topic Re: Negative Standard Deviation using proc MDC for mixed logit mdoel in Statistical Procedures

Negative Standard Deviation using proc MDC for mixed logit mdoel

Demographer — Wed, 23 Sep 2015 18:55:45 GMT

Hello,

I've perform a mixed logit model with proc MDC. For some of the random coefficients set in the model, I get negative standard deviation. How is it possible? I cannot show you the codes and output because I work in a secure lab, but the problem seems to be the same as the one presented here: http://compgroups.net/comp.soft-sys.sas/mixed-logit-proc-mdc/643485

Thanks

Re: Negative Standard Deviation using proc MDC for mixed logit mdoel

PaigeMiller — Wed, 23 Sep 2015 19:16:45 GMT

There are a number of statistical methods that try to estimate a variance, and wind up with a negative estimate for variance on some data sets.

I have always treated this as a zero variance for all practical purposes.

Re: Negative Standard Deviation using proc MDC for mixed logit mdoel

SteveDenham — Wed, 23 Sep 2015 19:36:13 GMT

The documentation states pretty clearly that for a mixed logit model:

The estimate of spread for normally, uniformly, and lognormally distributed coefficients can be negative. The absolute value of the estimated spread can be interpreted as an estimate of standard deviation for normally distributed coefficients.

So, I would suggest taking the absolute value as the estimate of the standard deviation. The documentation goes on to reference Brownstone and Train (1999) “Forecasting New Product Penetration with Flexible Substitution Patterns.” Journal of Econometrics 89:109–129.

Steve Denham

Re: Negative Standard Deviation using proc MDC for mixed logit mdoel

owenchen — Wed, 23 Sep 2015 21:01:29 GMT

The estimate of a standard error parameter in a mixed logit model could be negative.

For a normally distributed random parameter (ε ) in a mixed logit model, the random paramter (ε ) is transformed by a standard normal random variable η variable as follows:

ε = b + sη

where b is the mean and s^2 is the variance for ε. Random variable η is N(0,1).

When estimating mean b, and spread s, since there is no restriction on the sign of s, the estimate of s could be negative.

The absolute value of s should be interpreted as the standard error estimate.

Owen Chen