[R] ED50 from logistic model with interactions

From: Kate Stark <lhodgson_at_postoffice.utas.edu.au>
Date: Wed, 02 May 2007 11:37:22 +1000


I was wondering if someone could please help me. I am doing a logistic regression to compare size at maturity between 3 seasons. My model is:

fit <- glm(Mature ~ Season * Size - 1, family = binomial, data=dat)

where Mature is a binary response, 0 for immature, 1 for mature. There are 3 Seasons.

The Season * Size interaction is significant. I would like to compare the size at 50% maturity between Seasons, which I have calculated as:

Mat50_S1 <- -fit$coef[1]/fit$coef[4]
Mat50_S2 <- -fit$coef[2]/(fit$coef[4] + fit$coef[5])
Mat50_S3 <- -fit$coef[3]/(fit$coef[4] + fit$coef[6])

But I am not sure how to calculate the standard error around each of these estimates. The p.dose function from the MASS package does this automatically, but it doesn’t seem to allow interaction terms.

In Faraway(2006) he has an example using the delta method to calculate the StdErr, but again without any interactions. I can apply this for the first Season, as there is just one intercept and one slope coefficient, but for the other 2 Seasons, the slope is a combination of the Size coefficient and the Size*Season coefficient, and I am not sure how to use the covariance matrix in the delta calculation.

I could divide the data and do 3 different logistic regressions, one for each season, but while the Mat50 (i.e. mean Size at 50% maturity) is the same as that calculated by the separate lines regression, Im not sure how this may change the StdErr?



Kate Stark | PhD Candidate
Institute of Antarctic & Southern Ocean Studies & Tasmanian Aquaculture & Fisheries Institute University of Tasmania
Email: kate.stark at utas.edu.au

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