bfslice_eqp_c {dslice}

Dependency and conditional dependency detection between a level k (k > 1) categorical variable and a continuous variable via Bayes factor.

Description

Conditional dependency detection between a level k_x (k_x > 1) categorical variable x and a continuous variable y via Bayes factor given a level k_z categorical variable z with O(n^{1/2})-resolution. The basic idea is almost the same as bfslice_c. The only different is that bfslice_eqp_c groups samples into approximate O(n^{1/2}) groups which contain approximate O(n^{1/2}) samples and treat the groups as a sample to calculate Bayes facor. If k_z = 1, it is unconditional dependency detection method. It could be applied for non-parametric variable selecltion.

Usage

  bfslice_eqp_c(z, x, zdim, xdim, lambda, alpha)

Arguments

z

Vector: observations of given (preselected) categorical variable, 0,1,\ldots,k_z-1 for level k_z categorical variable, should be ranked according to values of continuous variable y with x in advanced, either ascending or descending.

x

Vector: observations of categorical variable, 0,1,\ldots,k_x-1 for level k_x categorical variable, should be ranked according to values of continuous variable y with z in advanced, either ascending or descending.

zdim

Level of z, equals k_z.

xdim

Level of x, equals k_x.

lambda

lambda corresponds to the probability that makes slice in each possible position. lambda should be greater than 0.

alpha

alpha is hyper-parameter of the prior distribution of frequency in each slice. alpha should be greater than 0 and less equal than k_x.

Value

Value of Bayes factor (nonnegative). Bayes factor could be treated as a statistic and one can take some threshold then calculates the corresponded Type I error rate. One can also take the value of Bayes factor for judgement.

References

Jiang, B., Ye, C. and Liu, J.S. Bayesian nonparametric tests via sliced inverse modeling. Bayesian Analysis, 12(1): 89-112, 2017.

See Also

bfslice_c, bfslice_eqp_u.

Examples

n <- 1000
mu <- 0.2

## Unconditional test
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep(0, n), rep(1, n))
z <- rep(0, 2*n)

## Conditional test
y <- c(rnorm(n, -mu, 1), rnorm(n, mu, 1))
x <- c(rep(0, n/5), rep(1, n), rep(0, 4*n/5))
z <- c(rep(0, n), rep(1, n))
z <- z[order(y)]

x <- x[order(y)]
zdim <- max(z) + 1
xdim <- max(x) + 1
lambda <- 1.0
alpha <- 1.0
bfval <- bfslice_eqp_c(z, x, zdim, xdim, lambda, alpha)