Defining model and likelihood function when using a (negative) lognormal distribution
Posted: 21 May 2025, 14:52
Dear Hess and Palma
I have looked through the example "Mixed logit model on Swiss route choice data, uncorrelated Lognormals in preference space" in https://apollochoicemodelling.com/examples.html, and I am wondering if I understand the following correctly:
When using a (negative) lognormal distribution, the list of utilities should be just the same as when using e.g. a normal distribution - that is a transformation should not be made, so that a new variable logtt1 (database$logtt1<-log(database$tt1)) replaces tt1 in the following (correspondingly for tt2)
List of utilities: these must use the same names as in mnl_settings, order is irrelevant
V = list()
V[["alt1"]] = b_tt * tt1 + b_tc * tc1 + b_hw * hw1 + b_ch * ch1
V[["alt2"]] = b_tt * tt2 + b_tc * tc2 + b_hw * hw2 + b_ch * ch2
The only thing that should be changed is in apollo_randCoeff - and then the starting value - when using a (negative) lognormal distribution, is that correct?
But interpretation is different, right, the resulting number -1.9962 is the log coefficient and it has to be transformed like this: exp(-1.9962)*-1 to -0,1358505 which is the acutal beta mean (although it should probably be done using the delta method), is that also correct?
Best wishes
Pea
I have looked through the example "Mixed logit model on Swiss route choice data, uncorrelated Lognormals in preference space" in https://apollochoicemodelling.com/examples.html, and I am wondering if I understand the following correctly:
When using a (negative) lognormal distribution, the list of utilities should be just the same as when using e.g. a normal distribution - that is a transformation should not be made, so that a new variable logtt1 (database$logtt1<-log(database$tt1)) replaces tt1 in the following (correspondingly for tt2)
List of utilities: these must use the same names as in mnl_settings, order is irrelevant
V = list()
V[["alt1"]] = b_tt * tt1 + b_tc * tc1 + b_hw * hw1 + b_ch * ch1
V[["alt2"]] = b_tt * tt2 + b_tc * tc2 + b_hw * hw2 + b_ch * ch2
The only thing that should be changed is in apollo_randCoeff - and then the starting value - when using a (negative) lognormal distribution, is that correct?
But interpretation is different, right, the resulting number -1.9962 is the log coefficient and it has to be transformed like this: exp(-1.9962)*-1 to -0,1358505 which is the acutal beta mean (although it should probably be done using the delta method), is that also correct?
Best wishes
Pea