© 1985 by Biometrika Trust
Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints
Department of Mathematics and Applied Mathematics, University of South Africa Pretoria 0001, South Africa
The analysis of moment structural models has become an important tool of investigation in behavioural, educational and economic studies. The chi-squared large-sample test is routinely employed to assess the goodness of fit of the model considered. However, in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met. Here we consider the case where the population value of the parameter vector is a boundary point of the feasible region. We show that in this case the asymptotic distribution of test statistic is a mixture of chi-squared distributions. The problem of finding the corresponding weights is discussed.
Key Words: Asymptotic normality • Chi-bar-squared statistic • Factor analysis • Heywood case • Moment structure • Test statistic
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