A Generalized Logistic Item Response Model Parameterizing Test Score Inappropriateness

Abstract

The person response curve has been suggested as a possible model for test score inappropriateness (Lumsden, 1977(Lumsden, , 1978Weiss, 1973). The two-parameter person response curve proposed by Lumsden includes a person slope parameter but abandons the notion of differential item relatedness to the underlying trait. As an alternative, a generalized logistic model is considered that includes all item parameters of the threeparameter logistic model (Birnbaum, 1968). In addition to the usual person location parameter, the model has extra person parameters representing two possible characterizations of test score inappropriateness: a slope parameter indicating the degree to which a person responds differently to items of varying difficulty, and an asymptote parameter measuring a person's proclivity to engage in effective guessing or to omit items in the presence of partial information. To assess the model's feasibility, statistical comparisons were made between parameter estimates from data simulated according to the model and the original simulation parameters. The results seem encouraging, but additional empirical study is needed before firm conclusions can be drawn.An important psychometric problem that has received considerable attention in recent years concerns the accuracy and validity of individual test scores. Traditional indices, such as coefficient alpha and the standard error of measurement, provide descriptive information for the group but completely ignore any variation in measurement error across persons. For the purpose of assessing the appropriateness of individual test scores, methods are needed that quantify measurement error at the level of the individual examinee. It is this problem that is considered here.Tatsuoka and Linn (1983) have distinguished two general classes of techniques for use in detecting atypical patterns of item responses produced by individuals. The essential difference between the two approaches is that one is based on ordinary descriptive statistics derived from the persons x items score matrix, whereas the other is modelbased.

Cognitive psychology meets psychometric theory: On the relation between process models for decision making and latent variable models for individual differences.

“…Strandmark and Linn (1987) presented a 2PL model for person fit (see al.so Ferrando, 2007;Reise, 20(M)). Of interest, their 2PL model is similar to the D-diffusion item response model.…”

The Influence of Test Characteristics on the Detection of Aberrant Response Patterns

“…One such model, which is similar to the generalized response aberrancy model in Strandmark and Linn (1987), is where a, is the item discrimination, and czp is the aberrancy level parameter. Equation 6 differs from the IRT model in Equation 1 in that (1) the a parameter is indexed by a, in order to clearly indicate that it is the slope parameter from a three-parameter item response function; and (2) the a, person parameter multiplicatively weights the a, item parameter.…”

A Pearson-Type-VII item response model for assessing person fluctuation

“…Model-based individual slopes were first introduced by Strandmark and Linn (1987). Their model was a generalized logistic model in which the individual slope parameter was a moderator of the common ICC slope.…”

“…Parallel to the theoretical developments, several models that take into account momentary fluctuation have been developed (Coombs, 1948a, b;Helmstader, 1957;Jackson, 1986;Levine & Rubin, 1979;Lumsden, 1977;Mosier, 1942;Reise, 2000;Strandmark & Linn, 1987;Tyler, 1968;Weiss, 1973). These models have widely differing objectives and terminology.…”