BILOG-MG

Overview of the Program’s Features and Capabilities

Housed within a Windows graphical point-and-click interface, BILOG-MG is designed for the IRT analysis of instruments comprising dichotomously scored sets or subsets of items intended to measure a single underlying attribute or latent dimension. As an extension of the BILOG program of Robert J. Mislevy and R. Darrell Bock to multiple groups of respondents, the program accommodates a broad range of practical applications that involve one or more than one group of respondents and one or more than one test form (version) of an instrument. The program offers an array of options for estimating the parameters of the items in an instrument, the scale scores of persons completing it, and the latent distributions of the groups or populations represented in the data. It also provides numerous indices and plots to inform and guide the development of instruments with good measurement properties.

Models for Dichotomously Scored Items

As a program specifically designed for the IRT analysis of dichotomously scored items, BILOG-MG relies on binary logistic functions to model the relationship between the characteristics of an item and the probability that a person with a given level of the underlying trait (typically denoted as θ) will respond to the item in one of two predefined categories. The categories may represent correct and incorrect responses to multiple-choice problems on a test of educational achievement, the presence or absence of symptoms recorded on a checklist of characteristics associated with a particular medical condition, or some other binary classification of the responses to the items in an instrument. The latent trait measured with the items may be verbal proficiency, spatial ability, generalized anxiety, or any number of other underlying attributes that an individual may possess. In educational applications, the underlying trait often represents some form of cognitive proficiency measured by correct and incorrect responses to a set of multiple-choice or short-answer questions. The discussion that follows frames the program’s features and models in those terms, referring to the underlying trait as proficiency and denoting the probability that a person with proficiency θ will respond to item j with a correct response (xj = 1) as P(xj = 1θ = Pjθ).

BILOG-MG implements three binary logistic functions for the IRT analysis of dichotomously scored items, the one-, two-, and three-parameter models. The names indicate the number of item parameters in each model. The two-parameter model, for example, expresses the probability of a correct response to item j as a function of a person’s proficiency and two parameters specific to item j that must be estimated from the

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