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

[Marc Schwartz]

On Jan 18, 2012, at 9:27 AM, Jerome Myers wrote:

> 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.



The confint.glm() function in V&R's MASS package provides "profile likelihood" confidence intervals for better coverage, as compared to the formula you have in (2), which presumes a normally distributed parameter estimate (eg. Wald type CI's).

If SPSS is using (2) for logistic regression by default, I would have to question why, but not being a user, would also have to think that they offer alternative methods.

Do a Google search for "profile likelihood confidence interval" which will lead you to a number of suitable references on theory.

HTH,

Marc Schwartz