enh: fractional Logit, Probit

[josef-pkt]

http://onlinelibrary.wiley.com/doi/10.1002/%28SICI%291099-1255%28199611%2911:6%3C619::AID-JAE418%3E3.0.CO;2-1/abstract

we need to replace the check for set (0, 1) with interval [0, 1]

partial skimming of the paper only:

uses QuasiMLE with Logit/Bernoulli and sandwich covariance for robust.
this means Logit with cov_type="white" or "H0" should already do everything.

They have a 2008 paper that uses Probit. in panel setting
http://www.sciencedirect.com/science/article/pii/S030440760800050X

the first article has 1417 citations in Google so there is a lot more similar.

[josef-pkt]

"
Interestingly, the robust standard errors from equation (9) in the context of ordinary logit
and probit are computed almost routinely by certain statistics and econometrics packages,
such as STATA@ and SST@. Unfortunately, the packages with which we are familiar
automatically transform the dependent variable used in logit or probit into a binary variable
before estimation, or do not allow non-binary variables at all (STATA@ and SST@ fall into
the first category). With the minor change of allowing for fractional y in so-called binary
response analysis, standard software packages could be used to estimate the parameters in
equation (4) and to perform asymptotically valid inference. Alternatively, programming the
estimator in a language such as GAUSS@, as we do for our application in Section 4, is fairly
straightforward.
"

Papke and Wooldridge 1996

GLM in Stata has been updated since then
http://www.stata.com/support/faqs/statistics/logit-transformation/

[josef-pkt]

@kshedden Does GEE work with fractional data in a logit or probit binary/binomial model?

I haven't looked at the example yet, it has panel data for a response variable that is a proportion

in the Papke Wooldrige 2008 article they use just GLM and GEE (among others)

for example

glm math4 lavgrexp alavgrexp lunch alunch lenroll alenroll y96-y01 if year>1994, fa(bin) link(probit) cluster(distid)
mat b = e(b)
xtgee math4 lavgrexp lunch lenroll alavgrexp alunch alenroll y96-y01, fa(bi) link(probit) corr(exch) robust from(b,skip)

Papke has the replication files on her (departmental) web page (her personal page gives me a permission error) http://www.econ.msu.edu/faculty/papke/

[kshedden]

It seems to work fine, I made a notebook:

http://nbviewer.ipython.org/urls/umich.box.com/shared/static/y0azjuau3t21b7p11m56.ipynb

On Sat, Oct 11, 2014 at 9:19 AM, Josef Perktold notifications@github.com
wrote:

@kshedden https://github.com/kshedden Does GEE work with fractional
data in a logit or probit binary/binomial model?

I haven't looked at the example yet, it has panel data for a response
variable that is a proportion

in the Papke Wooldrige 2008 article they use just GLM and GEE (among
others)

for example

glm math4 lavgrexp alavgrexp lunch alunch lenroll alenroll y96-y01 if year>1994, fa(bin) link(probit) cluster(distid)
mat b = e(b)
xtgee math4 lavgrexp lunch lenroll alavgrexp alunch alenroll y96-y01, fa(bi) link(probit) corr(exch) robust from(b,skip)

Papke has the replication files on her (departmental) web page (her
personal page gives me a permission error)
http://www.econ.msu.edu/faculty/papke/

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[jseabold]

PR?