How is the sigma^2 value (or MSE) for the link function computed in logistic regression in R? For example, if you have a logistic regression on certain dataset:
fit <- glm(y ~ x, data = test, family = "binomial")

If you do predict(fit, newdata, type = "link", se = TRUE), you will get a column named se.fit, which is the standard error for each predicted y value.
My questions are:

*

*How is the MSE value for the link function is computed here?
The variance of the fitting coefficients are basically the MSE times the variance-covariance matrix, there should be a way to compute the MSE value first. But for response variables that have 0 and 1 values, the link function corresponds to 0 and infinity. In this case, how does the model compute this value? Is there any way I can get the MSE value for the glm fitting in R?


*Is se.fit the standard error for the link function value of the fitted line at point x0, or the standard error for the predicted link function value of y at point x0?
 A: There are some statistical misunderstandings here.

*

*The mean squared error (MSE) is primarily associated with linear (OLS) models.  It isn't really used with logistic regression.  For example, calculating the MSE for a model and then multiplying it by the variance-covariance matrix is something that is done in linear regression, but not logistic regression.  You should not be trying to get the MSE from a glm model fitted with family=binomial.
The linear predictor (which I believe is what you mean by "link function" here) is not bound by 0 and infinity, but ranges from -infinity to +infinity.


*The se.fit value is on the scale of the linear predictor (i.e., the log odds of Y=1 at X=x0).  It would be for both the "fitted line at point x0" and the "predicted link function value of y at point x0", as they are the same thing.
In general, the standard error of a predicted point on the scale of the linear predictor needs to take into account the uncertainty of the estimated slope and intercept, and also how far the x-value of the predicted point is from the mean of x.
