convergence.diag: Convergence diagnostics

In FlexReg: Regression Models for Bounded Continuous and Discrete Responses

Convergence diagnostics

Description

The function returns some diagnostic measures to check for convergence to the equilibrium distribution of the Markov Chain(s). Moreover, it prints the number (and percentage) of iterations that ended with a divergence and that saturated the max treedepth, and the E-BFMI values for each chain for which E-BFMI is less than 0.2.

Usage

convergence.diag(
  model,
  diagnostics = "all",
  pars = NULL,
  additional.args = list()
)

Arguments

model	an object of class `flexreg`.
diagnostics	an optional character vector of diagnostics names. The default is to compute "all" diagnostics, otherwise one can specify a selection of diagnostics among "Rhat", "geweke", "raftery", "heidel", and "gelman".
pars	an optional character vector of parameter names. If pars is not specified, all parameters in the regression models are evaluated.
additional.args	a list containing additional arguments (see details)

Details

• "Rhat" returns the potential scale reduction factor on split chains. An R-hat greater than 1 is indicative of a bad mix of the chains. At convergence R-hat has to be less than 1.05. See rstan::Rhat for further details.

• "geweke" returns the z-scores, one for each parameter, for a test of equality between the means of the first 10% and last 50% of the chain. The fraction to use from the first and last part of the chain can be edited through the additional arguments frac1 and frac2. The sum of frac1 and frac2 has to be strictly less than 1. See coda::geweke.diag for further details.

• "raftery" returns the estimate of the "dependence factor" I. Values of I greater than 5 may indicate a strong autocorrelation. Additional parameters such as the quantile to be estimated (q), the desired margin of error of the estimate (r), and the probability (s) of obtaining an estimate between q-r and q+r can be passed as a list in the additional.args argument. See coda::raftery.diag for further details.

• "heidel" returns the p-values, one for each parameter, referred to a convergence test where the null hypothesis is that the sampled values come from a stationary distribution. It is possible to set the target value for ratio of halfwidth to sample mean (eps) and the significance level of the test (pvalue) into the additional.args argument. See coda::heidel.diag for further details.

• "gelman" returns the estimate of the potential scale reduction factor and the upper confidence limit. At least two chains are needed to compute the Gelman and Rubin's convergence diagnostic. Additional parameters such as the confidence level (confidence), a logical flag indicating whether variables should be transformed (transform), a logical flag indicating whether only the second half of the series should be used in the computation (autoburnin), and a logical flag indicating whether the multivariate potential scale reduction factor should be calculated for multivariate chains (multivariate) can be passed as a list in the additional.args argument. See coda::gelman.diag for further details.

Value

A print from check_hmc_diagnostics function and a list of convergence diagnostics.

References

Brooks, SP., Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7, 434-455.

Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In Bayesian Statistics 4 (ed JM Bernado, JO Berger, AP Dawid and AFM Smith). Clarendon Press, Oxford, UK.

Heidelberger P., Welch P.D. (1981). A spectral method for confidence interval generation and run length control in simulations. Comm. ACM. 24, 233-245.

Raftery, A.E. and Lewis, S.M. (1992). One long run with diagnostics: Implementation strategies for Markov chain Monte Carlo. Statistical Science, 7, 493-497.

Stan Development Team (2020). RStan: the R interface to Stan. R package version 2.19.3. https://mc-stan.org

Examples

## Not run: 
data("Reading")
FB <- flexreg(accuracy.adj ~ iq, data = Reading, type = "FB")
convergence.diag(FB,  diagnostics = c("Rhat", "geweke"), pars = "beta")


## End(Not run)

FlexReg documentation built on Sept. 29, 2023, 9:06 a.m.