Item Response Theory

6Multidimensional IRT Models

Not all of the characteristics which are conversationally described in terms of “more” or “less” can actually be measured. But any characteristic which lends itself to such description has the possibility of being reduced to measurement.

(Source: L.L. Thurstone)

Item factor analysis¹ plays an essential role in the development of tests or scales to measure behavioral tendencies that are considered to be a matter of degree but are observed only as discrete responses. Typical examples are the following:

• Tests of school science achievement based on responses to a number of exercises marked right or wrong.
• Social surveys in which degree of conservatism of the respondent is assessed by agreement or disagreement with positions on a variety of public issues.
• Patient self‐reports of satisfaction with the outcome of a medical treatment rated on a seven‐point scale.
• Inventory of activities favorable or unfavorable to general health reported in terms of frequency – never, up to once a month, up to once a week, more than once a week.
• Nutrition survey of food preference categorized as dislike very much, dislike moderately, neither like nor dislike, like moderately, like very much.

The main problem in constructing these kinds of response instruments is the lack of any definite rules for choosing items that best represent the concept to be measured. The content and wording of items that embody the concept are almost always up to the item writer. Once the instrument ...