[R] confint function in MASS package for logistic regression analysis

[William Dunlap]

Your original data must have looked something like the following:
  sib.data <- data.frame(sib=rep(c(0,1,0,1), c(159,4,162,37)),
                         sex=rep(c(0,0,1,1), c(159, 4, 162, 37)))
as that gives the 2x2 table you showed (with 'Response' -> 'sib'):
  > table(sib.data)
     sex
  sib   0   1
    0 159 162
    1   4  37
With that data we can recreate your results:
  > sib.glm <- glm(sib~sex,family=binomial,data=sib.data)
  > summary(sib.glm)$coefficients
               Estimate Std. Error   z value     Pr(>|z|)
  (Intercept) -3.682610  0.5062440 -7.274377 3.480223e-13
  sex          2.205931  0.5380361  4.099969 4.132054e-05

You can get confidence intervals matching SPSS's and
"the usual confidence interval formula" by calling
confint.default (which uses the variance of the coefficient
estimates, vcov(sib.glm), and the asymptotic formula you
gave).
  > confint.default(sib.glm)
                 2.5 %    97.5 %
  (Intercept) -4.67483 -2.690390
  sex          1.15140  3.260463

I believe special glm method for confint uses
"profile likelihood" to find the confidence intervals.

There are quite a few descriptions of that available.
  > confint(sib.glm)
  Waiting for profiling to be done...
                  2.5 %    97.5 %
  (Intercept) -4.861153 -2.823206
  sex          1.263976  3.428764

SPSS probably can do the same sort of calculation, as the
following SPSS document describes the algorithm:
http://publib.boulder.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.help%2Falg_genlin_gzlm_est_ci.htm 

Bill Dunlap
Spotfire, TIBCO Software
wdunlap tibco.com 

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Jerome Myers
> Sent: Wednesday, January 18, 2012 7:27 AM
> To: r-help at r-project.org
> Subject: [R] confint function in MASS package for logistic regression analysis
> 
> I have the following binary data set:
>                      Sex
> Response      0   1
>                 0 159 162
>                 1   4     37
>   My commands
>       library(MASS)
>          sib.glm=glm(sib~sex,family=binomial,data=sib.data)
>         summary(sib.glm)
> The coefficients in the output are
>              Estimate Std. Error z value Pr(>|z|)
>      (Intercept)  -3.6826     0.5062  -7.274 3.48e-13 ***
>           sex           2.2059     0.5380   4.100 4.13e-05 ***
> I have calculated the .95 confidencce interval for sex two ways:
>      (1) confint(sib.glm)   The result is
>                  2.5 %    97.5 %
> (Intercept) -4.861153 -2.823206
> sex          1.263976  3.428764
> 
> Using the usual confidence interval formula,
>      (2) 2.2059 +/- 1.96*.538 = 1.15142.  3.26038
> The results from (2) are identical to those from SPSS but do not agree
> with those from the confint function.
> 
>      I have reviewed the MASS pdf file and, seeing no solution there,
> have tried to get the Venables & Ripley book from the local college
> libraries but the only copies are out on loan. I suspect there is a
> simple explanation of the discrepancy, perhaps a modification to account
> for pre-asymptotic distribution. Or perhaps I misunderstand the
> application of the confint fuuction in the MASS package. If someone
> knows the explanation, I'd appreciate it.
> 
> --
> Jerome L. Myers
> 
> 
> 
> 
> 
> 
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> 
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