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

By Jacques A. Hagenaars, Allan L. McCutcheon

This learn introduces a number of fresh thoughts in latent classification research to a much wider viewers of researchers. some of the world's top innovators within the box of latent type research have contributed essays to the amount, each one featuring a key innovation to the elemental LCM and illustrating the way it can end up important in occasions regularly encountered in genuine learn.

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2. THE LATENT CLASS MODEL Now let us consider the latent class model in the situation in which variable A is an observed (or manifest) dichotomous or polytomous variable having I classes (i = 1, 2, . . , I), variable B is an observed (or manifest) dichotomous or polytomous variable having J classes ( j = 1, 2, . . , J ), and variable X is an unobserved (or latent) dichotomous or polytomous denote the joint variable having T classes (t = 1, 2, . . , T). Let πiABX jt probability that an observation is in class i on variable A, in class j on variable B, and in class t on variable X; let πitAX denote the conditional probability that an observation is in class i on variable A, given that the observation is in class t on variable X; let π jtBX denote the conditional probability that an observation is in class j on variable B, given that the observation is in class t on variable X; and let πtX denote the probability that an observation is in class t on variable X.

3 The crossclassified data in Table 4 were analyzed earlier by Stouffer and Toby (1951) and Lazarsfeld and Henry (1968) by using a particular latent class model that had five latent classes, and by Goodman (1974b) by using much simpler latent class models that had two latent classes and three latent classes. In the present exposition, we shall more fully examine the interpretation of the two-class and three-class latent class models in the analysis of the data in Table 4 and in other such tables, and we shall see how the use of such latent class models in the present context can change in a dramatic way our view of the meaning and the character of the underlying latent variable on which our attention is focused.

05 for the strictly universalistic, the mixed universalistically/ particularistically inclined, and the strictly particularistic, respectively. Models M1 and M3 make different statements about the heterogeneity of the individuals whose responses in situations of role conflict are described in Table 4. Model M1 states that there are two different types of individuals, and the model can be used to describe how these two types differ from each other; model M3 states that there are three different types of individuals, and the model can be used to describe how these three types differ from each other.

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