# What is the binomial residual in logits for an all-success trial?

In binomial regression, I have a trial where the model predicts 2 logits (88% predicted success rate) and one data point is 10 successes out of 10 trials (100% observed success rate). What is the residual for this particular data point?

My first hunch was to logit-transform this data point (logit(10/10)) and calculate the difference in logit-space. Naturally, this is wrong since the residual is infinite when $$successes = trials$$. The same would be true for Bernoulli models.

I am using JAGS to write an AR(N) (autoregressive) binomial model as part of a project to infer change points in time series. The autoregressive coefficient predicts the data point $$i$$ from the $$residual_{i-1}$$, so this is where the need to compute residuals steps in. I can see the literature on Pearson residuals as well as deviance residuals, but I am unsure how to relate them to the logit scale. There is a section that looks relevant here, but it is quite involved with matrix multiplication.

• Jan 20, 2020 at 14:04
• Thanks, @kjetilbhalvorsen. They are all about assessing residuals in frequentist settings where the likelihood is conditioned on a summary statistic of many data points. My question is about modeling "infinite" single data points (in a Bayesian setting). Jan 20, 2020 at 14:36