Re: st: command or method for logistic quantile regression in Stata

[Austin Nichols <austinnichols@gmail.com>]

Doug Hess <douglasrhess@gmail.com>:
The reference concerns fractional outcomes a la the fractional logit; see e.g.
http://www.stata.com/support/faqs/stat/logit.html
http://www.stata.com/meeting/12uk/Buis_proportions.pdf
http://cohesion.rice.edu/Conferences/Econometrics/emplibrary/wooldridge.pdf
http://www.stata.com/meeting/snasug08/abstracts.html#wooldridge
and see also -locpr- on SSC for an alternative conditional mean model.

Your second paragraph seems to describe breaking the RHS vars up into
dummies capturing quantiles; this is feasible and quite different from
your initial question.

I differ on one minor point with Maarten: quantile regression can make
sense for binary depvars, if we think each individual i has a
probability p and we want to model how the quantiles of p vary with X,
rather than how the mean of p varies with X. The issue is that you
need variation within i to identify such a model, i.e. you need panel
data. Here, quantile regression would be an alternative to -xtlogit-,
not -logit-, and it turns out that -qreg- with individual
heterogeneity is not so easy.

I was predicting an -xtqreg- forthcoming in Stata back in May 2008,
but I wouldn't hold my breath:
http://www.stata.com/statalist/archive/2008-05/msg00957.html

If you had sufficient panel data, you could easily estimate the
"between" quantile regression by regressing the mean outcome by person
on mean X by person with -qreg-; in such a case, you are back in the
land of fractional outcomes.

On Fri, Sep 17, 2010 at 5:58 PM, Doug Hess <douglasrhess@gmail.com> wrote:
> Thanks, Maarten. This article mentions the concept of "logistic
> quantile regression" for bounded dependent variables; would something
> like this suitable for binary variables? Cite:  "Logistic quantile
> regression for bounded outcomes." Matteo Bottai, Bo Cai and Robert E.
> McKeown. Statistics in medicine, Vol. 29, No. 2. (30 January 2010),
> pp. 309-317; link: http://www.citeulike.org/user/guhjy/article/6306738
>
> In other words, is there a good reason not to use the predicted
> probabilities from a logit model to then chop the data up into
> quantiles to see how some predictors variously impact across the
> probability of the BDV hitting 1? I guess that can be done with
> existing commands issued in steps, but I wasn't sure if there was code
> just for this or caveats or special steps to take, or if it was just a
> bad idea.
>
> Or can other transforms or link functions be used with binary
> dependent variables to allow for quantile regression?
>
> In essence I'm asking the question that Abelson in his book
> "Statistics as Principled Argument" encourages grad students to ask:
> "Hey, can we do that?"
>
> -Doug
>
>
> Date: Thu, 16 Sep 2010 07:39:28 +0000 (GMT)
> From: Maarten buis <maartenbuis@yahoo.co.uk>
> Subject: Re: st: command or method for logistic quantile regression in Stata
>
> - --- On Wed, 15/9/10, Doug Hess wrote:
>> Are there any special commands (or steps if there is not a
>> direct command) for running quantile regression for a binary
>> dependent variable in Stata?
>
> I don't think quantile regression makes much sense for binary
> variables. Any quantile of a binary regression can only be 0
> or 1 (maybe one arbitrary number in between if the order
> statistic required for your quantile isn't an integer). So
> whatever you do, you should end up with either a horizontal line
> at 0 or 1, or a step function switching between 0 or 1.
>
> Hope this helps,
> Maarten
>

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