cor_test: Bayesian correlation analysis
In BFpack: Flexible Bayes Factor Testing of Scientific Expectations

cor_test

R Documentation

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,
  nugget.scale = 0.999
)

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 3333 iterations per chain.
`burnin`	number of iterations for burnin (default is 2000).
`nugget.scale`	a scalar to avoid computational issues due to posterior draws for the corralations 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`.

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

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>

Talhouk, A., Doucet, A., & Murphy, K. (2012). Efficient Bayesian inference for multivariate probit models with sparse inverse correlation matrices. Journal of Computational and Graphical Statistics, 21(3), 739-757. <https://doi.org/10.1080/10618600.2012.679239>

Examples


# 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)

BFpack documentation built on June 9, 2025, 1:07 a.m.