# [R] polr (MASS) and lrm (Design) differences in tests of statistical signifcance

Paul Johnson pauljohn at ku.edu
Thu Sep 30 23:40:56 CEST 2004

```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
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 +

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
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

```