Parameter identifiability and estimation in some item response theory models

• Grant number: 22/11115-2
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: June 15, 2023
• End date: August 14, 2023
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Jorge Luis Bazan Guzman
• Grantee: Jorge Luis Bazan Guzman
• Visiting researcher: Jorge Andres Gonzalez Burgos
• Visiting researcher institution: Pontificia Universidad Católica de Chile, Chile
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Item response theory (IRT) and latent variables models are a set of statistical models which are widely used in different fields to model the either binary or count scored responses of individuals to certain stimuli. IRT models relate the probability of answering a test item to both individual's and item's parameters using what is called an item response function. These models, however, suffer from what is known as identifiability problems. An identifiability analysis is (and it should be) always performed as a previous step to parameter estimation and statistical inference in all statistical models. Lack of identifiability results in a meaningless statistical model, so the assessment and analysis of identifiability problems is extremely important because it is a condition necessary for ensuring coherent estimation and inferences on the parameters of interest.In this project, we will study identifiability and estimation problems in a particular class of IRT models for binary response data which allow for asymmetries of the item response function. The estimation of novel IRT models for count data will also be studied.As expected products of this project, we plan to submit at least two manuscripts to international journals in the fields of statistics and/or psychometrics. The project also pretends the collaboration of the visiting researcher as a co-supervisor of a doctoral student; participation as a member of the doctoral board committee of another student; research activities with members of the latent variable model group; presentation of a talk in the postgraduate program seminars' series; and the elaboration of a research project proposal to be submitted to international funding agencies. (AU)