Mixed Logit - elasticities

[katya2727]

Hello Prof. Hess and Prof. Palma,

I have a question regarding elasticities for the mixed logit model. Is it possible to use the part of the code below from MNL_SP_covariates.r to find elasticities for the mixed logit model? The formulas of relative probabilities are quite different in MNL and mixed logit as mixed logit does not follow the IIA assumption, so I was wondering we need to somehow account for that when calculating elasticities.

Thank you for all your work!

Best,
Katya

# ----------------------------------------------------------------- #
#---- MODEL PREDICTIONS AND ELASTICITY CALCULATIONS ----
# ----------------------------------------------------------------- #

### Use the estimated model to make predictions
predictions_base = apollo_prediction(model, apollo_probabilities, apollo_inputs, prediction_settings=list(runs=30))

### Now imagine the cost for rail increases by 1%
database$cost_rail = 1.01*database$cost_rail

### Rerun predictions with the new data
apollo_inputs = apollo_validateInputs()
predictions_new = apollo_prediction(model, apollo_probabilities, apollo_inputs)

### Return to original data
database$cost_rail = 1/1.01*database$cost_rail
apollo_inputs = apollo_validateInputs()

### work with predictions at estimates
predictions_base=predictions_base[["at_estimates"]]

### Compute change in probabilities
change=(predictions_new-predictions_base)/predictions_base

### Not interested in chosen alternative now, so drop last column
change=change[,-ncol(change)]

### First two columns (change in ID and task) also not needed
change=change[,-c(1,2)]

### Look at first individual
change[database$ID==1,]

### And person 9, who has all 4 modes available
change[database$ID==9,]

### Summary of changes (possible presence of NAs for unavailable alternatives)
summary(change)

### Look at mean changes for subsets of the data, ignoring NAs
colMeans(change,na.rm=TRUE)
colMeans(subset(change,database$business==1),na.rm=TRUE)
colMeans(subset(change,database$business==0),na.rm=TRUE)
colMeans(subset(change,(database$income<quantile(database$income,0.25))),na.rm=TRUE)
colMeans(subset(change,(database$income>=quantile(database$income,0.25))|(database$income<=quantile(database$income,0.75))),na.rm=TRUE)
colMeans(subset(change,(database$income>quantile(database$income,0.75))),na.rm=TRUE)

### Compute own elasticity for rail:
log(sum(predictions_new[,6])/sum(predictions_base[,6]))/log(1.01)

### Compute cross-elasticities for other modes
log(sum(predictions_new[,3])/sum(predictions_base[,3]))/log(1.01)
log(sum(predictions_new[,4])/sum(predictions_base[,4]))/log(1.01)
log(sum(predictions_new[,5])/sum(predictions_base[,5]))/log(1.01)

[stephanehess]

Hi

yes, they can be used. Note that they are likely not that different from MNL given that in prediction, you average across draws too to get demand forecasts

Stephane

[katya2727]

Hello Prof. Hess,

Thank you for the reply! Is there any better way to find those elasticities for mixed logit?

Thanks again,
Katya

[stephanehess]

Hi

those are the correct sample distribution elasticities, so there is no "better" way. You could investigate the use of posterior distributions, see the discussions in Train's hanbook for example

Best wishes

Stephane

[katya2727]

Hello Prof. Hess,

Got it! Thank you so much for the response.

Best,
Katya