2.4. Application: Math data set

The program BayesianModeling generates the syntaxes necessary for the Bayesian estimation of several models of the Item Response Theory, for posterior use in WinBUGS (see Spiegelhalter et al 1996) or OpenBUGS (Spiegelhalter et al 2007) program, using diverse MCMC methods. For this only is necessary to have a file of text with the data, generated from any statistics program or from Excel. In each column, usually appear the names of the items in the first line.

As an example, consider a data set of 14 items from a Mathematical test developed by the Unity of Measurement of the Educative Quality of Peru for the National Evaluation of the sixth degree of 1998 which were applied to a sample of 131 students of sixth degree of high socioeconomic level. These data have been used in Bazán, Branco and Bolfarine (2006) and Bazán, Bolfarine and Leandro (2006).

The released items are a sampling from a test that appears published in the following link:

http://www2.minedu.gob.pe/umc/admin/images/publicaciones/boletines/Boletin-13.pdf

In the table appears the identification corresponding to the number of item with the number in the UMEQ test.

Number of item of Math data | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14
Number of item in the UMEQ test | 1 | 8 | 9 | 11 | 12 | 13 | 21 | 25 | 32 | 5 | 17 | 30 | 2 | 10

The data file can be found in the file zip of the program and has the following structure:

I01 I02 I03 I04 I05 I06 I07 ... I12 I13 I14

1 1 0 1 1 0 1 ... 0 0 1

1 1 1 1 1 1 1 ... 0 1 1

. . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . . . . .

1 1 0 1 0 0 1 ... 0 1 1

As an example of application we consider an IRT model with asymmetric link, in this case we consider the skew normal ogive model with parameters of difficulty and of discrimination, this is a two-parameter skew probit IRT model (2SP)

, where is a parameter of penalty and denote the skew normal cdf.