Re: st: too good to be true : lr test in mlogit?

[Nick Cox <njcoxstata@gmail.com>]

I see nothing surprising here. The likelihood is the product of many
very small probabilities, so will be very small overall. The P-values
are at least in part a side-effect of using a very large sample size.
I don't know that a model with such a low pseudo-R-square is "too good
to be true", but it depends on your expectations. If this is analysis
of data on people, as I wildly guess, the Maarten Buis argument that
high levels of "explanation" are not to be expected given what else we
know about the many determinants and influences on human behaviour
could apply.

Present-day significance testing machinery was largely designed in the
first few decades of the 20th century to safeguard natural scientists
against over-interpreting results from very small samples. Present-day
social scientists in the early 21st century need other measures to
safeguard themselves against over-interpreting significance tests from
very large samples.

On Fri, May 13, 2011 at 9:12 AM, John Litfiba <cariboupad@gmx.fr> wrote:
> Dear all (again)
>
> I was wondering if my results seems too good to be true. I run a
> multinomial logit for yvar (caterical variable with 4 possible values)
> and I obtain the following results :
>
> 1) It is normal to obtain such a negative log likelihood when we use
> very large sample, right ? (n=2 millions here)
> 2) if the association (for example given by tabulation) show that
> there is strong association between yvar and xvar1 then it is
> plausible to obtain this fastastic LR statistic of... 140000 ??
>
>
> Many many thanks in advance
>
> mlogit yvar xvar1 xvar2
>
> Iteration 0:   log likelihood = -1953742.5
> Iteration 1:   log likelihood =   -1900152
> Iteration 2:   log likelihood = -1883338.4
> Iteration 3:   log likelihood =   -1880317
> Iteration 4:   log likelihood = -1880312.7
> Iteration 5:   log likelihood = -1880312.7
>
> Multinomial logistic regression                   Number of obs   =    2227058
>                                                  LR chi2(6)      =  146859.43
>                                                  Prob > chi2     =     0.0000
> Log likelihood = -1880312.7                       Pseudo R2       =     0.0376
>
> ------------------------------------------------------------------------------
>       order |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> yvar0 |  (base outcome)
> -------------+----------------------------------------------------------------
> yvar1           |
>      xvar1 |  -2.137044   .0104876  -203.77   0.000    -2.157599   -2.116489
>      xvar2|  -.0099444   .0001223   -81.32   0.000    -.0101841   -.0097047
>       _cons |   1.708873   .0125759   135.88   0.000     1.684225    1.733522
> -------------+----------------------------------------------------------------
> yvar2         |
>      xvar1 |   .8905294   .0734511    12.12   0.000     .7465678    1.034491
>      xvar2 |  -.0087927   .0003393   -25.92   0.000    -.0094576   -.0081277
>       _cons |  -3.672227   .0758592   -48.41   0.000    -3.820908   -3.523546
> -------------+----------------------------------------------------------------
> yvar3          |
>      xvar1 |  -3.826486   .0113315  -337.69   0.000    -3.848695   -3.804276
>      xvar2 |  -.0054125   .0002488   -21.76   0.000    -.0059002   -.0049249
>       _cons |   1.244583   .0180673    68.89   0.000     1.209171    1.279994
> ------------------------------------------------------------------------------
> *

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