Multidimensional item response theory models with general and specific latent traits for ordinal data

Martelli, Irene (2014) Multidimensional item response theory models with general and specific latent traits for ordinal data, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Metodologia statistica per la ricerca scientifica, 26 Ciclo. DOI 10.6092/unibo/amsdottorato/6347.
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Abstract

The aim of the thesis is to propose a Bayesian estimation through Markov chain Monte Carlo of multidimensional item response theory models for graded responses with complex structures and correlated traits. In particular, this work focuses on the multiunidimensional and the additive underlying latent structures, considering that the first one is widely used and represents a classical approach in multidimensional item response analysis, while the second one is able to reflect the complexity of real interactions between items and respondents. A simulation study is conducted to evaluate the parameter recovery for the proposed models under different conditions (sample size, test and subtest length, number of response categories, and correlation structure). The results show that the parameter recovery is particularly sensitive to the sample size, due to the model complexity and the high number of parameters to be estimated. For a sufficiently large sample size the parameters of the multiunidimensional and additive graded response models are well reproduced. The results are also affected by the trade-off between the number of items constituting the test and the number of item categories. An application of the proposed models on response data collected to investigate Romagna and San Marino residents' perceptions and attitudes towards the tourism industry is also presented.

Abstract
Tipologia del documento
Tesi di dottorato
Autore
Martelli, Irene
Supervisore
Dottorato di ricerca
Scuola di dottorato
Scienze economiche e statistiche
Ciclo
26
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
multidimensional item response theory; ordinal data; MCMC; additive model; Gibbs sampler.
URN:NBN
DOI
10.6092/unibo/amsdottorato/6347
Data di discussione
15 Maggio 2014
URI

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