey in which users were asked how strongly they agreed with a statement on a 5-point Likert scale. This response is my dependent variable - I want to find out what influences this answer.

In the same questionnaire, the users gave a lot of other data, including age, employment, gender, location, and answers to other Likert questions.

From all of these, I want to find the factors that are most strongly correlated with their answers to the dependent variable - so that I can say "The most important predictive factor for agreeing with the statement was X. Other important predictive factors were Y and Z."

What approach should I use? I've been reading around and it looks like the two best approaches might be:

  1. individual chi-squared tests for each column, then compare the probability of the chi-squared scores and see which is most significant
  2. a multiple linear regression model

I'm not completely clear on the second approach: specifically, whether I can use to pull out the importance of individual factors, and whether it's useful for analytical work rather than predictive work. I don't want to dive in without having a good understanding of the best approach.

Suggestions much appreciated.

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    $\begingroup$ Can you say something about what you mean by "analytical" versus "predictive" work? $\endgroup$ – EdM Sep 22 '14 at 15:45
  • $\begingroup$ Sorry - I'll try to be more clear. I'm looking for a way to say "the most important factors in the answers to question X were questions E and J, and demographic factors Y and Z". I don't want to build a model that given answers A, B, C, D... P and demographic factors Q, R... Y, Z can create a complicated (and hard to understand) equation accurately predict the answer to question X. Prediction isn't my use case, and I want an answer that is actionable - focus on E and J! Does that make things clearer? I hope so, thank you very much for looking at my question. $\endgroup$ – Richard Sep 22 '14 at 18:13
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Multiple regression provides opportunities for looking not only at how individual variables are related to your response of interest (from their regression coefficients), but also at how interactions among them may influence that response. For example: does variable E have a different relation to the response in demographic Y1 than in demographic Y2? For continuous variables like age and income, including them as continuous variables (possibly scaled) in regressions is generally preferable to breaking them down into arbitrary categories. Formulating the problem that way also makes it straightforward to examine correlations among the individual variables, which can be important for interpreting your present results and for design of future studies.

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  • $\begingroup$ (+1) Note the response is probably better treated as an ordinal categorical variable - a proportional odds multiple regression model might well suit. $\endgroup$ – Scortchi - Reinstate Monica Sep 23 '14 at 9:16
  • $\begingroup$ OK great - thank you. And just to be clear - I don't need to create a training and test set, because my goal isn't prediction. I can create the model across the whole dataset. Correct? $\endgroup$ – Richard Sep 23 '14 at 10:01
  • $\begingroup$ Depends on how much you care about generalization to the population of interest and the model's robustness. If you are, say, just trying to identify action items you can take (e.g., question E is "waiting time for checkout" in a store, and you can hire more cashiers), and your outcome is "overall customer satisfaction", then the whole-dataset model may point to potentially useful interventions. But no model will prove causality, and without model validation it may be unreliable to extend your model beyond your original dataset. $\endgroup$ – EdM Sep 23 '14 at 15:01

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