I am new to Bayesian modeling so I may be making a simple mistake.

I have count data with lots of zeros, so I decided to use a hurdle poisson model.

I ran the following code:

```
brm(count_long ~ img_num*TQ_mean,
data = mydata, family = hurdle_poisson, iter = 2000)
```

The img_num is a dummy variable and can be 0, 1, or 2. The TQ_mean is a continuous variable. I am interested in the interaction between them.

I could successfully the following results:

Population-Level Effects:

Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS

Intercept 1.99 0.03 1.93 2.05 1.00 1525 1906

img_num1 0.05 0.05 -0.05 0.14 1.00 1557 2055

img_num2 0.19 0.04 0.11 0.27 1.00 1420 2030

TQ_mean 0.05 0.02 0.02 0.09 1.00 1496 2378

img_num1:TQ_mean -0.13 0.03 -0.19 -0.07 1.00 1579 2171

img_num2:TQ_mean -0.16 0.02 -0.20 -0.11 1.00 1353 2173

For simplicity, let me explain about the condition in which img_num = 0.

The conditional_effects function showed me the picture in which the value of count_long (y-axis) is near 2 at the point where TQ_mean is 1. (It would be easier to understand if I could attach the image file)

I don’t think this figure is correct because as to img_num = 0 the value of count_long should be:

exp(1.99 + 0.05) = 7.69 (But it is about 2 in the figure)

I also tried to run the following code. Note that I used a poisson model instead of a hurdle poisson model.

```
tmpdata %>%
filter(count_long > 0) %>%
brm(count_long ~ img_num*TQ_mean,
data = ., family = poisson, iter = 2000)
```

I obtained the same coefficients as in the hurdle model, but the the conditional_effects function showed me a figure which have a different Y scale. In this figure, the value of count_long (y-axis) is near 8 at the point where TQ_mean is 1. This figure is understandable.

My question is that the figure using the hurdle poisson model is correct. If it is right, what do I misunderstand?

Operating System: Windows 11

Interface Version: brms 2.18.0

Compiler/Toolkit:

Thanks in advance.