ApolloChoiceModelling forum

I wonder why the estimates of sigma (standard deviation) from the Mixed Logit model are negative. An example is here.

Estimates:
Estimate s.e. t.rat.(0) Rob.s.e. Rob.t.rat.(0)
mu_log_b_tt -1.9834 0.08812 -22.507 0.11479 -17.278
sigma_log_b_tt -0.4662 0.07753 -6.013 0.07436 -6.269
mu_log_b_tc -1.0246 0.13792 -7.428 0.17908 -5.721
sigma_log_b_tc -0.9843 0.09134 -10.776 0.09383 -10.490
mu_log_b_hw -2.9339 0.08465 -34.661 0.09071 -32.345
sigma_log_b_hw 0.8163 0.11757 6.943 0.13150 6.208
mu_log_b_ch 0.6234 0.07391 8.434 0.08289 7.521
sigma_log_b_ch -0.8263 0.12050 -6.857 0.15557 -5.311

http://www.apollochoicemodelling.com/fi ... output.txt

Typically standard deviation cannot be negative. Kindly let me know if I misunderstand something.

Hi

there's nothing wrong with this - see the answer at http://apollochoicemodelling.com/faq.html

This happens if a random coefficient is coded as randCoeff[["beta"]]=mu+sigma*draws where draws is a random variate that is symmetrical around zero.

The sign of sigma is then irrelevant. You can of course report it as a positive estimate in any report

Stephane

Thank you Professor. I am not sure this is the best method to solve the problem or not but I tried to change the initial parameter setting to positive value and it gave a positive result.

There is no need to do that. As I said, it's not a "problem", if you look at how the model is actually coded. Positive or negative estimates have the same meaning if they multiply a standard Normal