Skip to contents

Additional Response Information

Source: R/formula-ad.R
addition-terms.Rd

Provide additional information on the response variable in brms models, such as censoring, truncation, or known measurement error. Detailed documentation on the use of each of these functions can be found in the Details section of brmsformula (under "Additional response information").

Usage

resp_se(x, sigma = FALSE)

resp_weights(x, scale = FALSE)

resp_trials(x)

resp_thres(x, gr = NA)

resp_cat(x)

resp_dec(x)

resp_bhaz(gr = NA, df = 5, ...)

resp_cens(x, y2 = NA)

resp_trunc(lb = -Inf, ub = Inf)

resp_mi(sdy = NA)

resp_index(x)

resp_rate(denom)

resp_subset(x)

resp_vreal(...)

resp_vint(...)

Arguments

x

A vector; Ideally a single variable defined in the data (see Details). Allowed values depend on the function: resp_se and resp_weights require positive numeric values. resp_trials, resp_thres, and resp_cat require positive integers. resp_dec requires 0 and 1, or alternatively 'lower' and 'upper'. resp_subset requires 0 and 1, or alternatively FALSE and TRUE. resp_cens requires 'left', 'none', 'right', and 'interval' (or equivalently -1, 0, 1, and 2) to indicate left, no, right, or interval censoring. resp_index does not make any requirements other than the value being unique for each observation.

sigma

Logical; Indicates whether the residual standard deviation parameter sigma should be included in addition to the known measurement error. Defaults to FALSE for backwards compatibility, but setting it to TRUE is usually the better choice.

scale

Logical; Indicates whether weights should be scaled so that the average weight equals one. Defaults to FALSE.

gr

A vector of grouping indicators.

df

Degrees of freedom of baseline hazard splines for Cox models. The knots of these splines are placed at the quantiles of the event times. In brms versions 2.23.1 and earlier, the knots were placed at the quantiles of both event and censoring times, which is generally not recommended. For backwards compatibility, models fitted with those older versions keep using the old placement in post-processing.

...

For resp_vreal, vectors of real values. For resp_vint, vectors of integer values. In Stan, these variables will be named vreal1, vreal2, ..., and vint1, vint2, ..., respectively.

y2

A vector specifying the upper bounds in interval censoring. Will be ignored for non-interval censored observations. However, it should NOT be NA even for non-interval censored observations to avoid accidental exclusion of these observations.

lb

A numeric vector or single numeric value specifying the lower truncation bound.

ub

A numeric vector or single numeric value specifying the upper truncation bound.

sdy

Optional known measurement error of the response treated as standard deviation. If specified, handles measurement error and (completely) missing values at the same time using the plausible-values-technique.

denom

A vector of positive numeric values specifying the denominator values from which the response rates are computed.

Value

A list of additional response information to be processed further by brms.

Details

These functions are almost solely useful when called in formulas passed to the brms package. Within formulas, the resp_ prefix may be omitted. More information is given in the 'Details' section of brmsformula (under "Additional response information").

It is highly recommended to use a single data variable as input for x (instead of a more complicated expression) to make sure all post-processing functions work as expected.

See also

brm, brmsformula

Examples

# \dontrun{
## Random effects meta-analysis
nstudies <- 20
true_effects <- rnorm(nstudies, 0.5, 0.2)
sei <- runif(nstudies, 0.05, 0.3)
outcomes <- rnorm(nstudies, true_effects, sei)
data1 <- data.frame(outcomes, sei)
fit1 <- brm(outcomes | se(sei, sigma = TRUE) ~ 1,
            data = data1)
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 1.1e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.015 seconds (Warm-up)
#> Chain 1:                0.018 seconds (Sampling)
#> Chain 1:                0.033 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 5e-06 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.05 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.015 seconds (Warm-up)
#> Chain 2:                0.014 seconds (Sampling)
#> Chain 2:                0.029 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 5e-06 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.05 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3: 
#> Chain 3: 
#> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.016 seconds (Warm-up)
#> Chain 3:                0.015 seconds (Sampling)
#> Chain 3:                0.031 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 5e-06 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.05 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
#> Chain 4: 
#> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.015 seconds (Warm-up)
#> Chain 4:                0.017 seconds (Sampling)
#> Chain 4:                0.032 seconds (Total)
#> Chain 4: 
summary(fit1)
#>  Family: gaussian 
#>   Links: mu = identity 
#> Formula: outcomes | se(sei, sigma = TRUE) ~ 1 
#>    Data: data1 (Number of observations: 20) 
#>   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#>          total post-warmup draws = 4000
#> 
#> Regression Coefficients:
#>           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept     0.56      0.08     0.38     0.72 1.00     2632     2008
#> 
#> Further Distributional Parameters:
#>       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sigma     0.31      0.07     0.18     0.48 1.00     2528     2091
#> 
#> 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).

