Extending the Basic Local Independence Model to Polytomous Data

Luca Stefanutti, Debora Chiusole, Pasquale Anselmi and Andrea Spoto ()
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Luca Stefanutti: University of Padua
Debora Chiusole: University of Padua
Pasquale Anselmi: University of Padua
Andrea Spoto: Department of General Psychology

Psychometrika, 2020, vol. 85, issue 3, No 7, 684-715

Abstract: Abstract A probabilistic framework for the polytomous extension of knowledge space theory (KST) is proposed. It consists in a probabilistic model, called polytomous local independence model, that is developed as a generalization of the basic local independence model. The algorithms for computing “maximum likelihood” (ML) and “minimum discrepancy” (MD) estimates of the model parameters have been derived and tested in a simulation study. Results show that the algorithms differ in their capability of recovering the true parameter values. The ML algorithm correctly recovers the true values, regardless of the manipulated variables. This is not totally true for the MD algorithm. Finally, the model has been applied to a real polytomous data set collected in the area of psychological assessment. Results show that it can be successfully applied in practice, paving the way to a number of applications of KST outside the area of knowledge and learning assessment.

Keywords: polytomous knowledge space theory; basic local independence model; probabilistic structures; polytomous items; Likert scale; psychological assessment (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11336-020-09722-5

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