Calculate, print and plot the Monte Carlo error of the samples from a 'JointAI' model, combining the samples from all MCMC chains.

- x
object inheriting from class 'JointAI'

- subset
subset of parameters/variables/nodes (columns in the MCMC sample). Follows the same principle as the argument

`monitor_params`

in`*_imp`

.- exclude_chains
optional vector of the index numbers of chains that should be excluded

- start
the first iteration of interest (see

`window.mcmc`

)- end
the last iteration of interest (see

`window.mcmc`

)- thin
thinning interval (integer; see

`window.mcmc`

). For example,`thin = 1`

(default) will keep the MCMC samples from all iterations;`thin = 5`

would only keep every 5th iteration.- digits
number of digits for the printed output

- warn
logical; should warnings be given? Default is

`TRUE`

.- mess
logical; should messages be given? Default is

`TRUE`

.- ...
Arguments passed on to

`mcmcse::mcse.mat`

`size`

represents 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 \(\lfloor n^{1/2} \rfloor\) and “`cuberoot`

” means size is \(\lfloor n^{1/3} \rfloor\).`g`

a function such that \(E(g(x))\) is the quantity of interest. The default is

`NULL`

, which causes the identity function to be used.`method`

any 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.`r`

The lugsail parameters (

`r`

) 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 also good choices although may lead to underestimates of the variance.`r > 5`

is not recommended.

- data_scale
logical; 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`

to be set when fitting the model)- plotpars
optional; list of parameters passed to

`plot()`

- ablinepars
optional; list of parameters passed to

`abline()`

- minlength
number of characters the variable names are abbreviated to

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.)

`plot(MCElist)`

: plot Monte Carlo error

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., \(MCSE/SD \le 0.05\)).

**Long variable names:**

The default plot margins may not be wide enough when variable names are
longer than a few characters. The plot margin can be adjusted (globally)
using the argument `"mar"`

in `par`

.

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

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

.