[R] polr (MASS) and lrm (Design) differences in tests of statistical signifcance
John Fox
jfox at mcmaster.ca
Fri Oct 1 02:34:53 CEST 2004
Dear Paul,
I tried polr() and lrm() on a different problem and (except for the
difference in signs for the cut-points/intercepts) got identical results for
both coefficients and standard errors. There might be something
ill-conditioned about your problem that produces the discrepancy -- I
noticed, for example, that some of the upper categories of the response are
very sparse. Perhaps the two functions use different forms of the
information matrix. I expect that someone else will be able to supply more
details.
I believe that the t-statistics in the polr() output are actually Wald
statistics.
I hope this helps,
John
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Paul Johnson
> Sent: Thursday, September 30, 2004 4:41 PM
> To: r help
> Subject: [R] polr (MASS) and lrm (Design) differences in
> tests of statistical signifcance
>
> Greetings:
>
> I'm running R-1.9.1 on Fedora Core 2 Linux.
>
> I tested a proportional odds logistic regression with MASS's
> polr and Design's lrm. Parameter estimates between the 2 are
> consistent, but the standard errors are quite different, and
> the conclusions from the t and Wald tests are dramatically
> different. I cranked the "abstol" argument up quite a bit in
> the polr method and it did not make the differences go away.
>
> So
>
> 1. Can you help me see why the std. errors in the polr are so
> much smaller, and
>
> 2. Can I hear more opinions on the question of t vs. Wald in
> making these signif tests. So far, I understand the t is
> based on the asymptotic Normality of the estimate of b, and
> for finite samples b/se is not exactly distributed as a t.
> But I also had the impression that the Wald value was an
> approximation as well.
>
> > summary(polr(as.factor(RENUCYC) ~ DOCS + PCT65PLS*RANNEY2
> + OLDCRASH
> + FISCAL2 + PCTMETRO + ADMLICEN, data=elaine1))
>
> Re-fitting to get Hessian
>
> Call:
> polr(formula = as.factor(RENUCYC) ~ DOCS + PCT65PLS * RANNEY2 +
> OLDCRASH + FISCAL2 + PCTMETRO + ADMLICEN, data = elaine1)
>
> Coefficients:
> Value Std. Error t value
> DOCS 0.004942217 0.002952001 1.674192
> PCT65PLS 0.454638558 0.113504288 4.005475
> RANNEY2 0.110473483 0.010829826 10.200855
> OLDCRASH 0.139808663 0.042245692 3.309418
> FISCAL2 0.025592117 0.011465812 2.232037
> PCTMETRO 0.018184093 0.007792680 2.333484
> ADMLICEN -0.028490387 0.011470999 -2.483688
> PCT65PLS:RANNEY2 -0.008559228 0.001456543 -5.876400
>
> Intercepts:
> Value Std. Error t value
> 2|3 6.6177 0.3019 21.9216
> 3|4 7.1524 0.2773 25.7938
> 4|5 10.5856 0.2149 49.2691
> 5|6 12.2132 0.1858 65.7424
> 6|8 12.2704 0.1856 66.1063
> 8|10 13.0345 0.2184 59.6707
> 10|12 13.9801 0.3517 39.7519
> 12|18 14.6806 0.5587 26.2782
>
> Residual Deviance: 587.0995
> AIC: 619.0995
>
>
> > lrm(RENUCYC ~ DOCS + PCT65PLS*RANNEY2 + OLDCRASH +
> FISCAL2 + PCTMETRO + ADMLICEN, data=elaine1)
>
> Logistic Regression Model
>
> lrm(formula = RENUCYC ~ DOCS + PCT65PLS * RANNEY2 + OLDCRASH +
> FISCAL2 + PCTMETRO + ADMLICEN, data = elaine1)
>
>
> Frequencies of Responses
> 2 3 4 5 6 8 10 12 18
> 21 12 149 46 1 10 6 2 2
>
> Frequencies of Missing Values Due to Each Variable
> RENUCYC DOCS PCT65PLS RANNEY2 OLDCRASH FISCAL2
> PCTMETRO ADMLICEN
> 5 0 0 6 0 5
> 0 5
>
> Obs Max Deriv Model L.R. d.f. P C
> Dxy
> 249 7e-05 56.58 8 0 0.733
> 0.465
> Gamma Tau-a R2 Brier
> 0.47 0.278 0.22 0.073
>
> Coef S.E. Wald Z P
> y>=3 -6.617857 6.716688 -0.99 0.3245
> y>=4 -7.152561 6.716571 -1.06 0.2869
> y>=5 -10.585705 6.742222 -1.57 0.1164
> y>=6 -12.213340 6.755656 -1.81 0.0706
> y>=8 -12.270506 6.755571 -1.82 0.0693
> y>=10 -13.034584 6.756829 -1.93 0.0537
> y>=12 -13.980235 6.767724 -2.07 0.0389
> y>=18 -14.680760 6.786639 -2.16 0.0305
> DOCS 0.004942 0.002932 1.69 0.0918
> PCT65PLS 0.454653 0.552430 0.82 0.4105
> RANNEY2 0.110475 0.076438 1.45 0.1484
> OLDCRASH 0.139805 0.042104 3.32 0.0009
> FISCAL2 0.025592 0.011374 2.25 0.0245
> PCTMETRO 0.018184 0.007823 2.32 0.0201
> ADMLICEN -0.028490 0.011576 -2.46 0.0138
> PCT65PLS * RANNEY2 -0.008559 0.006417 -1.33 0.1822
>
> >
>
> --
> Paul E. Johnson email: pauljohn at ku.edu
> Dept. of Political Science http://lark.cc.ku.edu/~pauljohn
> 1541 Lilac Lane, Rm 504
> University of Kansas Office: (785) 864-9086
> Lawrence, Kansas 66044-3177 FAX: (785) 864-5700
>
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