## Probit regression using the binomial family
n <- sample(1:10, 100, TRUE)  # number of trials
success <- rbinom(100, size = n, prob = 0.4)
x <- rnorm(100)
data2 <- data.frame(n, success, x)
fit2 <- brm(success | trials(n) ~ x, data = data2,
            family = binomial("probit"))
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 2.5e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.25 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.058 seconds (Warm-up)
#> Chain 1:                0.06 seconds (Sampling)
#> Chain 1:                0.118 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 5.2e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.52 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.058 seconds (Warm-up)
#> Chain 2:                0.062 seconds (Sampling)
#> Chain 2:                0.12 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 1.7e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3: 
#> Chain 3: 
#> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.056 seconds (Warm-up)
#> Chain 3:                0.055 seconds (Sampling)
#> Chain 3:                0.111 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 1.8e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.18 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
#> Chain 4: 
#> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.059 seconds (Warm-up)
#> Chain 4:                0.068 seconds (Sampling)
#> Chain 4:                0.127 seconds (Total)
#> Chain 4: 
summary(fit2)
#>  Family: binomial 
#>   Links: mu = probit 
#> Formula: success | trials(n) ~ x 
#>    Data: data2 (Number of observations: 100) 
#>   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#>          total post-warmup draws = 4000
#> 
#> Regression Coefficients:
#>           Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept    -0.34      0.05    -0.45    -0.24 1.00     3490     2664
#> x            -0.02      0.06    -0.13     0.09 1.00     2914     2397
#> 
#> 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).

## Survival regression modeling the time between the first
## and second recurrence of an infection in kidney patients.
fit3 <- brm(time | cens(censored) ~ age * sex + disease + (1|patient),
            data = kidney, family = lognormal())
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: Rejecting initial value:
#> Chain 1:   Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 1:   Stan can't start sampling from this initial value.
#> Chain 1: Rejecting initial value:
#> Chain 1:   Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 1:   Stan can't start sampling from this initial value.
#> Chain 1: 
#> Chain 1: Gradient evaluation took 2.4e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.24 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.874 seconds (Warm-up)
#> Chain 1:                0.37 seconds (Sampling)
#> Chain 1:                1.244 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: Rejecting initial value:
#> Chain 2:   Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 2:   Stan can't start sampling from this initial value.
#> Chain 2: Rejecting initial value:
#> Chain 2:   Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 2:   Stan can't start sampling from this initial value.
#> Chain 2: 
#> Chain 2: Gradient evaluation took 1.7e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.88 seconds (Warm-up)
#> Chain 2:                0.369 seconds (Sampling)
#> Chain 2:                1.249 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: Rejecting initial value:
#> Chain 3:   Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 3:   Stan can't start sampling from this initial value.
#> Chain 3: 
#> Chain 3: Gradient evaluation took 1.6e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3: 
#> Chain 3: 
#> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.977 seconds (Warm-up)
#> Chain 3:                0.361 seconds (Sampling)
#> Chain 3:                1.338 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 1.7e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
#> Chain 4: 
#> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.938 seconds (Warm-up)
#> Chain 4:                0.372 seconds (Sampling)
#> Chain 4:                1.31 seconds (Total)
#> Chain 4: 
summary(fit3)
#>  Family: lognormal 
#>   Links: mu = identity 
#> Formula: time | cens(censored) ~ age * sex + disease + (1 | patient) 
#>    Data: kidney (Number of observations: 76) 
#>   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#>          total post-warmup draws = 4000
#> 
#> Multilevel Hyperparameters:
#> ~patient (Number of levels: 38) 
#>               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sd(Intercept)     0.41      0.25     0.02     0.94 1.00      994     1867
#> 
#> Regression Coefficients:
#>               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept         2.66      0.96     0.78     4.55 1.00     2779     2619
#> age               0.02      0.02    -0.03     0.06 1.00     2388     2566
#> sexfemale         2.55      1.14     0.34     4.75 1.00     2502     2518
#> diseaseGN        -0.43      0.51    -1.45     0.57 1.00     2820     3194
#> diseaseAN        -0.53      0.50    -1.52     0.46 1.00     3290     2894
#> diseasePKD        0.58      0.70    -0.76     2.02 1.00     3512     2620
#> age:sexfemale    -0.02      0.03    -0.07     0.03 1.00     2498     2382
#> 
#> Further Distributional Parameters:
#>       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sigma     1.16      0.13     0.92     1.44 1.00     2743     2860
#> 
#> 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).

