cond_independence_test: Conditional independence test

In nvihrs14/tcherry: Learning the structure of tcherry trees

Description

Makes a conditional independece test based on a likelihood ratio test.

Usage

cond_independence_test(var1, var2, cond = c(), data, smooth = 0)

Arguments

var1, var2	Variables to test independence for.
cond	Vector of variable names to condition on. If empty, the test is just an independence test.
data	Data with realisations of the variables.
smooth	Additional cell counts when estimating probabilities. May be used to avoid zero probabilities.

Details

The calculated test statistic is

2 ∑ n_comb * log((P(var1, var2|cond)) / (P(var1|cond)P(var2|cond)))

where the sum is over all states of the variables, n_comb is the number of times the current combination of states has been seen in the data and the probability distributions are estimated. This estimation is done with maximum likelihood if smooth is set to 0. If this gives zero probabilities, the smooth argument must be used to prevent it in order to calculate the test size.

The test statistic follows assymptotically a chi-squared distribution with (n1 - 1)(n2 - 1)n_cond degrees of freedom, where n1 and n2 are the number of states for var1 and var2 and n_cond is the number of configurations of the states of the variables to be conditioned on.

Value

A list containing the following components:

• chi_sq_statistic The calculated test statistic.

• df Degrees of freedom.

• p_value The p-value of the test.

Author(s)

Katrine Kirkeby, [e-mail]

Maria Knudsen, [e-mail]

Ninna Vihrs, [e-mail]

Examples

set.seed(43)
var1 <- c(sample(c(1, 2), 100, replace = TRUE))
var2 <- var1 + c(sample(c(1, 2), 100, replace = TRUE))
var3 <- var1 + c(sample(c(0, 1), 100, replace = TRUE,
                        prob = c(0.9, 0.1)))
var4 <- c(sample(c(1, 2), 100, replace = TRUE))
var5 <- var2 + var3

data <- data.frame("var1" = as.character(var1),
                   "var2" = as.character(var2),
                   "var3" = as.character(var3),
                   "var4" = as.character(var4),
                   "var5" = as.character(var5))

cond_independence_test("var1", "var4", data = data, smooth = 0.1)
cond_independence_test("var2", "var3", cond = c("var1", "var5"),
                       data = data, smooth = 0.1)

nvihrs14/tcherry documentation built on Aug. 1, 2020, 6:25 p.m.