dclone (version 1.4-0)

lambdamax.diag: Maximum Eigenvalue of the Posterior Variance-Covariance Matrix

Description

Calculates the maximum eigenvalue of the posterior variance-covariance matrix

Usage

lambdamax.diag(x)
chisq.diag(x)

Arguments

x

An object of class mcmc or mcmc.list.

Value

• Returns a single vaue, the maximum of the eigenvalues of the unscaled variance covariance matrix of the estimated parameters.

encoding

UTF-8

Details

This 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. If only one parameter is dealt with, the unscaled posterior standard error is given. There is no critical value under which $\lambda_{max}$ is good enough. By default, 0.05 is used (see getOption("dclone")$diag).

References

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: http://journal.r-project.org/archive/2010-2/RJournal_2010-2_Solymos.pdf

See Also

Eigen decomposition: eigen

Examples

data(regmod)
lambdamax.diag(regmod)
chisq.diag(regmod)