[R-sig-DCM] What is a strong covariate in CBC/HB?

Thu Mar 3 16:56:01 CET 2011

Chris's point is that even though the covariate has a strong effect on utilities (which makes it a strong covariate), it matters not if it won't change any business decisions because it has no impact on share.  It is the difference between technical importance and practical importance. It's like statistical significance....given enough sample size two means can be statistically different but the difference can be of no practical importance (except for implying that you grossly overpaid for sample).

W. Michael Conklin
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-----Original Message-----
From: r-sig-dcm-bounces at r-project.org [mailto:r-sig-dcm-bounces at r-project.org] On Behalf Of Dimitri Liakhovitski
Sent: Thursday, March 03, 2011 9:15 AM
To: Wirth, Ralph (GfK SE)
Cc: R DCM List
Subject: Re: [R-sig-DCM] What is a strong covariate in CBC/HB?

That's funny - I was thinking about it and was about to address the same point (about shares), but Ralph was beat me to it.
Upon reflexion, my problem with using shares is this: if one tries to study covariates, defining the strengh of covariates in terms of changes in shares seems circular. It's like saying "Look, the shares for 2 groups are pretty different, so it's a strong covariate". Or: "Look, the shares for 2 groups are not very different, so it's not a strong covariate." Ralph is probably right that very different utilities might result in the same shares. In
fact: what if even very strong covariates produce a negligible difference in shares between groups? It would be a finding by itself, and that's what we are trying to find out. Hence, we need a definition of covariate strength that is pure and not outcome (share) related. Makes sense?
Until now I have not been able to define the relative strength/weakness of a covariate other than by referring to the spread of the means (like in Scenario 2). Probably, variance is also an important consideration, as Ralph mentioned. Not sure what else...

Ralph, do you happen to have the titles of these references?
Thanks!

Dimitri

On Thu, Mar 3, 2011 at 3:57 AM, Wirth, Ralph (GfK SE)
<ralph.wirth at gfk.com>wrote:

