estimating conditional medianWTP with a lognormal-cost estimates
Posted: 29 Apr 2021, 10:49
Hi I am estimating a model with lognormal cost and want to use the preference of space.
1. First I estimated the same model in preference of space and WTP space to compare the estimates. I assumed a lognormal distribution for cot: randcoeff[["log_cost" ]] =-exp(mu_log_cost + sigma_log_cost * draws_log_cost) .
I estimated the mean WTP (Battr/exp(mu_logcost+s/2)) and median MWTP (Battr/exp(mu_logcost)) in pref space. For instance, for the first attribute are 10.32 and 24.69, respectively. I also estimated the wtp space model, and the meanWTP obtained directly in the WTP space model is 27.12.
As you can see working with medians in this case is more informative as my wtp distribution is skewed.
2. Then I estimated the conditional estimates using apollo_conditionals.
I went ahead and applied the same formulas explained before with my conditional parameters for each individual but found that both the mean and the median the estimates were very different. The conditinal wtps have two digits and the unconditional wtps have one digit (i.e. medianMwtp for attr 1 is 24.69 compared to the conditional medianMWTP for attribute 1 is 2.38).
This made me think that maybe “Apollo_conditional()” formula is already making the transformation of the lognormal cost coefficient and the parameter it gives you as the output is already transformed (is mu_cost), so it does not need to be transformed anymore (as it is not mu_logcost).
I made a quick test using wtp= -coditionaBattr/condBcost to estimate the conditional wtps and I get numbers that are much more very similar to my original “unconditional estimates”. (i.e. medianMwtp for attr 1 is 24.69 and the mean of conditionalMWTP for attribute 1 is 29.85.
So to confirm this, my question is, does “Apollo_conditional()” output gives you the mu_cost estimate or the mu_logcost estimate?
3. Assuming that I am right and that I can use the conditional cost estimates directly to calculate WTPs without doing any transformation of the cost parameter (using wtp= -coditionaBattr/condBcost ). How would I go to estimate the obtain the median conditional WTP ?
Is there a way to change the Apollo_conditional() code to give you medians rather than the means of the cost parameters?
Thanks for your clarification and help!
Kind regards
Valeria Toledo
1. First I estimated the same model in preference of space and WTP space to compare the estimates. I assumed a lognormal distribution for cot: randcoeff[["log_cost" ]] =-exp(mu_log_cost + sigma_log_cost * draws_log_cost) .
I estimated the mean WTP (Battr/exp(mu_logcost+s/2)) and median MWTP (Battr/exp(mu_logcost)) in pref space. For instance, for the first attribute are 10.32 and 24.69, respectively. I also estimated the wtp space model, and the meanWTP obtained directly in the WTP space model is 27.12.
As you can see working with medians in this case is more informative as my wtp distribution is skewed.
2. Then I estimated the conditional estimates using apollo_conditionals.
I went ahead and applied the same formulas explained before with my conditional parameters for each individual but found that both the mean and the median the estimates were very different. The conditinal wtps have two digits and the unconditional wtps have one digit (i.e. medianMwtp for attr 1 is 24.69 compared to the conditional medianMWTP for attribute 1 is 2.38).
This made me think that maybe “Apollo_conditional()” formula is already making the transformation of the lognormal cost coefficient and the parameter it gives you as the output is already transformed (is mu_cost), so it does not need to be transformed anymore (as it is not mu_logcost).
I made a quick test using wtp= -coditionaBattr/condBcost to estimate the conditional wtps and I get numbers that are much more very similar to my original “unconditional estimates”. (i.e. medianMwtp for attr 1 is 24.69 and the mean of conditionalMWTP for attribute 1 is 29.85.
So to confirm this, my question is, does “Apollo_conditional()” output gives you the mu_cost estimate or the mu_logcost estimate?
3. Assuming that I am right and that I can use the conditional cost estimates directly to calculate WTPs without doing any transformation of the cost parameter (using wtp= -coditionaBattr/condBcost ). How would I go to estimate the obtain the median conditional WTP ?
Is there a way to change the Apollo_conditional() code to give you medians rather than the means of the cost parameters?
Thanks for your clarification and help!
Kind regards
Valeria Toledo