Item Response Theory

4Item Parameter Estimation – Binary Data

In God we trust, all others must bring data.

(Source: Edward Deming)

The practical use of scale‐score estimation procedures presented in Chapter 2 requires that we know the response functions of the items involved. Since there is no way to determine these functions on theoretical grounds, we have no alternative but to estimate them from a suitable sample of respondents. In the model‐based approach to item response theory (IRT), this means estimating the free parameters of the model that represents the response process.

In most applications, the aim of the estimation is to “calibrate” a test or scale – that is, to estimate parameter values that can be used in computing scores for persons who respond to the instrument on future occasions. Used in this way, item calibration plays much the same role as test norming in classical theory. Like the establishing of test norms, it necessarily assumes that conditions remain stable in the population of respondents while the current calibration is in force. This assumption is justified only when the procedure for administering the test or scale is identical at each use. Especially in cognitive testing, even small differences in the format of test booklets, or in the instructions to the respondents or timing of the test session, can appreciably affect the test scores. The effect may not be very apparent for any particular respondent, but if it is in the same direction for all respondents, the bias ...