MADPop (version 1.1.7)

UM.eqtest: Equality tests for two multinomial samples

Description

Generate multinomial samples from a common probability vector and calculate the Chi-square and Likelihood Ratio test statistics.

Usage

UM.eqtest(N1, N2, p0, nreps, verbose = TRUE)

Value

An nreps x 2 matrix with the simulated chi-squared and LR values.

Arguments

N1

Size of sample 1.

N2

Size of sample 2.

p0

Common probability vector from which to draw the multinomial samples. Can also be a matrix, in which case each simulation randomly draws with replacement from the rows of p0.

nreps

Number of replications of the simulation.

verbose

Logical. If TRUE prints message every 5000 replications.

Details

The chi-squared and likelihood ratio test statistics are calculated from multinomial samples \((Y_1^1, Y_2^1), \ldots, (Y_1^M, Y_2^M)\), where $$ Y_k^m \stackrel{\textrm{ind}}{\sim} \textrm{Multinomial}(N_k, p_0^m), $$ where \(p_0^m\) is the \(m\)th row of p0.

Examples

# bootstrapped p-value calculation against equal genotype proportions
# in lakes Michipicoten and Simcoe

# contingency table
popId <- c("Michipicoten", "Simcoe")
ctab <- UM.suff(fish215[fish215$Lake %in% popId,])$tab
ctab

# MLE of probability vector
p.MLE <- colSums(ctab)/sum(ctab)
# sample sizes
N1 <- sum(ctab[1,]) # Michipicoten
N2 <- sum(ctab[2,]) # Simcoe

# bootstrapped test statistics (chi^2 and LRT)
T.boot <- UM.eqtest(N1 = N1, N2 = N2, p0 = p.MLE, nreps = 1e3)

# observed test statistics
T.obs <- c(chi2 = chi2.stat(ctab), LRT = LRT.stat(ctab))
# p-values
rowMeans(t(T.boot) > T.obs)