Skip to contents

Fit a GLM based SDM

Source: R/model-run.R
fit_sdm.Rd

Fit the SDM Stan model (this function is not stable yet and have not been fully tested).

Usage

fit_sdm(
  .data,
  y_col,
  time_col,
  site_col,
  family = "gamma",
  formula_zero = ~1,
  formula_dens = ~1,
  iter_warmup = 1000,
  iter_sampling = 1000,
  chains = 4,
  parallel_chains = 4,
  seed,
  init = "cmdstan_default",
  ...
)

Arguments

.data

A data frame containing the data for the model.

y_col

A character specifying the name of the column in .data that contains the response variable.

time_col

A character specifying the name of the column in .data that contains the time variable.

site_col

A character specifying the name of the column in .data that contains the site variable.

family

a character specifying the family of the probability distribution assumed for density. The options are:

  • "gamma" (default): gamma parametrized in terms of its mean;

  • "lognormal": log-normal parametrized in terms of its mean;

  • "loglogistic": log-logistic parametrized in terms of its mean.

  • "lognormal_legacy" (default): log-normal with its usual parametrization;

formula_zero

A formula specifying the model for the zero inflation component. Defaults to ~ 1 (intercept only).

formula_dens

A formula specifying the model for the non-zero density component. Defaults to ~ 1 (intercept only).

iter_warmup

An integer specifying the number of warmup iterations for the MCMC sampler. Defaults to 1000.

iter_sampling

An integer specifying the number of sampling iterations for the MCMC sampler. Defaults to 1000.

chains

An integer specifying the number of MCMC chains. Defaults to 4.

parallel_chains

An integer specifying the number of chains to run in parallel. Defaults to 4.

seed

An integer specifying the random number seed.

init

A scalar specifying the initialization method. The default (NULL) represents the cmdstan default, a scalar greater than zero, say x, initialized all parameters from a uniform between -x and x, a 0 initialize all parameters at 0, "prior" (to initialize the model parameters using samples from their prior) or "pathfinder".

...

Passed on to the make_data() function used to build the input list for our cmdstanr model.

Value

A list containing the MCMC draws, the model data, the linear predictors formulas, and the (response, time, site) column names.

  • stanfit: The MCMC draws from the fitted model.

  • data: The data used to fit the model (as a list).

  • formulas: The data used to fit the model (as a list).

  • cols: Important column names.

See also

make_data()

Other models: fit_drm()

