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Dynamic estimation in the extended marginal Rasch model with an application to mathematical computer‐adaptive practice
Author(s) -
Brinkhuis Matthieu J.S.,
Maris Gunter
Publication year - 2020
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12157
Subject(s) - rasch model , comparability , computer science , simple (philosophy) , bayesian probability , matrix (chemical analysis) , missing data , data mining , algorithm , statistics , econometrics , mathematics , machine learning , artificial intelligence , epistemology , combinatorics , composite material , philosophy , materials science
We introduce a general response model that allows for several simple restrictions, resulting in other models such as the extended Rasch model. For the extended Rasch model, a dynamic Bayesian estimation procedure is provided, which is able to deal with data sets that change over time, and possibly include many missing values. To ensure comparability over time, a data augmentation method is used, which provides an augmented person‐by‐item data matrix and reproduces the sufficient statistics of the complete data matrix. Hence, longitudinal comparisons can be easily made based on simple summaries, such as proportion correct, sum score, etc. As an illustration of the method, an example is provided using data from a computer‐adaptive practice mathematical environment.