View source: R/mainFunctions.R
testMeanVariance | R Documentation |
The function performs the test of equality of two multivariate normal distrbutions (class1 and class2).
testMeanVariance(S, S1, S2, n1, n2)
S |
estimated covariance matrix for pooled sample |
S1 |
estimated covariance matrix in class 1 |
S2 |
estimated covariance matrix in class 2 |
n1 |
number of samples in class 1 |
n2 |
number of samples in class 2 |
The criterion for testing the equality of two normal distributions is the following:
Λ_c = n_1 * log( |S| / |S^1| ) + n_2 * log( |S| / |S^2| )
The asymptotic null distribution of the criterion, when the maximum likelihood estimates of the covariance matrices are used, is Chi square with |Γ| * (|Γ|+3) / 2 degrees of freedom, where G is the dimension of the underlying distributions.
The function returns a list that contain the test statistic (stat
) and the p-value test obtained of equality, using the asymptotic distribution (alpha
).
The asymptotic null distributions holds only when the maximum likelihood estimates of the covariance matrices are supplied.
parameters
if(require(mvtnorm)){ ## Generate two random samples of size 50 from two multivariate normal distributions # sample size n<-50 # true parameters of class 1 and class 2 param.class1<-simulation$condition1 param.class2<-simulation$condition2$`5`$`2` # simulated dataset data.class1<-rmvnorm(n = n,mean =param.class1$mu ,sigma =param.class1$S) data.class2<-rmvnorm(n = n,mean =param.class2$mu ,sigma=param.class2$S) data<-rbind(data.class1,data.class2) classes<-c(rep(1,nrow(data.class1)),rep(2,nrow(data.class2))) s<-cov(data) s1<-cov(data.class1) s2<-cov(data.class2) testMeanVariance(S = s,S1 =s1, S2 = s2, n1 = n, n2 = n) ## equivalently... # estimated parameters: maximum likelihood estimate est.param<-parameters(data = data,classes =classes ,shrink = FALSE) testMeanVariance(est.param$S,est.param$S1,est.param$S2,est.param$n1,est.param$n2) }
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