Weighted logistic regression in R - r

Question

Given sample data of proportions of successes plus sample sizes and independent variable(s), I am attempting logistic regression in R.
The following code does what I want and seems to give sensible results, but does not look like a sensible approach; in effect it doubles the size of the data set
datf <- data.frame(prop = c(0.125, 0, 0.667, 1, 0.9),
cases = c(8, 1, 3, 3, 10),
x = c(11, 12, 15, 16, 18))
datf2 <- rbind(datf,datf)
datf2$success <- rep(c(1, 0), each=nrow(datf))
datf2$cases <- round(datf2$cases*ifelse(datf2$success,datf2$prop,1-datf2$prop))
fit2 <- glm(success ~ x, weight=cases, data=datf2, family="binomial")
datf$proppredicted <- 1 / (1 + exp(-predict(fit2, datf)))
plot(datf$x, datf$proppredicted, type="l", col="red", ylim=c(0,1))
points(datf$x, datf$prop, cex=sqrt(datf$cases))
producing a chart like
which looks reasonably sensible.
But I am not happy about the use of datf2 as a way of separating the successes and failures by duplicating the data. Is something like this necessary?
As a lesser question, is there a cleaner way of calculating the predicted proportions?

Answer 1

No need to construct artificial data like that; glm can fit your model from the dataset as given.
> glm(prop ~ x, family=binomial, data=datf, weights=cases)
Call: glm(formula = prop ~ x, family = binomial, data = datf, weights = cases)
Coefficients:
(Intercept) x
-9.3533 0.6714
Degrees of Freedom: 4 Total (i.e. Null); 3 Residual
Null Deviance: 17.3
Residual Deviance: 2.043 AIC: 11.43
You will get a warning about "non-integer #successes", but that is because glm is being silly. Compare to the model on your constructed dataset:
> fit2
Call: glm(formula = success ~ x, family = "binomial", data = datf2,
weights = cases)
Coefficients:
(Intercept) x
-9.3532 0.6713
Degrees of Freedom: 7 Total (i.e. Null); 6 Residual
Null Deviance: 33.65
Residual Deviance: 18.39 AIC: 22.39
The regression coefficients (and therefore predicted values) are basically equal. However your residual deviance and AIC are suspect because you've created artificial data points.