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Independence Tests for Weighted Dependence Measures

Source: R/indep_test.R
indep_test.Rd

Computes a dependence measure and its asymptotic independence test for two numeric vectors.

Usage

indep_test(
  x,
  y,
  method = "pearson",
  weights = NULL,
  remove_missing = TRUE,
  alternative = "two-sided",
  seeds = NULL,
  y_continuous = TRUE
)

Arguments

x, y

numeric vectors of data values. x and y must have the same length.

method

the dependence measure; see Details for possible values.

weights

an optional vector of weights for the observations.

remove_missing

if TRUE, all pairwise incomplete observations are removed; if FALSE, the function throws an error if there are incomplete observations.

alternative

indicates the alternative hypothesis and must be one of "two-sided", "greater" or "less". You can specify just the initial letter. "greater" corresponds to positive association, "less" to negative association.

seeds

an optional integer vector used to break predictor ties for Chatterjee's xi. The default uses a fixed, reproducible ordering.

y_continuous

whether the response distribution is known to be continuous for Chatterjee inference. Set this to FALSE for a discrete response even if the sample contains no observed response ties.

Value

A one-row data frame containing the estimate, transformed test statistic, p-value, effective sample size, method, and alternative.

Details

Available methods:

  • "pearson": Pearson correlation

  • "spearman": Spearman's \(\rho\)

  • "kendall": Kendall's \(\tau\)

  • "blomqvist": Blomqvist's \(\beta\)

  • "hoeffding": Hoeffding's \(D\)

  • "chatterjee": Chatterjee's \(\xi\)

Partial matching of method names is enabled. This implementation of Hoeffding's \(D\) does not support tied observations; test results are invalid when ties are present. It supports only the two-sided alternative. The natural one-sided alternative for Chatterjee's \(\xi\) is "greater".

Chatterjee's \(\xi\) measures the dependence of y on x. Analytic inference with unequal weights requires a continuous response and assumes that weights are fixed or depend only on x. It is unavailable when the response is discrete or tied and weights are unequal.

Examples

x <- rnorm(100)
y <- rpois(100, 1)
w <- runif(100)

indep_test(x, y, method = "kendall")               # unweighted
#>      estimate  statistic   p_value n_eff  method alternative
#> 1 -0.01762804 -0.2317181 0.8167569   100 kendall   two-sided
indep_test(x, y, method = "kendall", weights = w)  # weighted
#>     estimate statistic   p_value    n_eff  method alternative
#> 1 0.01242062 0.1395713 0.8889987 74.08639 kendall   two-sided