Box's M-test for Homogeneity of Covariance Matrices
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# Box's M-test for Homogeneity of Covariance Matrices | |
boxM <- | |
function(mod, ...) UseMethod("boxM") | |
boxM.default <- function(Y, group) | |
{ | |
dname <- deparse(substitute(Y)) | |
if (!inherits(Y, c("data.frame", "matrix"))) | |
stop(paste(dname, "must be a numeric data.frame or matrix!")) | |
if (length(group) != nrow(Y)) | |
stop("incompatible dimensions!") | |
Y <- as.matrix(Y) | |
group <- as.factor(as.character(group)) | |
p <- ncol(Y) | |
nlev <- nlevels(group) | |
lev <- levels(group) | |
dfs <- tapply(group, group, length) - 1 | |
if (any(dfs < p)) | |
warning("there are one or more levels with less observations than variables!") | |
mats <- aux <- list() | |
for(i in 1:nlev) { | |
mats[[i]] <- cov(Y[group == lev[i], ]) | |
aux[[i]] <- mats[[i]] * dfs[i] | |
} | |
names(mats) <- lev | |
pooled <- Reduce("+", aux) / sum(dfs) | |
logdet <- log(unlist(lapply(mats, det))) | |
minus2logM <- sum(dfs) * log(det(pooled)) - sum(logdet * dfs) | |
sum1 <- sum(1 / dfs) | |
Co <- (((2 * p^2) + (3 * p) - 1) / (6 * (p + 1) * | |
(nlev - 1))) * (sum1 - (1 / sum(dfs))) | |
X2 <- minus2logM * (1 - Co) | |
dfchi <- (choose(p, 2) + p) * (nlev - 1) | |
pval <- pchisq(X2, dfchi, lower.tail = FALSE) | |
means <- aggregate(Y, list(group), mean) | |
rn <- as.character(means[,1]) | |
means <- means[,-1] | |
means <- rbind( means, colMeans(Y) ) | |
rownames(means) <- c(rn, "_all_") | |
logdet <- c(logdet, pooled=log(det(pooled))) | |
out <- structure( | |
list(statistic = c("Chi-Sq (approx.)" = X2), | |
parameter = c(df = dfchi), | |
p.value = pval, | |
cov = mats, pooled = pooled, logDet = logdet, means = means, | |
data.name = dname, | |
method = " Box's M-test for Homogeneity of Covariance Matrices" | |
), | |
class = c("htest", "boxM") | |
) | |
return(out) | |
} | |
boxM.formula <- function(formula, data, ...) | |
{ | |
form <- formula | |
mf <- model.frame(form, data) | |
if (any(sapply(2:dim(mf)[2], function(j) is.numeric(mf[[j]])))) | |
stop("Box's M test is not appropriate with quantitative explanatory variables.") | |
Y <- mf[,1] | |
if (dim(Y)[2] < 2) stop("There must be two or more response variables.") | |
if(dim(mf)[2]==2) group <- mf[,2] | |
else { | |
if (length(grep("\\+ | \\| | \\^ | \\:",form))>0) stop("Model must be completely crossed formula only.") | |
group <- interaction(mf[,2:dim(mf)[2]]) | |
} | |
boxM.default(Y=Y, group=group, ...) | |
} | |
boxM.lm <- function(y, ...) { | |
boxM.formula(formula(y), data=model.frame(y), ...) | |
} | |
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