BFpack (version 1.5.3)

cor_test: Bayesian correlation analysis

Description

Estimate the unconstrained posterior for the correlations using a joint uniform prior (Mulder and Gelissen, 2023) or a marginally uniform prior (Barnard et al., 2000, Mulder, 2016). Correlation matrices are sampled from the posterior using the MCMC algorithm of Talhouk et al. (2012).

Usage

cor_test(
  ...,
  formula = NULL,
  iter = 10000,
  burnin = 2000,
  method = "LKJ",
  nugget.scale = 0.999
)

Value

list of class cor_test:

• meanF posterior means of Fisher transform correlations

• covmF posterior covariance matrix of Fisher transformed correlations

• correstimates posterior estimates of correlation coefficients

• corrdraws list of posterior draws of correlation matrices per group

• corrnames names of all correlations

Arguments

...

matrices (or data frames) of dimensions n (observations) by p (variables) for different groups (in case of multiple matrices or data frames).

formula

an object of class formula. This allows for including control variables in the model (e.g., ~ education).

iter

total number of iterations from posterior. The total is split across three chains. By default, the total number of iterations is 10000, implying a rounded integer of 3333 iterations per chain.

burnin

number of iterations for burnin (default is 2000).

method

"LKJ" for onion method sampler of correlation matrix proposed by Lewandowski, Kurowicka, & Joe (2009), which is the default, or "LD" for 'PX-RPMH' correlation matrix sampler of Liu and Daniels (2009). "onion" method tends to mix better for larger correlation matrices.

nugget.scale

When using method = "LD", a nugget.scale can be used to avoid computational issues due to posterior draws for the correlations too close to 1 in absolute value. Posterior draws for the correlations are multiplied with this nugget.scale. So nugget.scale should be close to 1 (the default is .999). If the traceplots show that draws are stuck at 1 or -1 too long try a slightly smaller nugget.scale.

References

Barnard, J., McCulloch, R., & Meng, X. L. (2000). Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Statistica Sinica, 1281-1311. <https://www.jstor.org/stable/24306780>

Joe, H. (2006). Generating random correlation matrices based on partial correlations. Journal of Multivariate Analysis, 97(10), 2177-2189. <https://doi.org/10.1016/j.jmva.2005.05.010>

Mulder, J., & Gelissen, J. P. (2023). Bayes factor testing of equality and order constraints on measures of association in social research. Journal of Applied Statistics, 50(2), 315-351. <https://doi.org/10.1080/02664763.2021.1992360>

Mulder, J. (2016). Bayes factors for testing order-constrained hypotheses on correlations. Journal of Mathematical Psychology, 72, 104-115. <https://doi.org/10.1016/j.jmp.2014.09.004>

Lewandowski, D., Kurowicka, D., & Joe, H. (2009). Generating random correlation matrices based on vines and extended onion method. Journal of Multivariate Analysis, 100(9), 1989–2001. <https://doi.org/10.1016/j.jmva.2009.04.008>

Liu, X., & Daniels, M. J. (2006). A new algorithm for simulating a correlation matrix based on parameter expansion and reparameterization. Journal of Computational and Graphical Statistics, 15(4), 897-914. <https://doi.org/10.1198/106186006X160681>

Examples

# \donttest{
# Bayesian correlation analysis of the 6 variables in 'memory' object
# we consider a correlation analysis of the first three variable of the memory data.
fit <- cor_test(BFpack::memory[,1:3])

# Bayesian correlation of variables in memory object in BFpack while controlling
# for the Cat variable
fit <- cor_test(BFpack::memory[,c(1:4)],formula = ~ Cat)

# Example of Bayesian estimation of polyserial correlations
memory_example <- memory[,c("Im","Rat")]
memory_example$Rat <- as.ordered(memory_example$Rat)
fit <- cor_test(memory_example)

# Bayesian correlation analysis of first three variables in memory data
# for two different groups
HC <- subset(BFpack::memory[,c(1:3,7)], Group == "HC")[,-4]
SZ <- subset(BFpack::memory[,c(1:3,7)], Group == "SZ")[,-4]
fit <- cor_test(HC,SZ)

# }