On the multivariate asymptotic distribution of sequential Chi-square statistics

The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-square difference tests are asymptotically independent. Some Monte Carlo evidence on the applicability of the theory is provided. © 1985 The Psychometric Society.