Multiple Logistic Regression with Interaction between Quantitative and Qualitative Explanatory Variables

Question

As a follow up to this question, I fitted the Multiple Logistic Regression with Interaction between Quantitative and Qualitative Explanatory Variables. MWE is given below:

Answer 1

You use the drc package to fit logistic dose-response models.

First fit the model

require(drc)
mod <- drm(Kill/Total ~ Conc, 
           curveid = Type, 
           weights = Total, 
           data = df, 
           fct =  L.4(fixed = c(NA, 0, 1, NA)), 
           type = 'binomial')

Here curveid=specifies the grouping of the data and fct= specifies a 4 parameter logistic function, with parameters for lower and upper bond fixed at 0 and 1.

Note the differences to glm are negligible:

df2 <- with(data=df,
            expand.grid(Conc=seq(from=min(Conc), to=max(Conc), length=51),
                        Type=levels(Type)))
df2$Pred <- predict(object=mod, newdata = df2)

Here's a histgramm of the differences to the glm prediction

hist(df2$Pred - df1$Pred)

Estimate Effective Doses (and CI) from the model

This is easy with the ED() function:

ED(mod, c(50, 90, 95), interval = 'delta')

Estimated effective doses
(Delta method-based confidence interval(s))

     Estimate Std. Error   Lower  Upper
A:50   9.1468     2.3257  4.5885 13.705
A:90  39.8216     4.3444 31.3068 48.336
A:95  50.2532     5.8773 38.7338 61.773
B:50  16.2936     2.2893 11.8067 20.780
B:90  52.0214     6.0556 40.1527 63.890
B:95  64.1714     8.0068 48.4784 79.864
C:50  12.5477     1.5568  9.4963 15.599
C:90  33.4740     2.7863 28.0129 38.935
C:95  40.5904     3.6006 33.5334 47.648

For each group we get ED50, ED90 & ED95 with CI.