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

[Chris Chapman]

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.
>>
[[elided Hotmail spam]]
>>
>> Dimitri Liakhovitski
>> ninah.com
>>
>>         [[alternative HTML version deleted]]
>>
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