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Re: st: Hosmer-Lemeshow and other Pseudo Rsquares


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Hosmer-Lemeshow and other Pseudo Rsquares
Date   Mon, 14 May 2012 15:43:06 +0100

I find these things to be highly tribal. One large part of the
statistical world doesn't know at all about what another large part
regards as utterly standard. So, anything that might surprise your
reviewers might need to be explained very carefully.

On Mon, May 14, 2012 at 3:34 PM, Joseph Padgett <josephpadgett@gmail.com> wrote:
> Thanks, Nick. That's helpful.  I've seen these suggestions before, but
> wrapped in bigger discussions and not nearly as succinct.
>
> I am aware that the R square measures for logistic models are only
> guides and not sole determining factors, but it seems that researchers
> commonly report some form of it (sociology background here btw).
>
> So I've calculated both of your suggestions.  Any advice on reporting
> those?  Does either have an associated line of research that you're
> aware of that I should be referring to/citing when I'm reporting the
> calculation and results?
>
> On Mon, May 14, 2012 at 10:10 AM, Nick Cox <njcoxstata@gmail.com> wrote:
>> I suggest a few meta-rules for yourself:
>>
>> 1. Whatever you calculate should be defined and calculated
>> consistently across different models.
>>
>> 2. Whatever you calculate you promise to use with extreme caution
>> always flagging precisely how it is calculated.
>>
>> 3. You don't decide which model is "best" from these measures; you
>> just treat them as descriptive statistics.
>>
>> #1 sounds easy but can bite quite hard. I find the idea of R^2 as
>>
>> square of correlation between observed and predicted
>>
>> as the sense of R^2 that I like best but this grows out of a long
>> personal history of working with correlation and regression and one
>> that is dominated by working with continuous outcomes. People with a
>> long history the other way round might want you to look for
>>
>> 1 - (log likelihood for model) / (log likelihood for same model with
>> only a constant term)
>>
>> and could have similar warm feelings for that. Others would find the
>> whole idea of looking at goodness of fit without also assessing number
>> of parameters or model complexity in general quite misguided, but
>> those others can't agree on which of various *IC you should use, and
>> even those who have a favourite often say, "You should use ?IC except
>> that it usually favours over-simplified models" or some such.
>>
>> On the first option see
>>
>> FAQ     . . . . . . . . . . . . . . . . . . . . . . . Do-it-yourself R-squared
>>        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
>>        9/03    How can I get an R-squared value when a Stata command
>>                does not supply one?
>>                http://www.stata.com/support/faqs/stat/rsquared.html
>>
>> On Mon, May 14, 2012 at 2:47 PM, Joseph Padgett <josephpadgett@gmail.com> wrote:
>>
>>> I am working with a data set where students are nested within school.
>>>
>>> I have completed a thorough run of models starting with nulls and
>>> ending with full fixed- and random-effects with all controls and
>>> predictors and several models in between with various combinations of
>>> controls.  My dependent variable is a binary outcome.
>>>
>>> I have Haussman tests, LR tests, and Wald taken care of, but I would
>>> like to report some goodness-of-fit results for my models.  I am aware
>>> of the Hosmer-Lemeshow test statistic and it's interpretation, but I'm
>>> having a difficult time finding out how to compute it from my model
>>> results.  I would also like to consider alternatives such as Cox and
>>> Snell.
>>>
>>> I have run my models with each of xtlogit, xtmelogit, and gllamm.  I
>>> did this mostly to be able to learn a bit about the post estimation
>>> commands and different options with each command.  That being said, I
>>> don't know how to get the pseudo Rsquare measures after any of these
>>> and most explanations that I find refer only to the logit command and
>>> give examples using very simplistic models.
>>>
>>> I'm fairly certain there's something terribly obvious that I'm
>>> overlooking.  Any help would be greatly appreciated.
>>
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