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I'm doing a Poisson regression and using the confint function in R to generate confidence intervals for my regression coefficient. These result in different intervals than when I would calculate them manually using the normal approximation, i.e. the lower bound given by $\hat{\beta} - 1.96*\hat{\sigma}_\beta/\sqrt(n)$ and the upper bound by $\hat{\beta} + 1.96*\hat{\sigma}_\beta/\sqrt(n)$.

If the beta's were normally distributed, I would expect that using the confint function or the manual calculation has to yield the same result.

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The glm in R doesn't have a $\sigma$ or $\hat{\sigma}$ for Poisson regression. So one must wonder what $\sigma$ you are using to manually calculate these values. If you are calculating this value as one would do in a linear regression model, by calculating the unstandardized residual using the predicted and observed responses, this would not be correct due to the heteroscedasticity of the residual.

If you are using the vcov function and using the "bottom right variance" (of the regression parameter) to calculate these CI bounds, this will give the same result as the confint function in R.

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  • $\begingroup$ Yeah for more flex I’d recommend using Stan. $\endgroup$
    – j9000
    May 23 at 17:44
  • $\begingroup$ @j9000: But that would change to the use of Bayesian methods, and the OP might not want that ... $\endgroup$ May 24 at 1:10
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The confint function you used calculates the profile likelihood confidence interval. That will coincide with the symmetric confidence interval you expected if the log likelihood function is quadratic. For many glm's that will not be the case, and sometimes the difference can be dramatic.

See the links in comments for details and examples.

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