relabel: Relabel Factor Loadings from MCMC output

In relabeLoadings: Relabel Loadings from MCMC Output for Confirmatory Factor Analysis

Description

Uses the relabeling method of Erosheva and Curtis to correct for sign invariance in MCMC draws from confirmatory factor analysis (CFA) models.

Usage

relabel(obj, ...)

## Default S3 method:
relabel(obj, ...)

## S3 method for class 'matrix'
relabel(obj, random = FALSE, max.iter = 100, ...)

Arguments

obj	An object of the appropriate class. Currently, the method is implemented only for objects of S3 class matrix. The matrix should contain the MCMC draws from a Bayesian CFA model where no arbitrary restrictions are imposed on the loadings to enforce rotational invariance. For example, no loadings should have been arbitrarily constrained to be one. Columns of the matrix must have names of the form "Lam[1,1]", "Lam[1,2]", ..., where indices denote the structure of the loading matrix, i.e., missing idices indicate loadings that are constrained to be zero.
random	Logical value. If TRUE, random starting points will be used. If FALSE, starting values are chosen roughly to allow the largest loadings on each factor to have a positive sign or to allow the majority of loadings on a given factor to have a positive sign.
max.iter	Integer that specifies the maximum number of iterations of the algorithm before aborting procedure.

...

Not used.

Details

See the references.

Value

An S3 object of class relabel with the following components:

Lam	original (untransformed) draws of the loadings.
nuLam	transformed draws of the loadings.
nu.init	initial values for the sign-change parameters.
nu	final values of the sign change parameters used to compute nuLam.
m	final values of the mean parameters in the loss function.
s	final values of the standard deviation parameters in the loss function.
factor.idx	vector of integers indicating which columns of the posterior draws belong to which factor.
iter	number of iterations the algorithm took to converge.
loss	final value of the loss function after convergence.
converged	logical indicating whether the algorithm converged.

Author(s)

S. McKay Curtis and Elena Erosheva

References

Erosheva, E. A. and Curtis, S. M. (2011) "A relabeling scheme for confirmatory factor analysis." Technical report #589. University of Washington, Dept. of Statistics.

Examples

n <- 1000
p <- 8
set.seed(1)
mu <- as.numeric(t(cbind(
    matrix(rep(sample(c(-1, 1), size=n, replace=TRUE)*4, each=8), n, 8, byrow=TRUE),
    matrix(rep(sample(c(-1, 1), size=n, replace=TRUE)*4, each=8), n, 4, byrow=TRUE),
    matrix(rep(sample(c(-1, 1), size=n, replace=TRUE)*4, each=8), n, 4, byrow=TRUE))))
Lam <- matrix(rnorm(length(mu), mu, 1.0), n, 16, byrow=TRUE)
colnames(Lam) <- c(paste0("Lam[", 1:p, ",", 1, "]"),
                   paste0("Lam[", 1:4, ",", 2, "]"),
                   paste0("Lam[", 5:8, ",", 3, "]"))

par(mfrow=c(2, 8))
apply(Lam, 2, function(x) plot(density(x)))

## Relabeling removes the bimodality
out <- relabel(Lam)

par(mfrow=c(2, 8))
apply(out$nuLam, 2, function(x) plot(density(x)))

relabeLoadings documentation built on May 2, 2019, 3:22 a.m.