Normal-Ogive Multidimensional Model

  • Roderick P. McDonald


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
$$g\{ U\} \theta \} = \prod\limits_{i = 1}^k {{g_i}} \{ \left. {{U_i}} \right|\theta \} $$
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.)


Item Response Theory Latent Trait Latent Class Model Local Independence Computer Adaptive Test 
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© Springer Science+Business Media New York 1997

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  • Roderick P. McDonald

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