Abstract
Suppose that random factor models with k factors are assumed to hold for m, p-variate populations. A model for factorial invariance has been proposed wherein the covariance or correlation matrices can be written as Σ i = LC i L′ + σ i 2 I, where C i is the covariance matrix of factor variables and L is a common factor loading matrix, i = 1,…, m. Also a goodness of fit statistic has been proposed for this model. The asymptotic distribution of this statistic is shown to be that of a quadratic form in normal variables. An approximation to this distribution is given and thus a test for goodness of fit is derived. The problem of dimension is considered and a numerical example is given to illustrate the results.
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