Ordinal logistic regression with likert scales

Question

I'm currently have a bit of difficulty determining how to analyze this data via logistic regression analysis.

 - Q18 = DV (satisfaction score ranging from 1-10)
 - Q10_1 = IV (Customer Service likert score from 1-5)
 - Q10_2 = IV (Sales likert score from 1-5)
 - Q10_3 = IV (Performance likert score from 1-5)
 - Q10_4 = IV (price likert score from 1-5) 
 - Q10_5 = IV (proposal likret score from 1-5)
 - Q10_6 = IV (collateral likert score from 1-5)
 - Q10_7 = IV (reporting likert score from 1-5)
 - Q10_8 = IV (manager likert score from 1-5)

My guess is that you need to use an ordered logistic regression model but i'm not sure what to factor in my formula just the DV or everything? Which equation is correct here?

nps.olr <- polr(data = cs_aggmean, formula = factor(Q18) ~ Q10_1 + Q10_2 + Q10_3 + Q10_4 + Q10_5 + Q10_6 + Q10_7 + Q10_8)

or

nps.olr <- polr(data = cs_aggmean, formula = factor(Q18) ~ factor(Q10_1) + factor(Q10_2) + factor(Q10_3) + factor(Q10_4) + factor(Q10_5) + factor(Q10_6) + factor(Q10_7) + factor(Q10_8))

After that I'm have trouble interpreting the results. For the first model the odds ratio I believe is this after I exponentiate the coefficients:

exp(nps.olr$coefficients)
Q10_1 = 1.834354
Q10_2 = 1.354964
Q10_3 = 3.259454
Q10_4 = 1.269431
Q10_5 = 1.326062
Q10_6 = 1.432196
Q10_7 = 1.424732
Q10_8 = 1.010827

I appreciate any guidance here and of course just let me know if I need to supply more information! I should mention that I'm using R for software and that I'm less interested in making a predictive model and more in making recommendations on how to increase satisfaction from these variables.

Any common latent factors here, or do you really only have one Likert rating per construct? Also, how large is your sample dataset? — Nick Stauner, Jul 29 '14 at 17:49
yeah I'm sure there are latent variables present. The sample n=1376. I haven't done PCA are you suggesting I do PCA to understand how the constructs relate to one another? — moku, Jul 29 '14 at 18:30

score 3 · Accepted Answer · edited Jul 29 '14 at 20:10

The coefficients obtained from an ordinal logistic regression model are called proportional odds ratios; you interpret them just like the coefficients from binary logistic regression models.

In your case, I assume that the data are taken from a customer survey. The exponentiated coefficient value of 1.83 for Q10_1 means that one point increase in Q10_1 is associated with an 83% (i.e., 1.83 times) increase in the odds of a customer rating the DV one point higher, with all other predictors held constant. The same interpretation goes for the other variables.

It is hard to judge which variables are important just based on the coefficient values, but just eyeballing them, Q10_3 appears to be the "most important" predictor, assuming it is also significant (i.e., its 95% confidence interval does not include 1). That is, higher performance (I suppose perceived by customers) is associated with higher satisfaction. You should test if this is really the case using the step function or the varImp function in the caret package, although I'm not sure if the latter supports polr.

Also you should check the proportional odds assumption as well. See this webpage for detailed information.

See this on the matter of stepwise selection...It's not exactly a safe recommendation. — Nick Stauner, Jul 29 '14 at 20:14
Thanks @NickStauner for the splendid post. Something like step does "allows us to not think about the problem." — Masato Nakazawa, Jul 29 '14 at 20:32
Thank you for your post its very informative! The first model I used that doesn't factor the IVs is correct right? — moku, Jul 29 '14 at 21:33

Ordinal logistic regression with likert scales

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