# Attribute Importances for Latent Classes

Hi,

I am running a CBC model. After running HB I ran latent class analysis.

I noticed when I compared the reported attribute importance from an LC group membership output file (reported in the third block below the ZC average utilities) to an the arithmetic average I calculated manually from the respondent importances from the hb output file that I got different figures.

For example, if the LC membership file reported Attribute A's importance was 6.56 for segment 3, in my manual calculation for the respondents in segment 3 I'm getting 11.83 for Attribute A.

How can this discrepancy happen? How are the importance scores in the LC group membership file calculated?

This happens easily because the models are different and lead to different utilities at a different degree of aggregation.

Latent Class involves assuming a finite number of classes that share the same utilities.  HB involves fitting individual-level utilities.

As an extreme example, imagine we have two respondents with HB-estimated preferences for brands and prices as follows:

Respondent #1:

Brand A:  -50
Brand B: +50

Price 1:  +50
Price 2:  -50

Importance Attribute 1 = 50%
Importance Attribute 2 = 50%

Respondent #2:

Brand A:  +50
Brand B: -50

Price 1:  +50
Price 2:  -50

Importance Attribute 1 = 50%
Importance Attribute 2 = 50%

Thus, you can see that across these two respondents, the average importance scores are:

Importance Attribute 1 = 50%
Importance Attribute 2 = 50%

====================================

Next, let's imagine we were doing some sort of aggregate utility model, such as aggregate logit, or latent class with few classes...

Average utility estimation, for an aggregate model involving these same two respondent (n=2):

Brand A:  0
Brand B:  0

Price 1:  +50
Price 2:  -50

Importance Attribute 1 =  0%
Importance Attribute 2 = 100%

Thus, you can see that if we do individual-level estimation (say, from HB), we can achieve very different average importance scores (when importances are estimated at the individual level, and then averaged across respondents) than a model that involves aggregation.  This especially occurs when there are differences in opinion about the order or preference with attributes.
answered Aug 25 by Platinum (191,015 points)