> I'm not sure if you can evaluate the strength of covariates based on 
> preference shares. Completely different utility values can result in 
> the same preference shares, but still: the groups are different with 
> regard to their utilities, and this difference in utilities is what 
> covariates should explain. Based on this reasoning, I'd say group 2's covariate is "stronger".
> It's basically an ANOVA/t-test logic: the higher the value of the test 
> statistic, the stronger is the covariate that defines the investigated 
> groups.
>
> This issue reminds me a lot of the issue of how to simulate preference 
> segments. You can find a lot information about how to simulate them 
> (and about which segments are distinctive, which are not) in the papers of e.g.
> Vriens, Wedel, Wilms (I think 1997) and Andrews et al. (2002 or 2003).
>
>
>
>
>
>
>
> -----Ursprüngliche Nachricht-----
> Von: Chris Chapman [mailto:cnchapman at msn.com]
> Gesendet: Donnerstag, 3. März 2011 00:14
> An: Dimitri Liakhovitski; Wirth, Ralph (GfK SE)
> Cc: R DCM List
> Betreff: Re: [R-sig-DCM] What is a strong covariate in CBC/HB?
>
> I think I'm missing something here ... but seems that it depends on 
> the use.
> If you're using those to estimate share of preference (as I would 
> assume), then Scenario 2 would be "stronger" because the predicted 
> preference share differences are larger: (excuse the formatting)
>
> Scenario 1                Raw utilities
>        A=Features 1+3  B=Features 2+4  exp(A)              exp(B)
>  sumPref
> A       Pref B
> Group 1     -1                  1                   0.367879441
> 2.7182818283.08616127   12%     88%Group 2          1                   -1
>            2.718281828
> 0.367879441     3.08616127      88%     12%
>
> Scenario 2                Raw utilities
>        A=Features 1+3  B=Features 2+4  exp(A)          exp(B)  sumPref
> A       Pref B
> Group 1     -2                  2               0.135335283
> 7.3890560997.524391382      2%      98%Group 2           2
>  -2              7.389056099
> 0.135335283     7.524391382     98%     2%
>
> OTOH, if the use is to predict something else from the utilities 
> (questionable, since they probably should be zero-centered diffs 
> instead), then the utilities shown are just linear transforms of one 
> another (assuming the utilities have the same property as their 
> means).
> cor(mean.scenario1,mean.scenario2) = 1.0.   In that case, the predictions
> would be the same either way, in which case they're equally "strong".
>
> And of course, as you noted WRT Ralph's comment, it depends on variance.
>  If
> the variance is equal in both cases (e.g., 1) then Scenario 2 could be 
> regarded as "stronger" because the mean difference has a larger effect 
> size.
>
> But I'm not sure if that's what you're asking ... :-)
>
> --------------------------------------------------
> From: "Dimitri Liakhovitski" <dimitri.dcm at gmail.com>
> Sent: Wednesday, March 02, 2011 10:26 AM
> To: "Wirth, Ralph (GfK SE)" <ralph.wirth at gfk.com>
> Cc: "R DCM List" <r-sig-dcm at r-project.org>
> Subject: Re: [R-sig-DCM] What is a strong covariate in CBC/HB?
>
> > I totally agree with everything you've written, Chris. But let me 
> > stick for a second to actual values of utilities. I am not asking: 
> > is this
> covariate
> > strong/weak for practical reasons, but rather: which of the 2 is 
> > stronger/weaker.
> >
> > Now to what Ralph's written: So, the variance is small (within 
> > group) would imply a stronger covariate. Agreed. How about the 
> > means? For example, let's discuss only 1 attribute with 4 levels.
> >
> > Covariate Scenario 1:
> > Group 1's beta means are -2, -1, +1, and +2.
> > Group 2's beta means are +2, +1, -1, and -2.
> >
> > Covariate Scenario 2:
> > Group 1's beta means are -4, -2, +2, and +4.
> > Group 2's beta means are +4, +2, -2, and -4.
> >
> > Which covariate is stronger?
> > Dimitri
> >
> >
> > On Wed, Mar 2, 2011 at 1:07 PM, Wirth, Ralph (GfK SE)
> > <ralph.wirth at gfk.com>wrote:
> >
> >> I'd say if the groups that are defined by the covariate are very 
> >> different with regard to their preferences (i.e. utility 
> >> parameters) and at the same time the members of each group are very 
> >> homogeneous, then the covariate is a "strong" covariate.
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >> -----Ursprüngliche Nachricht-----
> >> Von: r-sig-dcm-bounces at r-project.org [mailto:
> >> r-sig-dcm-bounces at r-project.org] Im Auftrag von Dimitri 
> >> Liakhovitski
> >> Gesendet: Mittwoch, 2. März 2011 19:04
> >> An: R DCM List
> >> Betreff: [R-sig-DCM] What is a strong covariate in CBC/HB?
> >>
> >> Guys, I could ask some of you individually but it's always better 
> >> to
> talk
> >> to
> >> several smart guys at a time.
> >> Some of you know I am working on a project for an ART-Forum which 
> >> explores the issue of covariates in CBC/HB estimation: Is 
> >> estimation with covariates useful?
> >>
> >> I have a question: what do YOU THINK is a "strong" covariate? (and 
> >> let's assume we know what the true utilities and their dependence 
> >> on the covariate
> >> are)
> >> I am looking less for a mathematical answer (although it's OK if it 
> >> is) and more for a conceptual answer, maybe even with examples. 
> >> Like: assume we have a covariate with only 2 levels (i.e., 
> >> respondents belong to 2 groups):
> >> what
> >> should their preferences be like in order for us to be able to say:
> group
> >> membership a strong covariate / weak covariate? And if we have 3 groups?
> >> Also, I am looking less for a "correct" answer and more for your 
> >> opinions.
> >>
> >> Looking forward to your replies!
> >>
> >> Dimitri Liakhovitski
> >> ninah.com
> >>
> >>         [[alternative HTML version deleted]]
> >>
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