Abstract
A feature common to most models considered in the first part of this book may be easily depicted by Figure 1. In latent trait models, the point of departure is a set of manifest categorical variables (indicators, items, say A, B, and C), which may be related to each other in some way (cf. the curved lines). The crucial assumption now is that these relationships are conceived as being due to some continuous latent variable X. That is, if the model holds, the relationships between the manifest variables will vanish and the structure will be depicted by the straight lines going from X to A, B, and C. Several people, however, have questioned whether this procedure is advisable in all instances. Latent trait models strive for a relatively sophisticated scaling property of the latent variable (most models aim at least at an interval scale) which often remains unused for subsequent interpretation of the data. In fact, we are often simply interested in certain groups or types of persons (see Rost, Chapter 7, this volume), that means that we need no more than a categorical or nominal latent variable. This is exactly what latent class models assume.
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Langeheine, R. (1988). New Developments in Latent Class Theory. In: Langeheine, R., Rost, J. (eds) Latent Trait and Latent Class Models. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5644-9_5
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