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How can I tell how much influence my covariate had on the estimation?

I wonder how I can tell how much influence a single covariate had on the estimation? Is there a separate utility estimate for the covariate? If not, is there any way to get an "unbiased" estimate for the other variables in a HB estimation?

Thanks in advance,
asked Apr 5, 2017 by Ulf

1 Answer

0 votes
The alpha file (that our HB routine saves) contains the regression weights for the coded covariates variables.  The alpha is the vector of utilities representing the population (upper-level) estimate.  If you have no covariates in your model, then alpha vector just contains an estimate for the population mean preferences at each iteration.  There are thousands of estimates of alpha (one for each iteration), so often the first 5K or 10K are ignored because they are viewed as premature and prior to convergence.  The remaining estimates of alpha are viewed as the distribution of uncertainty around the population estimates of preferences for the attributes and levels in your study.

But if you have covariates in your model, the alpha vector actually are regression weights to apply to the covariates.  It includes a set of utility intercepts (utilities for each attribute level for respondents who are coded as a vector of zeros on all the covariate regression variables).  For example, if you had a categorical covariate where 1=TypeAPerson, 2=TypeBPerson, then utilities in the alpha file will begin with the intercept utility values (the utilities for the attributes and levels for respondents who are  TypeBPerson).  (The reference category in the dummy-coding of covariates is the LAST level.)  Following the intercept utility values (on the same row, as they are part of the alpha vector), the ADJUSTMENT to the utility weights are then reported for respondents who are TypeAPerson.  In other words, for any attribute level in the experiment, a TypeAPerson has an average utility weight equal to the intercept for that attribute level plus the adjustment regression weight associated with a TypeAPerson.  

For example, let's say that one of the utility weights in your experiment is for Red.  If the utility weight in the intercept portion of the alpha vector was a 1.0 and the utility weight for Red for the TypeAPerson was 0.5, then you know that TypeAperson weight was 1.0 + 0.5 = 1.5.  And, the TypeBPerson weight was equal to the intercept, or 1.0.  Those two groups differ on average by 0.5 for preference for Red.

The larger the elements in the vector associated with utility adjustments for respondents who are TypeAPerson, the more meaningful your covariate was in capturing heterogeneity (differences in preference between TypeA and TypeB people).

A good review article for how to find meaningful covariates and interpret the results is found at: http://www.sawtoothsoftware.com/download/techpap/HBCovariates.pdf
answered Apr 6, 2017 by Bryan Orme Platinum Sawtooth Software, Inc. (198,315 points)