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Re: st: statistical significance of cut points in ordered logit


From   Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: statistical significance of cut points in ordered logit
Date   Mon, 17 May 2010 17:40:40 +0530

Grace,

That is not how it works. There is an error term involved in these
probability calculations as well. Specifically, for the observation
where xb=16.55703,
Pr(y=1|x) = Pr(xb+u <= cut1) = Pr(u <= -.1289)
which, together with the assumed logistic distribution for the "u"s
implies  Pr(y=1|x) = invlogit(-.1289) = .46781954. Similarly,
Pr(y=2|x) = Pr(cut1 <= xb+u <= cut2) = Pr(-.1289 <= u <= 1.56567) =
invlogit(1.56567)-invlogit(-.1289) = .35934591
and so on. If you were to write off the error term i.e., base
inference on the expected probabilities (xb), you'd have certainties
and not probabilities.

T

2010/5/17 Martin Weiss <martin.weiss1@gmx.de>:
>
> <>
>
> " I got the material http://www.nd.edu/~rwilliam/xsoc63993/l91.pdf provided
> by Maarten, which is helpful."
>
>
>
> Just to be sure, the material you are referring to is provided by Richard
> Williams, Maarten probably pointed you to it.
>
> HTH
> Martin
>
>
> -----Ursprüngliche Nachricht-----
> Von: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Grace Jessie
> Gesendet: Montag, 17. Mai 2010 13:47
> An: statalist@hsphsun2.harvard.edu
> Betreff: Re: st: statistical significance of cut points in ordered logit
>
>
> Statalists,
> I got the material http://www.nd.edu/~rwilliam/xsoc63993/l91.pdf provided by
> Maarten, which is helpful. Thank you!
> After typing the following in the Stata, I found some obersavtions were
> suprising to me(see table A). In table A, For example,xb[1] is obviously
> bigger than the coefficient of cut1,so the value for Y should equal 2.
> However, from the values for pr1 pr2 pr3, the value for pr1 is the biggest,
> which means the most likely outcome for Y is 1. Why not consistent?  The
> doubt with other observations in table A is the same.
> Additionally, what does the statistical significance of cut points in
> ordered logit mean, which has not been answered in the posting before? I
> found there are no z or P>|z| for cut points, though I could get it.
>
> use http://www.nd.edu/~rwilliam/stats2/statafiles/shuttle2.dta, clear
> ologit distress date temp, nolog
> Ordered logistic regression                       Number of obs   =
> 23
>                                                  LR chi2(2)      =
> 12.32
>                                                  Prob> chi2     =
> 0.0021
> Log likelihood =  -18.79706                       Pseudo R2       =
> 0.2468
> ----------------------------------------------------------------------------
> --
>    distress |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
> Interval]
> -------------+--------------------------------------------------------------
> --
>        date |    .003286   .0012662     2.60   0.009     .0008043
> .0057677
>        temp |  -.1733752   .0834473    -2.08   0.038     -.336929
> -.0098215
> -------------+--------------------------------------------------------------
> --
>       /cut1 |   16.42813   9.554813                      -2.29896
> 35.15522
>       /cut2 |   18.12227   9.722293                     -.9330729
> 37.17761
> ----------------------------------------------------------------------------
> --
> predict xb,xb
> predict pr1 pr2 pr3
>
> table A
>  +--------------------------------------------------------------------+
>  | distress   date   temp         xb        pr1        pr2        pr3 |
>  |--------------------------------------------------------------------|
>  |     None   8732     70   16.55703   .4678189    .359285   .1728961 |
>  |   1 or 2   9341     81   16.65107   .4444934   .3687458   .1867608 |
>  |   3 plus   9434     75   17.99692   .1723883   .3589076    .468704 |
>  |   1 or 2   9461     76   17.91227   .1848028   .3675054   .4476918 |
>  +--------------------------------------------------------------------+
> Hope for any help!
>
> Regards,
> Grace
>
>
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To every ω-consistent recursive class κ of formulae there correspond
recursive class signs r, such that neither v Gen r nor Neg(v Gen r)
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