A skew item response model

By Jorge L. Bazán, Máaarcia D. Branco, Heleno Bolfarine. 2006

103 citations recorded by the source corpus.

We introduce a new skew-probit link for item response theory (IRT) by considering an accumulated skew-normal distribution. The model extends the symmetric probit-normal IRT model by considering a new item (or skewness) parameter for the item characteristic curve. A special interpretation is given for this parameter, and a latent linear structure is indicated for the model when an augmented likelihood is considered. Bayesian MCMC inference approach is developed and an efficiency study in the estimation of the model parameters is undertaken for a data set from Tanner (1996, p. 190) by using the notion of effective sample size (ESS) as defined in Kass et al. (1998) and the sample size per second (ESS/s) as considered in Sahu (2002). The methodology is illustrated using a data set corresponding to a Mathematical Test applied in Peruvian schools for which a sensitivity analysis of the chosen priors is conducted and also a comparison with seven parametric IRT models is conducted. The main conclusion is that the skew-probit item response model seems to provide the best fit.

Subfields: Computer Networks and Communications, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/46dbbd9677f3de4ed792cdb8b77a523945faca52

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In Computer Networks and Communications

1. Máaarcia D. Branco
2. Heleno Bolfarine
3. Jorge L. Bazán

In Management Science and Operations Research

1. Máaarcia D. Branco
2. Heleno Bolfarine
3. Jorge L. Bazán

In Statistics and Probability

1. Heleno Bolfarine
2. Jorge L. Bazán
3. Máaarcia D. Branco
4. Marc G. Genton
5. Adelchi Azzalini
6. Reinaldo Boris Arellano-Valle
7. Victor Hugo Lachos
8. M. Chris Jones

Citations in the corpus

• A Framework for Skew-Probit Links in Binary Regression (2010, methodology): “Moreover, by considering time of execution for the different models in Table 2, we note that in the sp class of links, the execution time is high as was also observed in Bazán et al. (2006) for the BBB sp link when applied to item response theory models.”