I was thinking to (sub)-sample the Females -- e.g., if M=200 and F=300, then take a sub-sample F=200 or whatever the proportion should be for the population.  Use that sub-sample of F along with the whole sample of M, and estimate HB from that.  And ideally, repeat for multiple samples of F=200.  However, your idea #1 below to over-sample the M -- to take M=300 along with the F=300 -- would be an alternative.  Stretching a sample is a little more problematic than reducing it, but if the over-sampling is modest and is bootstrapped then it is certainly a defensible approach.

In either case, doing the sub- or over- sampling before HB makes more sense than sampling the utilities afterward because you'd be trying to get the sample right for the population to make sure the HB estimates are unbiased.  That raises another issue, which is whether your problem makes more sense to be considered using betas (individual utilities) vs. alphas (population utility estimates).  Alpha is very highly correlated with mean beta (r >= 0.97 on the occasions I've looked at them) but if you are concerned with potentially fine differences within the population, then that might be an issue to consider. For instance, whether it makes sense to do aggregate-level preference share estimates using the alphas instead of the betas.

As for doing sub- or over-sampling, the call between the two probably depends on the exact proportional differences.  If the oversampling needed for M is not huge (say, 1.1x to 1.6x or thereabouts), and if bootstrapping is possible within your time constraints (say, to run the HB model >20x to get empirical 95% credible intervals) then oversampling seems appropriate.  However, if the sample is large enough that it's not an issue OR if 20x runs are not possible due to time constraints, then sub-sampling F and/or using covariates seems like a good approach.

I hope that helps ... and, in case it's not obvious, these are just my "working" reflections and I'd be happy to hear other views that are different!  Good luck,

-- chris



From: Dimitri Liakhovitski 
Sent: Thursday, February 24, 2011 6:33 PM
To: Chris Chapman 
Cc: walt@dataanalyticscorp.com ; r-sig-dcm@r-project.org 
Subject: Re: [R-sig-DCM] Weighting in DCMs


Chris, this is very helpful. One clarifying question. When you say in (2): "sample the respondents prior to fitting to match the population prevalence (and ideally, bootstrap that sampling and model the "empirical" credible distribution)." - what exactly do you mean? Let's assume I don't have enough males. Do you mean - bootstrap my males (their DCM responses) until I have "enough" males - and then run the HB estimation on the "new" sample with more males? Or do you mean: after the estimation is run and we have to simulate shares - then bootstrap my males (their utilities) - until I have "enough" males - and then estimate shares on the "new" sample with more males?

Thanks for clarifying!
Dimitri


On Thu, Feb 24, 2011 at 1:22 PM, Chris Chapman <cnchapman@msn.com> wrote:

  Good question.  I think weighting post-hoc is perhaps better than nothing when a difference is expected -- but is almost certainly problematic since the assumption in the (prior) model fitting stage would have been that the overall sample was a "random" sample of the population.  So I'd only consider that if there is no other option, e.g., if all I had was summary statistics.

  Instead, I'd suggest one (or both) of these options: (1) if you believe apriori that gender is so important, then fit it as a covariate or (if really important or highly differently distributed) as a separate sample, in which case you'll have estimates that could be used separately or (arguably) combined according to general mixture models; (2) sample the respondents prior to fitting to match the population prevalence (and ideally, bootstrap that sampling and model the "empirical" credible distribution).

  Personally, barring other information and with the open issues around covariates, I'd probably assume that the goal is to get a good population estimate and not so much to focus on gender differences or covariates, in which case #2 would be my default, and which is similar to handling it with sample quotas but perhaps even better.

  As for explaining to the client, with #1, I'd probably say "we specifically modeled the contribution of gender using all the information so weighting is not necessary."  For #2, the client might complain at "overpaying" or "throwing away" sample, so I'd likely say something like "resampling to ensure population match is part of good data cleaning, and -- if I bootstrapped -- no one was actually lost because we resampled [or bootstrapped] to see the effect across the whole sample".  However, since I'm my own client and analyst, that might be a harder sell to someone else :-)

  If the client can handle it (or you're curious) it would be interesting to compare this to the weighting approach.  I'd be interested to hear other thoughts,

  -- chris

  --------------------------------------------------
  From: "Data Analytics Corp." <walt@dataanalyticscorp.com>
  Sent: Thursday, February 24, 2011 5:46 PM
  To: <r-sig-dcm@r-project.org>
  Subject: Re: [R-sig-DCM] Weighting in DCMs 



    Hi,

    I don't have an answer to this, but I would like to hear arguments pro and con on the weighting.

    Thanks,

    Walt

    ________________________

    Walter R. Paczkowski, Ph.D.
    Data Analytics Corp.
    44 Hamilton Lane
    Plainsboro, NJ 08536
    ________________________
    (V) 609-936-8999
    (F) 609-936-3733
    walt@dataanalyticscorp.com
    www.dataanalyticscorp.com
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    On 2/24/2011 12:31 PM, Dimitri Liakhovitski wrote:

      Everyone, hi!

      it's not an R-related question - but it'd be great to hear your arguments.
      Sometimes we run a DCM (HB) for a sample and then the clients say: Would you
      please weight the results - our sample has too many women.

      I know there is a number of arguments against doing this. Which ones did you
      find working best with your clients?

      Thank you!
      Dimitri

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