ApolloChoiceModelling forum

Hello everyone,

I am running a mixed logit model from unlabeled stated choice experiment with four attributes.

I will try to explain in general a similar situation to my problem.

1) Attribute A
2) Attribute B
3) Cash back
4) Total Cost

Now i can think of three ways to estimate the parameters

a) Keeping everything same and estimating parameters for all the four attributes.

b) I make slight modifications to the data after data collection as following and estimate four parameters.

1) Attribute A
2) Attribute B
3) Cash back
4) Net cost = (Total cost - Cash back)

c) Reducing the four attributes to three after data collection and estimate 3 parameters.

1) Attribute A
2) Attribute B
3) Net cost ( Total cost - Cash back)

Now here are some outputs scenarios from different models and i want direction on which is the best way to model.

- For model a) and b) the final likelihood are almost same with similar AIC and BIC estimates but the correlation between the parameter
estimates from a) for Cash back and Total Cost is higher than the correlation between the estimates of b) between Cash back and Net cost which seems obvious (and correlation among other attributes also reduces). The parameter estimates of Attribute A and Attribute B changes in small magnitude compared to that of cash back parameter, parameter estimate for cost also changes significantly but not as much as with the magnitude of Cash back (Cash back parameter has high significant change).


Again modelling as per the c) the models worsen comparatively more slightly (with LL: may be with reduction in explaining variables) and the parameter estimates of attribute A and B changes slightly but Net Cost has a significant change.


So, my question here is as the questions were asked in format a) should i stick with design a), or as correlation between attributes (among all) reduces in model b) should i use model b) assuming the respondents had attribute processing strategy while selecting the alternatives or even model c). (my questions comes as these different results shows different tradeoff values and i am sorry if this is in fact a straight forward question).

Hi

my view is as follows:

model a) is the one that corresponds to the data as shown to the respondent (I believe) and makes no assumptions about i) whether people react differently to cash back and cost (which is quite likely to be the case) and ii) whether people can calculate (which is quite unlikely to be the case from my experience).

model b) already makes an assumption that people can calculate and also that the reduction in cost is valued the same way as in increase, although you still allow for a separate effect for cash back.

model c) assumes that people can calculate and that cash back has the direct opposite effect of cost.

It seems like your data is clearly rejecting c) and possibly also b) as you say there are small differences. I would look at model a) and test the difference between the parameters

Stephane

Thank you for the swift response Dr. Hess, what do you mean by test the difference between parameters in last part?

Hi

I mean testing whether the parameters for cash back and cost are significantly different from each other, using e.g. the delta method

Stephane