Dear braintrust,

A couple of years ago I submitted a post on the way to determine risk factors associated with a latent disease status that is assessed by a test with imperfect sensitivity and specificity (see original post).

So basically, this is a logistic regression where the outcome (Y) is measured by an imperfect test. For my database, I have my imperfect test “TUS” which is an imperfect test (Sensitivity Se, Specificity Sp).

My predictors (X) are *T_rectal, Ear, Eye, Cough, Nasal. My latent dependent variable is the true disease status.*

My commented code looks like the following:

```
#first of all I write the non linear formula
bform <- bf(
TUS ~ q, #test result of the individual which is a Bernoulli event
nlf(p ~ inv_logit(T_rectal+Ear+Eye+Cough+Nasal)), #logistic model written directly
nlf(q ~ p * Se + (1 - p) * (1 - Sp)), #q depends on the TP (true positive) and FP (false positive
Se + Sp ~ 1, #put the Se and Sp as value to add in the model but with no data from them (only derived from the prior)
nl = TRUE, #we use a non linear formula
family = bernoulli("identity")
)
bprior <- set_prior("beta(4.62,0.86)", nlpar = "Se", lb = 0, ub = 1) + #prior Se
set_prior("beta(77.55,4.4)", nlpar = "Sp", lb = 0, ub = 1) #prior Sp
summary( brm(bform, data = bd, #dataset is named bd
prior = bprior, # uses default priors except for and Sp
warmup = 500,
iter = 3000,
chains = 4,
init= "0",
cores=2,
seed = 123))
```

What I don’t understand is that when looking for the model output I only obtain the posterior from 2 parameters (Se and Sp)

I don’t obtain the regression coefficients from my predictors X (T_rectal, Ear, Eye, Cough, Nasal)

```
Family: bernoulli
Links: mu = identity
Formula: TUS ~ q
p ~ inv_logit(T_rectal + Ear + Eye + Cough + Nasal)
q ~ p * Se + (1 - p) * (1 - Sp)
Se ~ 1
Sp ~ 1
Data: bd (Number of observations: 482)
Draws: 4 chains, each with iter = 3000; warmup = 500; thin = 1;
total post-warmup draws = 10000
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Se_Intercept 0.40 0.03 0.33 0.47 1.00 5935 6306
Sp_Intercept 0.96 0.02 0.93 0.99 1.00 5775 4804
Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
prior class coef group resp dpar nlpar lb ub source
beta(4.62,0.86) b Se 0 1 user
beta(4.62,0.86) b Intercept Se 0 1 (vectorized)
beta(77.55,4.4) b Sp 0 1 user
beta(77.55,4.4) b Intercept Sp 0 1 (vectorized)
```

So I’ve struggled months to find what was not correct from my model and would like to know if you would have any idea to be able to look for the coefficients of X and characteristics of the logistic part of my model.

Many many thanks in advance