Hi,
I am estimating mixed logit models with mode choice panel data (multiple trips on multiple days) and have some questions regarding calculating logsums (and changes in consumer surplus before and after an attribute is modified).
1) Am I correct in assuming that the standard output from apollo_modelOutput(model) shows only the parameters as defined in apollo_beta, and that these have to be plugged into the respective formula for the distribution chosen for the random parameters to get the mean and sd (eg. for a lognormal)?
2) After estimation, I calculate the conditional distributions. Assuming a negative lognormal distribution for cost and time attributes, I use the conditional mean estimate for the random parameters in calculating predicted observed utility for each mode and trip. Am I correct in assuming that the "apollo_conditionals" function calculates the mean and sd of the negative lognormal distribution and not just the parameters as defined in apollo_beta?
3) With regard to a negative loguniform distribution for the random parameters, how do I convert the conditional distribution output to a mean parameter value that I can use to calculate the predicted observed utility?
4) Does it make sense to calculate the VOT for each mode by dividing the conditional mean for each individual for each time parameter by the conditional mean for each individual for the cost parameter? Or should I directly estimate the model in WTP space and use the conditional parameter estimates from there?
5) Finally and somewhat unrelated, what might be a reason for getting a negative "Rho-squared vs equal shares" value? In a similar vein, what might be a reason for getting a "Rho-squared vs observed shares" equal to 1?
Thank you in advance and kind regards
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Using logsums to calculate changes in utility in different scenarios
-
stephanehess
- Site Admin
- Posts: 1142
- Joined: 24 Apr 2020, 16:29
Re: Using logsums to calculate changes in utility in different scenarios
Hi
1) correct. You should then use apollo_unconditionals (which gives you the same as the formula would)
2) correct.
3) not sure what you mean. The apollo_conditionals function already deals with the distributional transform
4) no, this would be incorrect as that would be a ratio of means. I would recommend instead working with sample level distributions (apollo_unconditionals) and then work out the mean of ratios, not ratio of means
5) that means that your model is not better than a model with constants only
Stephane
1) correct. You should then use apollo_unconditionals (which gives you the same as the formula would)
2) correct.
3) not sure what you mean. The apollo_conditionals function already deals with the distributional transform
4) no, this would be incorrect as that would be a ratio of means. I would recommend instead working with sample level distributions (apollo_unconditionals) and then work out the mean of ratios, not ratio of means
5) that means that your model is not better than a model with constants only
Stephane