The present paper gives a general introduction to the linear logistic test model (Fischer, 1973), an extension of the Rasch model with linear constraints on item parameters, along with eRm (an R package to estimate different types of Rasch models; Mair, Hatzinger, & Mair, 2014) functions to estimate the model and interpret its parameters. The…

This chapter introduces three applications of Bayesian inference to common and novel issues in second language research. After a review of the critiques of conventional hypothesis testing, our focus centers on ways Bayesian inference can be used for dealing with missing data, for testing theory-driven substantive hypotheses without a default null…

Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…

This article presents a psychometric model for estimating ability and item-selection strategies in self-adapted testing. In contrast to computer adaptive testing, in self-adapted testing the examinees are allowed to select the difficulty of the items. The item-selection strategy is defined as the distribution of difficulty conditional on the…