A large sample analysis of the magnitudinal model in multivariate analysis
Titel:
A large sample analysis of the magnitudinal model in multivariate analysis
Auteur:
Chakravorti, S.R. Guttman, Irwin
Verschenen in:
Communications in statistics
Paginering:
Jaargang 16 (1987) nr. 7 pagina's 1995-2002
Jaar:
1987
Inhoud:
Suppose [image omitted] are (p × 1) random vectors, and that interest focuses on whether or not the socalled magnitudinal model [image omitted] holds. [c > 0 is called the magnitudinal effect.] This paper proceeds as follows. On the basis of random samples of size N1 and N2 on [image omitted] respectively, and assuming [image omitted] , we find the limiting distribution of [image omitted] is the maximum likelihood estimate of [image omitted] . We then find the limiting distribution of the [(p-1)×1] vector [image omitted] , and A is any 'contrast' producing matrix, such as the Helmert matrix, so that [image omitted] is a vector of contrasts of contrasts of the cj. We are interested in [image omitted] if and only if [image omitted] . Using the limiting distribution of [image omitted] , we propose a large sample test of [image omitted] , and we illustrate with examples from two different subject areas.
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