An item response tree model with not-all-distinct end nodes for non-response modelling

Yu Wei Chang*, Nan Jung Hsu, Rung Ching Tsai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The non-response model in Knott et al. (1991, Statistician, 40, 217) can be represented as a tree model with one branch for response/non-response 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 non-responses. However, in questionnaires or educational tests, non-responses 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 a tree model with four end nodes, not all distinct, for non-response modelling. 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 data from the 2012 Programme for International Student Assessment (PISA). The analysis shows that the proposed tree model has a better fit to PISA data than other existing models, providing a useful tool to distinguish the sources of non-responses.

Original languageEnglish
Pages (from-to)487-512
Number of pages26
JournalBritish Journal of Mathematical and Statistical Psychology
Issue number3
Publication statusPublished - 2021 Nov


  • Laplace-approximated maximum likelihood estimation
  • item response theory tree model
  • non-response

ASJC Scopus subject areas

  • Statistics and Probability
  • Arts and Humanities (miscellaneous)
  • General Psychology


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