Maximum likelihood estimation is one of the backbones of statistical analysis. It is used to obtain parameter estimates for a wide variety of models, including regression, factor analysis, and item response theory (IRT) analyses, among many others. When these estimates are based on data that are only marginally or partially observed, the procedure is called marginal maximum likelihood estimation (MMLE).
This article uses IRT analyses, a context in which the MMLE strategy is most common, to describe the assumptions, mathematics, and procedures of MMLE. The various models contained within the IRT family allow researchers to obtain estimates of an individual’s level of a latent trait of interest, typically referred to as θ, as well as information about the items, including their location on the θ scale ...
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