dclone (version 1.2-0)

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.

Details

This diagnostics can be used to test for the data cloning convergence. 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, 0.1 is used (see getOption("dclone.crit")).

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.

See Also

Eigen decomposition: eigen

Examples

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