computeContCells: Pairwise Contingency Tables

Description

Computes a contingency table for each pair of rows of a matrix, and stores all contigency table in a matrix.

Usage

computeContCells(data, computeExp = TRUE, justDiag = FALSE, 
   check = TRUE, n.cat = NULL)

Arguments

data

a numeric matrix consisting of integers between 1 and n.cat. It is assumed that each row of these matrix represents a variable. Missing values and different numbers of categories a variable can take are allowed.

computeExp

should the numbers of observations expected under the null hypothesis that the respective two variables are independent also be computed? Required when computeContCells is used to compute Pearson's \(\chi^2\)-statistic.

justDiag

should only the diagonal elements of the contingency tables, i.e.\ \(n_{ii}\), \(i = 1, \dots\), n.cat, be computed?

check

should data be checked more thoroughly? It is highly recommended to use check = TRUE.

n.cat

integer specifying the maximum number of levels a variable can take. If NULL, this number will be computed. It is highly recommended not to change the default.

Value

A list consisting of two matrices each consisting of \(m * (m - 1) / 2\) rows and n.cat\(^2\) columns, where \(m\) is the number of rows of data. One of these matrices called mat.obs contains in each row the values of the contingency table for a particular pair of rows of data, where the contigency table of the variables represented by the ith and jth row of data is shown in the \(j + m * (i - 1) - i * (i - 1) / 2\) row of mat.obs. The other matrix called mat.exp consists of the corresponding numbers of observations expected under the null hypothesis that the respective two variables are independent.

References

Schwender, H.\ (2007). A Note on the Simultaneous Computation of Thousands of Pearson's \(\chi^2\)-Statistics. Technical Report, SFB 475, Deparment of Statistics, University of Dortmund.

Examples

Run this code

# NOT RUN {
# Generate an example data set consisting of 5 rows (variables)
# and 200 columns (observations) by randomly drawing integers 
# between 1 and 3.

mat <- matrix(sample(3, 1000, TRUE), 5)

# Generate the matrix containing the contingency tables for each
# pair of rows of mat.

out <- computeContCells(mat)

# out contains both the observed numbers of observations 
# summarized by contingency tables

out$mat.obs

# and the number of observations expected under the null hypothesis
# of independence.

out$mat.exp

# If, e.g., only the observed number of observations having the same 
# value is of interest, call

computeContCells(mat, computeExp = FALSE, justDiag = TRUE)

# }