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Abstract:
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The non-response model in Knott, Albanese, and Galbraith (1991) can be represented as a tree model with one branch for response/non-response (NR) and another branch for correct/incorrect response, and each branch probability is characterized by an item response theory model. In the model, it is assumed that there is only one source of NRs. However, in questionnaires or educational tests, NRs might come from different sources, such as test speededness, inability to answer, lack of motivation, and sensitive questions. To better accommodate such more realistic underlying mechanisms, we propose a not-all-distinct four end nodes tree model for NR modeling. The Laplace-approximated maximum likelihood estimation for the proposed model is suggested. The validation of the proposed estimation procedure and the advantage of the proposed model over traditional methods are demonstrated in simulations. For illustration, the methodologies are applied to 2012 Programme for International Student Assessment (PISA) data. The analysis shows that the proposed tree model has a better fit to PISA data compared with other existing models, providing a useful tool to distinguish the sources of NR.
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