- Operating System: Mac
- brms Version: 2.10.3

I’ve inherited some count data of self-reported behaviors. The response format was limited in that the lowest count one could endorse was 1 and the highest count one could endorse was 6. The way I see it, this implies each 1 is a mixture of 1s and 0s and each 6 is a mixture of 6s and above. I believe these could be considered censored count data and I’d like to model them with the Poisson likelihood.

Here’s a simplified version of the data. The `y`

values are the true counts. The `y_cens`

values are the counts after censoring as described, above.

```
# load packages
library(tidyverse)
library(brms)
# simulate data
set.seed(1)
s <-
tibble(y = rpois(n = 1e3, lambda = 3)) %>%
mutate(y_cens = ifelse(y < 1, 1,
ifelse(y > 6, 6, y)))
```

The `cens()`

argument in `brms::brm()`

requires an additional column in the data indicating the censoring status of each observation. Here’s my attempt.

```
s <-
mutate(censored = ifelse(y == 1, "left",
ifelse(y > 6, "right", "none")))
```

Here’s my model setup.

```
fit <-
brm(data = s,
family = poisson,
y_cens | cens(censored) ~ 1)
```

The model output seems to looks good.

```
print(fit)
```

```
Family: poisson
Links: mu = log
Formula: y_cens | cens(censored) ~ 1
Data: s (Number of observations: 1000)
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 4000
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 1.11 0.02 1.07 1.14 1.00 1649 2219
Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
is a crude measure of effective sample size, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
```

Does it appear I’ve correctly interpreted how to work with censored count data?