LR Tests for some Linear Hypotheses in an Extended Growth Curve Model
Yasunori Fujikoshi, Takashi Kanda, Megu Ohtaki · American Journal of Mathematical and Management Sciences · 2006
SYNOPTIC ABSTRACTIn this paper we consider the problem of testing some linear hypotheses in an extended growth curve model which is described for the data set of k clusters. The model includes the one whose mean structure consists of polynomial growth curves with k different degrees. First we derive likelihood ratio tests for adequacy of the extended growth curve model. Next we consider to test a general linear hypothesis of the parameter matrix for each of k clusters. In general, we propose to use Wald type test. However, likelihood ratio tests are derived for two important special cases. It is shown that the null distributions of our likelihood ratio statistics can be expressed as products of independent lambda statistics. We also give a numerical example.