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I am running a logistic regression and have determined that Risk Ratios are better to explain my results than odds ratios. I have a dichotomous variable but I have both categorical and continuous predictor variables. My question is, if I use the Relative risk estimation by Poisson regression with robust error variance which coefficients do I report. The ones from the original logistic regression or the ones produced using the Poisson regression, which I only ran to get the RR. If it's the Poisson coefficients have I changed the regression from a logistic to a Poisson regression? or is it just a genearal linear model used to get the RR? And if so what type of diagnostics do I run. I've never used Poisson regressions before but it seems the only way to get the risk ratio's for both my categorical and continuous variables. I am a little confused.

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Logistic regression and Poisson regression are modelling different things. In the first one, you are modelling the logit of the probability that your dichotomous variable is 1, where you can estimate probabilities and odds ratios.

With Poisson regression you are modelling expected frequencies in a cell, your output will be expected values. In this case you can compare the expected number of events given one profile versus another one. If your frequencies are events in some interval of space/time, you can model the rate and only in this case you can compare Relative Rates, also named RR. I don't think there's such estimation as a Relative Risk with Poisson Regression.

Logit and Poisson regression are different models that apply to different views of the same scenario - depending on how you define your response variable Y. (With a binomial distribution in the first case and Poisson in the second)

If you use Poisson regression, then provide results for that model, not only Relative Rates but also goodness of fit (use Deviance) and significance of effects (Wald test are ok).

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My question is, if I use the Relative risk estimation by Poisson regression with robust error variance which coefficients do I report.

It depends on what you want to convey. If you want to talk about relative risks, then you should report the outputs of the Poisson regression.

If it's the Poisson coefficients have I changed the regression from a logistic to a Poisson regression?

Yes

or is it just a genearal linear model used to get the RR?

No, it is a Poisson regression.

And if so what type of diagnostics do I run.

Since Poisson regression is a GLM, a deviance goodness of fit test will tell you if your model fits the data.

You can also take a look at the deviance residuals.

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