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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.

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