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

Area of Science:

• Statistics
• Educational Measurement
• Psychometrics

Background:

• Traditional non-response models often assume a single source, which is unrealistic for complex data like surveys and educational tests.
• Real-world non-responses can stem from diverse factors including test speededness, lack of motivation, or question sensitivity.
• Existing models may not adequately capture the multifaceted nature of non-response behaviors.

Purpose of the Study:

• To propose a novel tree model for non-response modeling that accommodates multiple underlying sources.
• To develop and validate an estimation procedure for the proposed model.
• To demonstrate the model's superiority over traditional methods using simulation and real-world data.

Main Methods:

• A generalized tree model with four end nodes was developed to represent diverse non-response mechanisms.
• Laplace-approximated maximum likelihood estimation was employed for model parameter estimation.
• Extensive simulations were conducted to validate the estimation procedure and compare the proposed model with existing approaches.
• The model was applied to data from the 2012 Programme for International Student Assessment (PISA).

Main Results:

• The proposed tree model demonstrated a superior fit to the 2012 PISA data compared to traditional models.
• Simulation studies confirmed the validity of the Laplace-approximated maximum likelihood estimation procedure.
• The model effectively distinguished between different sources of non-response in the analyzed dataset.
• The proposed model offers a more nuanced understanding of non-response patterns.

Conclusions:

• The developed four-node tree model provides a more realistic and flexible framework for non-response analysis.
• The Laplace-approximated maximum likelihood estimation is a viable method for parameter estimation in this model.
• This approach offers significant advantages over traditional methods in accurately modeling complex non-response.
• The model serves as a valuable tool for researchers seeking to understand and address diverse non-response sources in large-scale assessments.