factor.switching-package {factor.switching}

Post-Processing MCMC Outputs of Bayesian Factor Analytic Models

Description

A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to generate samples from the posterior distribution. The package applies a series of rotation, sign and permutation transformations (Papastamoulis and Ntzoufras (2022) <DOI:10.1007/s11222-022-10084-4>) into raw MCMC samples of factor loadings, which are provided by the user. The post-processed output is identifiable and can be used for MCMC inference on any parametric function of factor loadings. Comparison of multiple MCMC chains is also possible.

There are three alternative schemes for minimizing the objective function.

1. Exact rsp_exact

2. Partial Simulated Annealing rsp_partial_sa

3. Full simulated annealing rsp_full_sa

The exact algorithm solves 2^q assignment problems per MCMC iteration, where q denotes the number of factors of the fitted model. For typical values of the number of factors (e.g. q<11) the exact scheme should be preferred. Otherwise, the two approximate algorithms based on simulated annealing may be considered. The Partial simulated annealing is more efficient than the full simulated annealing scheme.

In cases of parallel MCMC chains, applying the RSP algorithm for each chain separately will identify the factor loadings within each chain. However, the results will not be comparable between chains. The comparison of multiple MCMC chains is doable via the compareMultipleChains function.

Details

The DESCRIPTION file: Index of help topics:

compareMultipleChains   Compare multiple chains
credible.region         Compute a simultaneous credible region
                        (rectangle) from a sample for a vector valued
                        parameter.
factor.switching-package
                        Post-Processing MCMC Outputs of Bayesian Factor
                        Analytic Models
plot.rsp                Plot posterior means and credible regions
procrustes_switching    Orthogonal Procrustes rotations
rsp_exact               Rotation-Sign-Permutation (RSP) algorithm
                        (Exact scheme)
rsp_full_sa             Rotation-Sign-Permutation (RSP) algorithm (Full
                        Simulated Annealing)
rsp_partial_sa          Rotation-Sign-Permutation (RSP) algorithm
                        (Partial Simulated Annealing)
small_posterior_2chains
                        Example data
switch_and_permute      Apply sign switchings and column permutations
weighted_procrustes_switching
                        Weighted Orthogonal Procrustes rotations

Author(s)

Panagiotis Papastamoulis

Maintainer: Panagiotis Papastamoulis

References

Papastamoulis, P. and Ntzoufras, I. (2022). On the identifiability of Bayesian Factor Analytic models. Statistics and Computing, 32, 23 (2022) https://doi.org/10.1007/s11222-022-10084-4.

See Also

rsp_exact, plot.rsp, compareMultipleChains

Examples

	# load 2 chains each one consisting of a 
	#	small mcmc sample of 100 iterations
	#	with p=6 variables and q=2 factors.
	data(small_posterior_2chains)
	Nchains <- length(small_posterior_2chains)
	reorderedPosterior <- vector('list',length=Nchains)
	# post-process the 2 chains
	for(i in 1:Nchains){
		reorderedPosterior[[i]] <- rsp_exact( lambda_mcmc = small_posterior_2chains[[i]], 
				maxIter = 100, 
				threshold = 1e-6, 
				verbose=TRUE )
	}
	#	plot posterior summary for chain 1:
	plot(reorderedPosterior[[1]])
	#	plot posterior summary for chain 2:
	plot(reorderedPosterior[[2]])
	# make them comparable
	makeThemSimilar <- compareMultipleChains(rspObjectList=reorderedPosterior)
	# plot the traces of both chains
	oldpar <- par(no.readonly =TRUE)
	par(mfcol=c(2,6),mar=c(4,4,2,1))
	plot(makeThemSimilar,auto.layout=FALSE,density=FALSE,
		ylim=c(-1.1,1.1),smooth=FALSE,col=c('red','blue'))
	legend('topright',c('post-processed chain 1', 
		'post-processed chain 2'),lty=1:2,col=c('red','blue'))
	par(oldpar)
	# you can also use the summary of mcmc.list
	summary(makeThemSimilar)