Re: [S] Diff logit reg output b/w sas & Splus

Kent E. Holsinger (kent@darwin.eeb.uconn.edu)
08 May 1998 11:34:27 -0400

Edward,

The p-values reported by anova() from S-Plus are obtained from a
likelihood ratio test comparing a model with the preceding
reported for factor F comes from comparing the likelihood of this
model

dvt ~ A + B + C + D + E

with this one

dvt ~ A + B + C + D + E + F

The S-Plus results are telling you that once terms A-E have been added
to the model adding F to the model improves the fit only marginally (P
= 0.096).

The p-values reported by SAS are based on an approximation that
depends on the large sample normality of parameter estimates. In the
case of parameter F, the Wald chi-square is intended to reflect
comparison of the following two models

dvt ~ A + B + C + D + E + G + EF
dvt ~ A + B + C + D + E + F + G + EF

The statistic is obtained by taking squaring the ratio of the
parameter to its estimated standard error. The p-value is obtained
assuming that this statistic follows a chi-squared distribution with 1
degree of freedom. Because the parameter estimates and standard errors
are, as you note, very similar. Wald statistics computed from the
S-Plus output are very similar to those reported by SAS. In fact,

> chi <- (0.5814527/0.2379988)^2
> chi
[1] 5.968693
> 1 - pchisq(chi, 1)
[1] 0.01456207
>

The t-value reported by S-Plus is calculated by dividing the parameter
estimate by its estimated standard error. (Can anyone tell me how many
degrees of freedom should be used in getting a p-value from this? Just
curious.)

You should read the short discussion of the Hauck-Donner effect on
p. 237 of V&R2. A Wald test is not only less powerful than a
likelihood-ratio test, it may also show aberrant behavior.

Kent

```--
Kent E. Holsinger                Kent@Darwin.EEB.UConn.Edu
http://darwin.eeb.uconn.edu
-- Department of Ecology & Evolutionary Biology
-- University of Connecticut, U-43
-- Storrs, CT   06269-3043

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