# Interpret estimates of population level effects in zero inflated poisson models

Hi, I would like to understand how to interpret the coefficient in a zero inflated poisson model. All my predictors are scaled. Given the output below:

``````Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Eff.Sample
Intercept                           0.75      0.21     0.31     1.12       4998
x                                  0.07      0.08    -0.08     0.22      11347
``````

To interpret the estimate value of X, if it was a model with poisson link function, I would:
exp(0.07), subtract 1, and interpret the obtained number (0.072508) as:
“all other things being equal, if you increase the X of 1 unit the Y will increase of 7%” correct?

Do I interpret the zero inflated in the same way or I should apply some transformation?

Moreover the intercept estimate is 0.75 but in the marginal plot is around 1.6/1.7 (see figure). Why? What transformation was applied?

• Operating System: Windows 10
• brms Version: 2.9.0

The exp transform does not allow to interprete in the form of percent of anything, so I am unsure where you got this from. Rather exp(0.07) is the multipicative factor by which the predictions of the conditional (poisson) component change if you change x by 1.

The marginal plot shows the mean of the whole distribution that is combined zero-inflated and poisson component. To get predictions for the individual components, use argument “dpar”.

Thank you Paul.

Sorry for asking further clarification, “use argument “dpar”” to what function?

My aim is to interpret the results in the original scale to understand the biological relevance of them. To get the prediction for both components (zero-inflated and poisson) if I change x by 1…so, after exp(0.07) what should I do?

Thanks a lot.

To the function you are using that is marginal_effects

Thank you,
It’s still not clear to me how to back-transform the estimates to the original scale.
Which means to know numerically what happens to Y when I change X by 1.
I can see graphically that at each increase of X by 1, Y increases of ~0.125 but how do I get to this number from my 0.07 estimate returned in the summary?

This is the case also for other link function (such as skew normal)
Do you know a reference that I can look up to understand how to to do it?
Thanks again and I know this is due to my poor understanding of the math behind the model.