## Poisson model with truncated counts
fit4 <- brm(count | trunc(ub = 104) ~ zBase * Trt,
            data = epilepsy, family = poisson())
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 0.000472 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 4.72 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 1: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 1: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 1: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 1: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 1: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 1: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 1: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 1: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 1: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 3.22 seconds (Warm-up)
#> Chain 1:                3.356 seconds (Sampling)
#> Chain 1:                6.576 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 0.000297 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 2.97 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 2: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 2: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 2: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 2: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 2: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 2: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 2: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 2: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 2: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 2: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 2: 
#> Chain 2:  Elapsed Time: 3.066 seconds (Warm-up)
#> Chain 2:                3.102 seconds (Sampling)
#> Chain 2:                6.168 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: Rejecting initial value:
#> Chain 3:   Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 3:   Stan can't start sampling from this initial value.
#> Chain 3: 
#> Chain 3: Gradient evaluation took 0.000314 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 3.14 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3: 
#> Chain 3: 
#> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 3: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 3: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 3: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 3: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 3: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 3: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 3: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 3: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 3: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 3: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 3: 
#> Chain 3:  Elapsed Time: 2.962 seconds (Warm-up)
#> Chain 3:                3.158 seconds (Sampling)
#> Chain 3:                6.12 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: Rejecting initial value:
#> Chain 4:   Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 4:   Stan can't start sampling from this initial value.
#> Chain 4: 
#> Chain 4: Gradient evaluation took 0.00027 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 2.7 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4: 
#> Chain 4: 
#> Chain 4: Iteration:    1 / 2000 [  0%]  (Warmup)
#> Chain 4: Iteration:  200 / 2000 [ 10%]  (Warmup)
#> Chain 4: Iteration:  400 / 2000 [ 20%]  (Warmup)
#> Chain 4: Iteration:  600 / 2000 [ 30%]  (Warmup)
#> Chain 4: Iteration:  800 / 2000 [ 40%]  (Warmup)
#> Chain 4: Iteration: 1000 / 2000 [ 50%]  (Warmup)
#> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling)
#> Chain 4: Iteration: 1400 / 2000 [ 70%]  (Sampling)
#> Chain 4: Iteration: 1600 / 2000 [ 80%]  (Sampling)
#> Chain 4: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 4: 
#> Chain 4:  Elapsed Time: 3.021 seconds (Warm-up)
#> Chain 4:                3.105 seconds (Sampling)
#> Chain 4:                6.126 seconds (Total)
#> Chain 4: 
summary(fit4)
#>  Family: poisson 
#>   Links: mu = log 
#> Formula: count | trunc(ub = 104) ~ zBase * Trt 
#>    Data: epilepsy (Number of observations: 236) 
#>   Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#>          total post-warmup draws = 4000
#> 
#> Regression Coefficients:
#>            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept      1.96      0.04     1.89     2.03 1.00     2139     2384
#> zBase          0.57      0.02     0.53     0.62 1.00     1816     2130
#> Trt1          -0.23      0.06    -0.34    -0.12 1.00     2289     2334
#> zBase:Trt1     0.01      0.03    -0.05     0.07 1.00     1768     2144
#> 
#> 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).
# }