multilm.summaries {multilm} | R Documentation |
summary.multilm(object, test="Hotelling")
The Hotelling T^2 test is not very useful when the number of observations is
limited but many variables are included in the model. This problem is solved
by the stabilized multivariate test procedures by Laeuter et.al., which are
available in summary.multilm
. All these test procedures follow the same
principle: generate a vector d (or a matrix
D) as a function of W = (Y - bar{Y})^{top}(Y - bar{Y}) ,
where Y is the matrix of responses. Then analyse the original test problem using
the low dimensional, artificial "responses" Yd or YD by T^2.
The procedures SS, PC-q, PC-1 and CS differ in the way the vector d
or the matrix D is defined. SS, CS and PC-1 test always reduce the
original problem into a one dimensional problem. Naturally, one would use
the univariate procedures instead of a univariate T^2 test. Because of the lack
of a simple standard procedure for testing any linear hypothesis H0: Kβ =
0, we use T^2, which reduces to the F-test in the univariate case.
The test statistic, degrees of freedom and the p-value of the test.
Torsten Hothorn <hothorn@statistik.uni-dortmund.de>
Laeuter, J; Glimm, Ekkehard; Kropf, S. (1998): Multivariate Tests Based On Left-spherically Distributed Linear Scores, The Annals of Statistics, Vol. 26, No. 5, pp. 1972-1988
# Edgar Anderson's famous iris data data(iris) # one-classification MANOVA, Y response matrix, X designmatrix Y <- as.matrix(iris[,1:4]); x <- c(rep(1,50), rep(0,150), rep(1, 50), rep(0,150), rep(1,50)) X <- matrix(x, ncol=3) # restrictions: sum of effects equal zero Z <- c(0,1,1,1); # test for equal effects K <- cbind(0,diag(2),-1); # model (this method returns a multilm object) mod <- multilm(Y ~ X, K,Z); # output and stable tests summary(mod) # Hotelling T^2: pvalue = 0 summary(mod, "SS") # SS-Test: pvalue = 0 summary(mod, "PC-q") # PC-q-Test: pvalue = 0 summary(mod, "PC-1") # PC-1-Test: pvalue = 0 summary(mod, "CS") # CS-Test: pvalue = 0 # the iris data is to good -> simulate a "bad" multivariate dataset # only 8 observations in 2 groups, 4 variables observ <- c(1:4,51:54); rY <- Y[observ,] rX <- X[observ,1:2] rZ <- c(0,1,1); rK <- c(0,1,-1); rmod <- multilm(rY ~ rX, rK, rZ); summary(rmod) # T^2: pvalue = .00052 summary(rmod, "SS") # SS-Test: pvalue = .008 summary(rmod, "PC-q") # PC-q-Test: pvalue = .000012 summary(rmod, "PC-1") # PC-1-Test: pvalue = .0000038 summary(rmod, "CS") # CS-Test: pvalue = .0002