Local independence or local item independence is an important assumption for latent variable models such as latent class models, factor analytical models, and item response theory (IRT) models. The basic concept of local independence is that the response to an item (or a question) is independent of that to any other items conditional on the latent variable(s) being measured. Thus, local independence is also known as conditional independence. For instance, a mathematics achievement test is purported to measure a general mathematical ability. After removing the measured general mathematical ability, there are no relationships between any pairs of test items, indicating that the mathematics test items meet the assumption of local independence. If local independence is not met by test items, these items are considered local ...
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