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MAE in choice simulation, Logit or LCA?


I have determined the overall MAE of my LCA-4group model. I have used a Count analaysis to get the observed shares and the LCA model with the Randomized First Choice simulator to get the predicted shares. This leads to an overal MAE of -1.15 for the LCA-4group model.

When I do the same for Logit analysis (Count for observed shares and Randomized First Choice simulator for predicted shares), I get a much lower MAE, namely -0.02.

(This might be due to my small sample?)

2 Questions:

1. The logit analysis has 1 attribute less than the LCA, since it is not significant in the logit, however it is sigificant for some segments in the LCA. Can I still compare the MAE of the two models, or do I need to use the Logit model including the insignificant attribute in order to compare the MAE of the two models?

2. In both cases, the MAE of the Logit model is lower than that of the LCA model. Does this mean that I should use the Logit model in the choice simulator? I really want the choice shares per segment, is there a way I can motivate my choice for still using the LCA model?

Thank you in advance!

asked Nov 23, 2018 by Floor (310 points)

1 Answer

+1 vote
Best answer
It seems strange to me that your MAE is a negative number.  MAE (Mean Absolute Error) values are always positive.  For example, let's imagine that the actual shares of choice (from counts) for three product concepts in a holdout task are A=30%, B=40%, C=30%.  And, let's say your predicted choice shares (using RFC) are A=40%, B=30%, C=30%.  Your MAE would be: [|0.40-0.30|+|0.30-0.40|+|0.30-0.30|}/3, or [0.10+0.10+0.00}/3, or 0.20/3, or 0.0667.

For MAE calculations to be very stable, you should have  about four or five holdout choice tasks or more.  So, although the illustration I showed above involved just one choice task, these calculations should be made across the four or five choice tasks and the absolute errors of prediction are averaged across the multiple choice tasks.

If you only have three or fewer holdout choice tasks to compute your MAE, then there is probably not enough data to tell if one model does a better job than another model of predicting the holdouts.

Next, it is strange to think about dropping any attributes from a conjoint model.  Generally, we include all attributes in the models, because we include an attribute in the experiment because of prior hypothesis that it is meaningful at least to some groups of respondents.  And, even if a 1-group solution or even a 4-group solution makes it look like an attribute didn't matter to anybody, it may just be due to an aggregation fallacy (see example directly below).

Aggregate logit can sometimes make it look like an attribute is not significant if different respondents or groups of respondents disagree about the order of preference for an attribute (like brand or color, for example).  Let's say there are two colors in an attribute: red & green.  Half of the respondents think that red is preferred and the other half thinks that green is preferred.  In aggregate (the pooled logit solution), the two utilities may be very close to zero and not be significantly different from zero (their T-ratios do not cross the critical value of 1.96).

Next, most Sawtooth Software users employ HB estimation of utilities for their final model.  It generally has proven more accurate for use in the market simulator than aggregate logit.  Often, Latent Class analysis can perform almost at the level  of HB for predicting aggregate shares of preference, but HB still tends to provide more accuracy and flexibility during analysis, because utilities are estimated at the individual level.
answered Nov 23, 2018 by Bryan Orme Platinum Sawtooth Software, Inc. (190,165 points)
selected Nov 23, 2018 by Floor