Using Logistic Approximations of Marginal Trace Lines to Develop Short Assessments

Test developers often need to create unidimensional scales from multidimensional data. For item analysis, marginal trace lines capture the relation with the general dimension while accounting for nuisance dimensions and may prove to be a useful technique for creating short-form tests. This article describes the computations needed to obtain logistic approximations of marginal trace lines for graded response items derived from multidimensional bifactor item response theory (IRT) models. Next, the properties of marginal-trace-line-based likelihoods are evaluated and compared with other bifactor IRT methods. It is noted that for the dimension of interest, the likelihoods computed from marginal item response functions are not equivalent to the conditional likelihoods from the multidimensional IRT model. The authors then propose a method that evaluates the degree of item-level dimensionality and allows for the selection of subsets of items (i.e., short form) that result in scaled scores and standard errors that are equivalent to other multidimensional IRT-based scoring procedures. Finally, a real-data application is provided, which illustrates the utility of logistic approximations of marginal trace lines in the creation of a content-diverse short form.