Delta method for lognormal parameters
Posted: 17 Feb 2021, 14:49
Dear Stephane Hess,
I estimated a mixed logit model with lognormal random parameters.
According to the manual, I used the following expression:
exp(mu_log_beta + sigma_log_beta_inter * draws_beta_inter)
Furthermore, I used the Delta method to calculate the mean and standard deviation of the lognormal coefficient "beta".
Using the Delta method in Apollo, I also obtain the robust t-ratio for "SD for exp(N( mu_log_beta , sigma_log_beta_inter )".
Now I am struggling with the interpretation of the results. According to the estimation results, "sigma_log_beta_inter" is significantly different from zero. Therefore, I conclude that significant inter-individual heterogeneity is present. However, the t-ratio from the Delta method does not confirm this result. The SD of the lognormal "beta" is not significantly different from zero.
Now I wonder if I should use the one or the other for my statement on the significance of inter-individual heterogeneity. Is there an easy answer?
Kind regards
Andy
I estimated a mixed logit model with lognormal random parameters.
According to the manual, I used the following expression:
exp(mu_log_beta + sigma_log_beta_inter * draws_beta_inter)
Furthermore, I used the Delta method to calculate the mean and standard deviation of the lognormal coefficient "beta".
Using the Delta method in Apollo, I also obtain the robust t-ratio for "SD for exp(N( mu_log_beta , sigma_log_beta_inter )".
Now I am struggling with the interpretation of the results. According to the estimation results, "sigma_log_beta_inter" is significantly different from zero. Therefore, I conclude that significant inter-individual heterogeneity is present. However, the t-ratio from the Delta method does not confirm this result. The SD of the lognormal "beta" is not significantly different from zero.
Now I wonder if I should use the one or the other for my statement on the significance of inter-individual heterogeneity. Is there an easy answer?
Kind regards
Andy