Download Applied Latent Class Analysis by Jacques A. Hagenaars, Allan L. McCutcheon PDF

By Jacques A. Hagenaars, Allan L. McCutcheon

ISBN-10: 0521594510

ISBN-13: 9780521594516

This research introduces a number of fresh ideas in latent classification research to a much wider viewers of researchers. some of the world's major innovators within the box of latent type research have contributed essays to the amount, every one providing a key innovation to the elemental LCM and illustrating the way it can end up important in events ordinarily encountered in real examine.

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Using this model, Peirce found that the proportion θ of the time that an infallible predictor is used can be determined by the following formula: θ = (P11 P22 − P12 P21 ) P1B P2B = P11 P1B − P12 P2B ; (6) see Peirce (1884) and Goodman and Kruskal (1959). Peirce’s model can be viewed as a latent structure in which the observed cross-classification in the 2 × 2 table {A, B} is obtained from a mixture of the two 2 × 2 tables, which we described previously, pertaining to an unobserved (or latent) infallible predictor and an unobserved (or latent) ignorant predictor, respectively, where the proportion of the time that each kind of latent predictor is used is unknown.

Instead of imposing the additional constraints of Equations (8a) and (8b) as in Peirce’s model, let us consider, for example, the model obtained with the imposition of the simple constraint π2X = 0 in the three-class latent class model. With this model, there is just one kind of infallible predictor (rather than the two kinds) in the model, and the proportion θ of the time that the infallible predictor is used can be determined simply by θ = P11 − P12 P21 /P22 , (9) with θ = π1X. Similarly, with the imposition of the constraint π1X = 0 (rather than the constraint π2X = 0) in the three-class latent class model, it is the other kind of infallible predictor that is in the model, and the corresponding proportion θ of the time that this infallible predictor is used can be determined simply by θ = P22 − P12 P21 /P11 , (10) with θ = π2X.

Next let us consider a somewhat different situation. ” These can be viewed as latent categories or latent classes or latent types of individuals; and we can consider the latent variable E for “endowment” (favorable endowment or not favorable endowment) as a latent dichotomous variable. Further suppose that it is this latent variable E that affects what the mental health status is of the individual, and also that it is parental socioeconomic status that affects what the endowment status E is (favorable or not favorable) of the individual.

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