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EQUATIONS FOR THE LATENT CLASS MODEL
Let η = (η0, . . .η4) denote the stage of understanding of a child, with ηk = 1 if the child is in Stage k and 0 if not. Let π = (π0,...,π4) denote the population proportions of children in these classes; that is, πk = p (ηk = 1). Let xj represent a response to Task j, 1 if correct and 0 if not; j runs from 1 to 24.