Diagnostic checks for assessing MCMC convergence of a Bayesian model

The focus is restricted to full Bayesian models in cost-effectiveness analyses based on the function selection(), pattern(), hurdle() or lmdm(), with convergence of the MCMC chains that is assessed through graphical checks of the posterior distribution of the parameters of interest, Examples are density plots, trace plots, autocorrelation plots, etc. Other types of posterior checks are related to some summary MCMC statistics that are able to detect possible issues in the convergence of the algorithm, such as the potential scale reduction factor or the effective sample size. Different types of diagnostic tools and statistics are used to assess model convergence using functions contained in the package ggmcmc. Graphics and plots are managed using functions contained in the package ggplot2 and ggthemes.

Usage

diagnostic(x, type = "denplot", param = "all", theme = NULL, ...)

Arguments

x: An object of class missingHE containing the posterior results of a full Bayesian model implemented using the function selection(), pattern(), hurdle() or lmdm().
type: Type of diagnostic check to be plotted for the model parameter selected. Available choices include: histogram for histogram plots, denplot for density plots, traceplot for trace plots, acf for autocorrelation plots, running for running mean plots, compare for comparing the distribution of the whole chain with only its last part, cross for cross correlation plots, Rhat for the potential scale reduction factor, geweke for the geweke diagnostic, pairs for posterior correlation among the parameters,caterpillar for caterpillar plots.
param: Name of the family of parameters to process, as given by a regular expression. For example the mean parameters for the effect and cost variables can be specified using mu.e and mu.c, respectively. Different types of models may have different parameters depending on the assumed distributions and missing data assumptions. To see a complete list of all possible parameters by types of models assumed see details.
theme: Type of ggplot theme among some pre-defined themes, mostly taken from the package ggthemes. For a full list of available themes see details.
...: Additional parameters that can be provided to manage the graphical output of diagnostic.

Value

A ggplot2 object containing the plots specified in the argument type

Details

Depending on the types of plots specified in the argument type, the output of diagnostic can produce different combinations of MCMC visual posterior checks for the family of parameters indicated in the argument param. For a full list of the available plots see the description of the argument type or see the corresponding plots in the package ggmcmc.

The parameters that can be assessed through diagnostic are only those included in the object x (see Arguments). Specific character names must be specified in the argument param according to the specific model implemented. The available names and the parameters associated with them are:

mu.e: the mean of the effects across treatment arms.
mu.c: the mean of the costs across treatment arms.
sd.e: the standard deviation of the effects.
sd.c: the standard deviation of the costs.
alpha: the regression coefficients for the effects.
beta: the regression coefficients for the costs.
beta.f: the regression coefficients for the costs related to the effects predictor if present.
alpha.time: the autoregressive coefficients for the effects if present (only with the function lmdm()).
beta.time: the autoregressive coefficients for the costs if present (only with the function lmdm()).
random.alpha: the regression random effects coefficients for the effects if present.
random.beta: the regression random effects coefficients for the costs if present.
random.alpha.time: the autoregressive random effects coefficients for the effects if present (only with the function lmdm()).
random.beta.time: the autoregressive random effects coefficients for the costs if present (only with the function lmdm()).
p.e: the probability of missingness or structural values for the effects (only with the function selection(), hurdle() or lmdm()).
p.c: the probability of missingness or structural values for the costs (only with the function selection(), hurdle() or lmdm()).
gamma.e: the regression coefficients of missingness or structural values for the effects (only with the function selection(), hurdle() or lmdm())
gamma.c: the regression coefficients of missingness or structural values for the costs (only with the function selection() or hurdle() or lmdm())
random.gamma.e: the random effects regression coefficients of missingness or structural values for the effects if present (only with the function selection(), hurdle() or lmdm()).
random.gamma.c: the random effects regression coefficients of missingness or structural values for the effects if present (only with the function selection(), hurdle() or lmdm()).
pattern: the probabilities of the missingness patterns (only with the function pattern()).
delta.e: the mnar parameter for the effects if present (only with the function selection(), pattern() or lmdm()).
delta.c: the mnar parameter for the costs if present (only with the function selection(), pattern() or lmdm()).
random.delta.e: the random effects mnar parameters for the effects if present (only with the function selection() or lmdm()).
random.delta.c: the random effects mnar parameters for the costs if present (only with the function selection() or lmdm()).
all: all available parameters stored in x.

When the object x is created using the function pattern, pattern-specific standard deviation (sd.e, sd.c) and regression coefficient parameters (alpha, beta) for both outcomes can be visualised. The parameters associated with a missingness mechanism can be accessed only when x is created using the function selection(), pattern() or lmdm(), while the parameters associated with the model for the structural values mechanism can be accessed only when x is created using the function hurdle().

The argument theme allows to customise the graphical output of the plots generated by diagnostic and allows to choose among a set of possible pre-defined themes taken form the package ggthemes. For a complete list of the available character names for each theme, see ggthemes.

References

Gelman, A. Carlin, JB., Stern, HS. Rubin, DB.(2003). Bayesian Data Analysis, 2nd edition, CRC Press.

Brooks, S. Gelman, A. Jones, JL. Meng, XL. (2011). Handbook of Markov Chain Monte Carlo, CRC/Chapman and Hall.

Author

Andrea Gabrio

Examples

# For examples see the function [selection()], [pattern()], [hurdle()] or [lmdm()].
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