post.sign.switch {BayesFM}

Perform sign switchting on posterior MCMC sample

Description

This function performs a sign switch on the MCMC draws to restore the consistency of the signs of the factors loadings and of the correlations of the latent factors a posteriori.

Usage

post.sign.switch(mcmc, benchmark = NULL, benchmark.threshold = 0.5)

Arguments

mcmc

Object of class 'befa'.

benchmark

Vector of integers of length equal to the maximum number of latent factors. Each element indicates which factor loading is used as a benchmark for the sign switch. If NULL, the factor loadings with the highest posterior probabilities of being different from zero in each column of the factor loading matrix are used as benchmarks.

benchmark.threshold

Minimum posterior probability for a factor loading to be considered as a benchmark.

Details

The signs of the factor loadings, as well as of the corresponding correlations of the latent factors, are switched for each MCMC iteration such that the factor loadings defined as benchmarks are positive. The sign switch can only be performed if post.column.switch has been run before. See section 4.3 (p.42) of CFSHP for more details.

If a latent factor has no benchmarks, or if its benchmark is equal to zero at some MCMC iteration, then no sign switch is performed on the corresponding loadings and correlations for this particular factor or MCMC iteration.

Note that in complicated models where the sampler visits several models with different numbers of latent factors, it may not be relevant to use the default value of benchmark, as the posterior probabilities that the factor loadings are different from zero would be computed across models. Instead, the user might consider finding the highest posterior probability model first, and use its top elements in each column of the factor loading matrix as benchmarks to perform the sign switch.

Value

This function returns the same 'befa' object, where the signs of the factor loadings and of the factor correlations have been switched appropriately to restore the identification of the factor model with respect to sign switching.

Author(s)

Rémi Piatek [e-mail]

References

G. Conti, S. Frühwirth-Schnatter, J.J. Heckman, R. Piatek (2014): “Bayesian Exploratory Factor Analysis”, Journal of Econometrics, 183(1), pages 31-57, doi: 10.1016/j.jeconom.2014.06.008.

See Also

post.column.switch for column switching of the factor loading matrix and of the correlation matrix of the latent factors to restore identification a posteriori.

Examples

set.seed(6)
Y <- simul.dedic.facmod(N = 100, dedic = rep(1:3, each = 5))
mcmc <- befa(Y, Kmax = 5, iter = 1000)
mcmc <- post.column.switch(mcmc)

# factor loadings corresponding to variables 1, 6, 11, 12 and 13 are
# used as benchmarks:
mcmc1 <- post.sign.switch(mcmc, benchmark = c(1, 6, 11, 12, 13))

# factor loadings with the highest posterior probability of being different
# from zero in each column are used as benchmark:
mcmc2 <- post.sign.switch(mcmc)