Calculate, print and plot the Monte Carlo error of the samples from a JointAI model.

MC_error(
x,
subset = NULL,
exclude_chains = NULL,
start = NULL,
end = NULL,
thin = NULL,
digits = 2,
warn = TRUE,
mess = TRUE,
...
)

# S3 method for MCElist
plot(x, data_scale = TRUE, plotpars = NULL, ablinepars = list(v = 0.05), ...)

## Arguments

x object inheriting from class 'JointAI' subset of parameters/variables/nodes (columns in the MCMC sample). Uses the same logic as the argument monitor_params in *_imp. optional vector of the index numbers of chains that should be excluded the first iteration of interest (see window.mcmc) the last iteration of interest (see window.mcmc) thinning interval (see window.mcmc) number of digits for output logical; should warnings be given? Default is TRUE. (Note: this applies only to warnings given directly by JointAI.) logical; should messages be given? Default is TRUE. (Note: this applies only to messages given directly by JointAI.) Arguments passed on to mcmcse::mcse.mat sizerepresents the batch size in bm'' and the truncation point in bartlett'' and tukey''. Default is NULL which implies that an optimal batch size is calculated using the batchSize() function. Can take character values of sqroot'' and cuberoot'' or any numeric value between 1 and n/2. sqroot'' means size is floor(n^(1/2)) and cuberoot'' means size is floor(n^(1/3)). ga function such that $$E(g(x))$$ is the quantity of interest. The default is NULL, which causes the identity function to be used. methodany of bm'', obm'', bartlett'', tukey''. bm'' represents batch means estimator, obm'' represents overlapping batch means estimator with, bartlett'' and tukey'' represents the modified-Bartlett window and the Tukey-Hanning windows for spectral variance estimators. rthe lugsail parameter that converts a lag window into its lugsail equivalent. Larger values of r'' will typically imply less underestimation of cov'', but higher variability of the estimator. Default is r = 3'' and r = 1,2'' are good choices. r > 5'' is not recommended. Non-integer values are ok. show the Monte Carlo error of the sample transformed back to the scale of the data (TRUE) or on the sampling scale (this requires the argument keep_scaled_mcmc = TRUE in the JointAI model) optional; list of parameters passed to plot() optional; list of parameters passed to abline()

## Value

An object of class MCElist with elements unscaled, scaled and digits. The first two are matrices with columns est (posterior mean), MCSE (Monte Carlo error), SD (posterior standard deviation) and MCSE/SD (Monte Carlo error divided by post. standard deviation.)

## Methods (by generic)

• plot: plot Monte Carlo error

## Note

Lesaffre & Lawson (2012) [p. 195] suggest the Monte Carlo error of a parameter should not be more than 5% of the posterior standard deviation of this parameter (i.e., $$MCSE/SD \le 0.05$$).

## References

Lesaffre, E., & Lawson, A. B. (2012). Bayesian Biostatistics. John Wiley & Sons.

The vignette Parameter Selection provides some examples how to specify the argument subset.

## Examples

mod <- lm_imp(y ~ C1 + C2 + M2, data = wideDF, n.iter = 100)

MC_error(mod)#>                est   MCSE    SD MCSE/SD
#> (Intercept)  35.99 1.5053 26.07   0.058
#> C1          -27.15 1.0508 18.20   0.058
#> C2            0.90 0.0400  0.69   0.058
#> M22          -0.35 0.0697  0.59   0.119
#> M23           0.15 0.0836  0.63   0.133
#> M24          -1.09 0.0683  0.56   0.121
#> sigma_y       2.22 0.0091  0.16   0.058
plot(MC_error(mod), ablinepars = list(lty = 2))