# How would I compute the Standard Error (SE) from a "response" type predicted value in r

I am using the predict function in r to obtain a "response" type output (probability of event occurring), but using se.fit=TRUE doesn't work in that case.

As stated in the comment in this thread,

When using type="response", the prediction is back-transformed with the anti-link function (e.g. plogis for the logit-link). Using type="response"and se.fit=T yields non-sensical values

It follows that I should predict both the raw and response scores if I am interested in obtaining the SE. How would I go about applying the correct transformation to the SE values so that they are on the same scale as my "response" type probabilities?

Thank you

• You can back-transform the limits of the prediction intervals if the software gives that but you cannot obtain the standard error. Jun 7, 2018 at 15:46
• Thanks. I've actually been thinking of moving to a Kaplan Meier, or Cox survival analysis since the data mostly lends itself to the type of analysis which makes it very simple to obtain a probability and Confidence Interval (CI) (except that interactions are more troublesome). Jun 7, 2018 at 17:43

As stated by medewy in the comments,

You can back-transform the limits of the prediction intervals if the software gives that but you cannot obtain the standard error

Co create a function to use the predict function:

Using a Kaplam Meier model gives an easy confidence interval, but is more descriptive than anything.

For simpler models, COX survival analyses also provides the confidence interval when using the prediction feature, and works well if you have data that fits the distribution assumptions very well.

For more complex models, you can play with different distributions using survreg to fit fully parametric models. However, you are limited in the number of clustering variables (can't have interactions with multiple clusters), and still need to have a intrinsically linear relationship.

If you need even more control over certain moderators, then structural equations or decision trees with survival analyses are pretty much necessary. Predicted scores are still available, but you need to look into the specific prediction functions used for the different SEM packages.