[R] Odds ratios in logistic regression models with interaction

[Laviolette, Michael]

Thanks. I came to the same realization after the original post and was able to get the correct results with the coefficient vector and covariance matrix by setting up as a contrast. Linear model contrast estimation in R doesn't seem straightforward. I turned up several packages, but any recommendations you might have would be very useful. Thanks again. --M.L.

a <- 25   # age for which to compute OR's
d <- c(1, 1, a, a) - c(1, 0, a, 0)   # contrast
est.ln.or <- crossprod(coef(fit3.16), d)
se.ln.or <- sqrt(t(d) %*% vcov(fit3.16) %*% d)
exp(est.ln.or)
# [1,] 3.899427
exp(est.ln.or - 1.96 * se.ln.or)
# [1,] 1.712885
exp(est.ln.or + 1.96 * se.ln.or)
# [1,] 8.877148

-----Original Message-----
From: peter dalgaard [mailto:pdalgd at gmail.com] 
Sent: Thursday, August 04, 2016 9:12 AM
To: Laviolette, Michael
Cc: r-help at r-project.org
Subject: Re: [R] Odds ratios in logistic regression models with interaction

I suspect that "you can't get there from here"... a1$fit and a2$fit are not independent, so you can't work out the s.e. of their difference using sqrt(a1$se.fit^2+a2$se.fit^2). 

You need to backtrack a bit and figure out how a1$fit-a2$fit relates to coef(fit3.16). I suspect it is actually just the age times the interaction term, but since you give no output and your code uses a bunch of stuff that I haven't got installed, I can't be bothered to check....  

Once you have your desired value in the form t(a) %*% coef(...), then use the result that V(t(a) %*% betahat) == t(a) %*% vcov() %*% a  (asymptotically).

-pd

On 03 Aug 2016, at 15:08 , Laviolette, Michael <Michael.Laviolette at dhhs.nh.gov> wrote:

> I'm trying to reproduce some results from Hosmer & Lemeshow's "Applied Logistic Regression" second edition, pp. 74-79. The objective is to estimate odds ratios for low weight births with interaction between mother's age and weight (dichotomized at 110 lb.). I can get the point estimates, but I can't find an interval option. Can anyone provide guidance on computing the confidence intervals? Thanks. -Mike L.
> 
> library(dplyr)
> data(birthwt, package = "MASS")
> birthwt <- birthwt %>%
>  mutate(low = factor(low, 0:1, c("Not low", "Low")),
>         lwd = cut(lwt, c(0, 110, Inf), right = FALSE,
>                   labels = c("Less than 110", "At least 110")),
>         lwd = relevel(lwd, "At least 110"))
> 
> # p. 77, Table 3.16, Model 3
> fit3.16 <- glm(low ~ lwd * age, binomial, birthwt) # p. 78, 
> interaction plot visreg::visreg(fit3.16, "age", by = "lwd", xlab = 
> "Age",
>               ylab = "Estimated logit") # p. 78, covariance matrix
> vcov(fit3.16)
> # odds ratios for ages 15, 20, 25, 30
> age0 <- seq(15, 30, 5)
> df1 <- data.frame(lwd = "Less than 110", age = age0)
> df2 <- data.frame(lwd = "At least 110", age = age0)
> a1 <- predict(fit3.16, df1, se.fit = TRUE)
> a2 <- predict(fit3.16, df2, se.fit = TRUE) # p. 79, point estimates 
> exp(a1$fit - a2$fit)
> 
> # How to get CI's?
> # Age    OR     (95% CI)
> # ----------------------
> # 15   1.04 (0.29, 3.79)
> # 20   2.01 (0.91, 4.44)
> # 25   3.90 (1.71, 8.88)
> # 30   7.55 (1.95, 29.19)
> 
> 
> 
> 
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> 
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--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com