Author

lcgodoy

Examples

if (instantiate::stan_cmdstan_exists()) {
  data(sum_fl)
  fit_sdm(.data = sum_fl,
          y_col = "y",
          time_col = "year",
          site_col = "patch",
          seed = 2025)$stanfit$summary()
}
#> Running MCMC with 4 parallel chains...
#> 
#> Chain 1 Iteration:    1 / 2000 [  0%]  (Warmup) 
#> Chain 1 Iteration:  100 / 2000 [  5%]  (Warmup) 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 2 Iteration:    1 / 2000 [  0%]  (Warmup) 
#> Chain 2 Iteration:  100 / 2000 [  5%]  (Warmup) 
#> Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 2 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 2 
#> Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 2 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 2 
#> Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 2 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 2 
#> Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 2 Exception: gamma_lpdf: Inverse scale parameter[1] is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 306, column 4 to column 49)
#> Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 2 
#> Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 2 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 2 
#> Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 2 Exception: gamma_lpdf: Inverse scale parameter[1] is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 306, column 4 to column 49)
#> Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 2 
#> Chain 3 Iteration:    1 / 2000 [  0%]  (Warmup) 
#> Chain 3 Iteration:  100 / 2000 [  5%]  (Warmup) 
#> Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 3 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 3 
#> Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 3 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 3 
#> Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 3 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 3 
#> Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 3 Exception: gamma_lpdf: Inverse scale parameter[1] is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 306, column 4 to column 49)
#> Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 3 
#> Chain 4 Iteration:    1 / 2000 [  0%]  (Warmup) 
#> Chain 4 Iteration:  100 / 2000 [  5%]  (Warmup) 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: gamma_lpdf: Random variable is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 285, column 4 to column 54)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: gamma_lpdf: Inverse scale parameter[1] is 0, but must be positive finite! (in '/tmp/RtmpBXDoDm/model-247b2f7245c9.stan', line 306, column 4 to column 49)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 1 Iteration:  200 / 2000 [ 10%]  (Warmup) 
#> Chain 2 Iteration:  200 / 2000 [ 10%]  (Warmup) 
#> Chain 3 Iteration:  200 / 2000 [ 10%]  (Warmup) 
#> Chain 4 Iteration:  200 / 2000 [ 10%]  (Warmup) 
#> Chain 1 Iteration:  300 / 2000 [ 15%]  (Warmup) 
#> Chain 2 Iteration:  300 / 2000 [ 15%]  (Warmup) 
#> Chain 1 Iteration:  400 / 2000 [ 20%]  (Warmup) 
#> Chain 3 Iteration:  300 / 2000 [ 15%]  (Warmup) 
#> Chain 4 Iteration:  300 / 2000 [ 15%]  (Warmup) 
#> Chain 2 Iteration:  400 / 2000 [ 20%]  (Warmup) 
#> Chain 1 Iteration:  500 / 2000 [ 25%]  (Warmup) 
#> Chain 3 Iteration:  400 / 2000 [ 20%]  (Warmup) 
#> Chain 4 Iteration:  400 / 2000 [ 20%]  (Warmup) 
#> Chain 1 Iteration:  600 / 2000 [ 30%]  (Warmup) 
#> Chain 2 Iteration:  500 / 2000 [ 25%]  (Warmup) 
#> Chain 4 Iteration:  500 / 2000 [ 25%]  (Warmup) 
#> Chain 1 Iteration:  700 / 2000 [ 35%]  (Warmup) 
#> Chain 2 Iteration:  600 / 2000 [ 30%]  (Warmup) 
#> Chain 3 Iteration:  500 / 2000 [ 25%]  (Warmup) 
#> Chain 4 Iteration:  600 / 2000 [ 30%]  (Warmup) 
#> Chain 1 Iteration:  800 / 2000 [ 40%]  (Warmup) 
#> Chain 2 Iteration:  700 / 2000 [ 35%]  (Warmup) 
#> Chain 3 Iteration:  600 / 2000 [ 30%]  (Warmup) 
#> Chain 1 Iteration:  900 / 2000 [ 45%]  (Warmup) 
#> Chain 2 Iteration:  800 / 2000 [ 40%]  (Warmup) 
#> Chain 3 Iteration:  700 / 2000 [ 35%]  (Warmup) 
#> Chain 4 Iteration:  700 / 2000 [ 35%]  (Warmup) 
#> Chain 4 Iteration:  800 / 2000 [ 40%]  (Warmup) 
