Normal-Ogive Multidimensional Model

  • Roderick P. McDonald
Chapter

Abstract

In an attempt to provide a unified foundation for common factor analysis, true score theory, and latent trait (item response) theory, McDonald (1962a, 1962b, 1967) defined a general strong principle of local independence and described a general latent trait model, as follows: Let U be a n × 1 random vector of manifest variables—test or possibly binary item scores and θ a k × 1 random vector of latent traits—not yet defined. The strong principle of local independence, which defines θ and the dimension k of the vector U, states that
$$g\{ U\} \theta \} = \prod\limits_{i = 1}^k {{g_i}} \{ \left. {{U_i}} \right|\theta \} $$
(1)
where g{ } is the conditional density of U and g i { } is the conditional density of the ith component. (Note that θ is not necessarily continuous and may consist of a dummy variable defining a latent class model.)

Keywords

Item Response Theory Latent Trait Latent Class Model Local Independence Computer Adaptive Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Roderick P. McDonald

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