Help in understanding zero inflated neg binomial model summary I'm writing this topic because I would need to get some more information about model conversion in brms (zero-inflated_negbinomial) model.
Let's say I have this model result :
Where I want to model how many fish are being caught by fishermen at a state park. Visitors are asked how long they stayed, their job area and how many fish were caught. Some visitors do not fish, but there is no data on whether a person fished or not. Some visitors who did fish did not catch any fish, so there are excess zeros in the data because of the people that did not fish.”
I used the bmrs package in R
summary(fit_zinb1)

 Family: zero_inflated_negbinomial 
  Links: mu = log; shape = identity; zi = identity 
Formula:  count ~ job_area + time
   Data: data (Number of observations: 225) 
  Draws: 2 chains, each with iter = 1200; warmup = 600; thin = 5;
         total post-warmup draws = 240

Population-Level Effects: 
                       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept              -1.01      0.17    -1.35    -0.67 1.00     2878     2555
job_area_agriculture   0.87      0.04     0.79     0.96 1.00     3021     2668
job_area_business      -1.37      0.10    -1.56    -1.18 1.00     2736     2836
Time                    0.80      0.09     0.63     0.99 1.00     2792     2416

Family Specific Parameters: 
   Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
zi     0.41      0.05     0.32     0.49 1.00     2889     2706

where Job area has 3 modalities : (Politic (Intercept), Agriculture and Business)
from the following summary, could I say the following sentences :

*

*On average, 0.41% of zeros are zero from people who fish but did not catch anything and 59% are coming from people who do not fish at all.

*Do I have to transform the Estimate coefs if I want to say that on average, people with a job in business are catch -1.37 less fish than Politics?  and If yes how do I transform it ? By an exponential ?

*For each unite of time, the number of fish caught is equal to 0.80.


*

*See my comment.


*To interpret the estimated coefficients, apply the inverse link.  In this case you've used a log link so you would need to exponentiate the coefficients.  So people in the business category would catch fewer fish than the reference category. How many fewer?  By a factor of $\exp(-1.37) \approx 0.25$.  So they would catch only about a quarter as many fish as the reference category.


*For each unit of time, the number of fish caught increases by a factor of $\exp(0.8) \approx 2.25$, so it doubles and adds a quarter as compared to someone who fished only one unit of time less.

