For logistic regression, Predict.glm() outputs $p$ or $ln(p/1-p)$?
It returns the log odds. You can see that with this basic example,

# Create a perfect correlated data.
data &lt;- data.frame(x = c(1,0,1,0), y = c(T, F, T, F))

# Estimate the model.
model &lt;- glm(y ~ x, data)

# Show predictions.
predict(model)
##        1         2         3         4 
## 23.56607 -23.56607  23.56607 -23.56607

# Compute the inverse of the log odd to come to your prediction. 
boot::inv.logit(predict(model))
##           1            2            3            4 
##1.000000e+00 5.826215e-11 1.000000e+00 5.826215e-11 


If logit would return probabilities you could not take the inverse to come to your predicted values.