#> Chain 1 Iteration: 1000 / 2000 [ 50%]  (Warmup) 
#> Chain 1 Iteration: 1001 / 2000 [ 50%]  (Sampling) 
#> Chain 2 Iteration:  900 / 2000 [ 45%]  (Warmup) 
#> Chain 3 Iteration:  800 / 2000 [ 40%]  (Warmup) 
#> Chain 4 Iteration:  900 / 2000 [ 45%]  (Warmup) 
#> Chain 2 Iteration: 1000 / 2000 [ 50%]  (Warmup) 
#> Chain 2 Iteration: 1001 / 2000 [ 50%]  (Sampling) 
#> Chain 3 Iteration:  900 / 2000 [ 45%]  (Warmup) 
#> Chain 1 Iteration: 1100 / 2000 [ 55%]  (Sampling) 
#> Chain 3 Iteration: 1000 / 2000 [ 50%]  (Warmup) 
#> Chain 3 Iteration: 1001 / 2000 [ 50%]  (Sampling) 
#> Chain 4 Iteration: 1000 / 2000 [ 50%]  (Warmup) 
#> Chain 4 Iteration: 1001 / 2000 [ 50%]  (Sampling) 
#> Chain 2 Iteration: 1100 / 2000 [ 55%]  (Sampling) 
#> Chain 1 Iteration: 1200 / 2000 [ 60%]  (Sampling) 
#> Chain 4 Iteration: 1100 / 2000 [ 55%]  (Sampling) 
#> Chain 2 Iteration: 1200 / 2000 [ 60%]  (Sampling) 
#> Chain 3 Iteration: 1100 / 2000 [ 55%]  (Sampling) 
#> Chain 1 Iteration: 1300 / 2000 [ 65%]  (Sampling) 
#> Chain 4 Iteration: 1200 / 2000 [ 60%]  (Sampling) 
#> Chain 2 Iteration: 1300 / 2000 [ 65%]  (Sampling) 
#> Chain 3 Iteration: 1200 / 2000 [ 60%]  (Sampling) 
#> Chain 1 Iteration: 1400 / 2000 [ 70%]  (Sampling) 
#> Chain 2 Iteration: 1400 / 2000 [ 70%]  (Sampling) 
#> Chain 3 Iteration: 1300 / 2000 [ 65%]  (Sampling) 
#> Chain 4 Iteration: 1300 / 2000 [ 65%]  (Sampling) 
#> Chain 1 Iteration: 1500 / 2000 [ 75%]  (Sampling) 
#> Chain 2 Iteration: 1500 / 2000 [ 75%]  (Sampling) 
#> Chain 4 Iteration: 1400 / 2000 [ 70%]  (Sampling) 
#> Chain 1 Iteration: 1600 / 2000 [ 80%]  (Sampling) 
#> Chain 2 Iteration: 1600 / 2000 [ 80%]  (Sampling) 
#> Chain 3 Iteration: 1400 / 2000 [ 70%]  (Sampling) 
#> Chain 1 Iteration: 1700 / 2000 [ 85%]  (Sampling) 
#> Chain 2 Iteration: 1700 / 2000 [ 85%]  (Sampling) 
#> Chain 3 Iteration: 1500 / 2000 [ 75%]  (Sampling) 
#> Chain 4 Iteration: 1500 / 2000 [ 75%]  (Sampling) 
#> Chain 1 Iteration: 1800 / 2000 [ 90%]  (Sampling) 
#> Chain 2 Iteration: 1800 / 2000 [ 90%]  (Sampling) 
#> Chain 3 Iteration: 1600 / 2000 [ 80%]  (Sampling) 
#> Chain 4 Iteration: 1600 / 2000 [ 80%]  (Sampling) 
#> Chain 1 Iteration: 1900 / 2000 [ 95%]  (Sampling) 
#> Chain 2 Iteration: 1900 / 2000 [ 95%]  (Sampling) 
#> Chain 3 Iteration: 1700 / 2000 [ 85%]  (Sampling) 
#> Chain 2 Iteration: 2000 / 2000 [100%]  (Sampling) 
#> Chain 4 Iteration: 1700 / 2000 [ 85%]  (Sampling) 
#> Chain 2 finished in 3.5 seconds.
#> Chain 1 Iteration: 2000 / 2000 [100%]  (Sampling) 
#> Chain 3 Iteration: 1800 / 2000 [ 90%]  (Sampling) 
#> Chain 4 Iteration: 1800 / 2000 [ 90%]  (Sampling) 
#> Chain 1 finished in 3.7 seconds.
#> Chain 3 Iteration: 1900 / 2000 [ 95%]  (Sampling) 
#> Chain 4 Iteration: 1900 / 2000 [ 95%]  (Sampling) 
#> Chain 3 Iteration: 2000 / 2000 [100%]  (Sampling) 
#> Chain 4 Iteration: 2000 / 2000 [100%]  (Sampling) 
#> Chain 3 finished in 3.9 seconds.
#> Chain 4 finished in 3.9 seconds.
#> 
#> All 4 chains finished successfully.
#> Mean chain execution time: 3.7 seconds.
#> Total execution time: 4.0 seconds.
#> 
#> # A tibble: 1,406 × 10
#>    variable       mean    median     sd    mad        q5      q95  rhat ess_bulk
#>    <chr>         <dbl>     <dbl>  <dbl>  <dbl>     <dbl>    <dbl> <dbl>    <dbl>
#>  1 lp__      -1366.    -1365.    1.43   1.22   -1369.    -1.36e+3  1.00    1531.
#>  2 lxi[1]       -1.24     -1.19  0.545  0.528     -2.23  -4.60e-1  1.00     899.
#>  3 phi[1]        0.716     0.713 0.0573 0.0580     0.629  8.16e-1  1.00    2082.
#>  4 beta_r[1]     3.90      3.90  0.0759 0.0758     3.78   4.02e+0  1.00    2206.
#>  5 beta_t[1]     0.611     0.521 0.626  0.637     -0.261  1.81e+0  1.00     919.
#>  6 xi[1]        -0.329    -0.305 0.160  0.160     -0.631 -1.08e-1  1.00     899.
#>  7 rho[1]        0.339     0.339 0.0252 0.0238     0.298  3.81e-1  1.00    3980.
#>  8 rho[2]        0.339     0.339 0.0252 0.0238     0.298  3.81e-1  1.00    3980.
#>  9 rho[3]        0.339     0.339 0.0252 0.0238     0.298  3.81e-1  1.00    3980.
#> 10 rho[4]        0.339     0.339 0.0252 0.0238     0.298  3.81e-1  1.00    3980.
#> # ℹ 1,396 more rows
#> # ℹ 1 more variable: ess_tail <dbl>