Convert standard deviations to Odds-Ratios in Mixed Logit

[Michael Frith]

Hi, apologies if I dont explain myself fully. I have estimated a model using mixlogit and it returns the results as coefficients (e.g. -0.20) whereas in my area odds ratios are typically used (and i find them easier to interpret too). When I ran models with conditional logit I would add OR to report the results as odds-ratios but I cannot do this with mixlogit. Does anyone know how to convert the coefficients, S.E., S.D.? (In conditional logit, exp(b) would convert the coefficient but it wouldnt be case for converting S.D.)

Many thanks

[Maarten Buis]

There are several things you can do to make your question easier to answer: mixlogit is a user written program, so you need to tell us where you got it from. In this case there are at least three locations (2 at SJ and 1 at SSC) containing different versions. We need to make sure we are talking about the same thing. Also posting under our real name has a long tradition on this list. We believe that it has contributed to a friendly and professional atmosphere on this list. It would be nice if you did the same by changing your login name to your real name. You can do so by using the "contact us" button at the bottom of every page.

To answer your question: Exponentiating the coefficients will result in odds ratios. The rule for transforming the standard errors is discussed in:

M.L. Buis (2014) "Stata tip 116: Where did my p-values go? (part 3)", The Stata Journal, 14(1) pp. 218-220.

[Michael Frith]

Apologies Maarten. My name should be changed soon. I installed mixlogit from within Stata13 (SJ7-4 st0133_1).

[Maarten Buis]

Instead of computing the standard errors manually, you can type after estimating your mixlogit model:

est table, b se eform

[Michael Frith]

Thank you Maarten for both. I had tried 'Postestimation/Manage Estimation Results/Table of Estimation Results' - same as:

est table

and my concern (although it was only for S.D.) was that I may be forcing Stata to simply exponeniate all values. Perhaps my interpretation may be incorrect, for example, I have run mixlogit with 9 random normally distributed predictor variables. The mean coefficient as shown for one variable (call it variable A) is: -0.81, SD = 0.86. This is all new to me so I assumed the mean +- S.D. gives a rough distribution of the majority of individuals' preferences (i.e. the majority prefer A to be negative) (I do have the formula to calculate it as used in several Train papers etc.). When I run

est table, b se eform

the OR = 0.44 and S.D. = 2.37, do I interpret this S.D. differently to 'mean +- S.D.'? Thank you, I really appreciate your help.

[Maarten Buis]

The exponentiated coefficients in the mean equation are the odds ratios for an "average" individual. In that sense you would interpret the odds ratio as you would in a normal regression. Except that the odds ratio for the random coefficients differ across individuals/groups/.... The extend of these differences is measured by the SD equation. Also, these are estimates, so the coefficients are uncertain, which is measured by the standard deviation. I don't understand whether you are looking for the uncertainty or the variability of the coefficients.

[Michael Frith]

Thank you again. From my understanding, standard deviation measures the variability of the coefficients (e.g. some prefer high A, others low A) and standard error measures the uncertainty of the coefficients. Although I understand the importance of S.E. (uncertainty in estimates), I'm keen at the moment on S.D. (the variability)

[Michael Frith]

Hi Maarten, I apologise I may have misunderstood you earlier (maths nor economics is not really my field sorry). I think I have correctly estimated the S.D. of the OR using the Delta Method (by converting to S.D. to variance before the Delta Method and converting back to S.D. afterwards). If this does not make sense I apologise (it does appear to return the appropriate figures at least - which would be worrying). Thank you for all your help, let me know if this does not make sense