On the revival of the Rasch model-based LLTM: From constructing tests using item generating rules to measuring item administration effects

Abstract

The “linear logistic test model” (LLTM) breaks down the item parameter of the Rasch model into a linear combination of certain hypothesized elementary parameters. Apart from the originally intended primary application of generating an indefinite number of items composed of whichever item difficulties the examiner chooses, there are many other potential applications. They all deal with measuring certain item administration effects. This paper illustrates several of these approaches as well as how to design data sampling using the respective LLTM’s structure matrix. These approaches deal with: a) Rasch model item calibration using data sampled consecutively in time but partly from the same examinees; b) measuring position effects of item presentation, in particular, learning and fatigue effects – specific for each position, as well as linear or non-linear; c) measuring content-specific learning effects; d) measuring warming-up effects; e) measuring effects of speeded item presentation; f) measuring effects of different item response formats. It is pointed out that the given LLTM approaches have the advantage of “elegance,” as a hierarchical system of concurrent (alternative) hypotheses can be tested.