These functions calculates diagnostics for evaluating data cloning convergence.
lambdamax.diag(x, ...)
# S3 method for mcmc.list
lambdamax.diag(x, ...)chisq.diag(x, ...)
# S3 method for mcmc.list
chisq.diag(x, ...)
lambdamax.diag returns a single value, the maximum of the
eigenvalues of the
unscaled variance covariance matrix of the estimated parameters.
chisq.diag returns two test statistic values
(mean squared error and r-squared) with empirical and theoretical
quantiles.
An object of class mcmc or mcmc.list.
Other arguments to be passed.
Khurram Nadeem, knadeem@math.ualberta.ca
Peter Solymos, solymos@ualberta.ca
These diagnostics can be used to test for the data cloning convergence
(Lele et al. 2007, 2010).
Asymptotically the posterior distribution of the parameters approaches
a degenerate multivariate normal distribution. As the distribution
is getting more degenerate, the maximal eigenvalue (\(\lambda_{max}\))
of the unscaled covariance matrix is decreasing.
There is no critical value under which \(\lambda_{max}\) is good
enough. By default, 0.05 is used (see getOption("dclone")$diag).
Another diagnostic tool is to check if the joint posterior distribution
is multivariate normal. It is done by chisq.diag as described by
Lele et al. (2010).
Lele, S.R., B. Dennis and F. Lutscher, 2007. Data cloning: easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods. Ecology Letters 10, 551--563.
Lele, S. R., K. Nadeem and B. Schmuland, 2010. Estimability and likelihood inference for generalized linear mixed models using data cloning. Journal of the American Statistical Association 105, 1617--1625.
Solymos, P., 2010. dclone: Data Cloning in R. The R Journal 2(2), 29--37. URL: https://journal.r-project.org/archive/2010-2/RJournal_2010-2_Solymos.pdf
Eigen decomposition: eigen
data(regmod)
lambdamax.diag(regmod)
chisq.diag(regmod)
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