fraction.subtraction.qmatrix: Fraction Subtraction Q-Matrix

Description

The Q-Matrix corresponding to Tatsuoka (1984) fraction subtraction data set.

Usage

data(fraction.subtraction.qmatrix)

Arguments

Format

The fraction.subtraction.qmatrix data frame consists of $J = 20$ rows and $K = 8$ columns, specifying the attributes that are believed to be involved in solving the items. Each row in the data frame represents an item and the entries in the row indicate whether an attribute is needed to master the item (denoted by a "1") or not (denoted by a "0"). The attributes for the fraction subtraction data set are the following:

alpha1: convert a whole number to a fraction,
alpha2: separate a whole number from a fraction,
alpha3: simplify before subtracting,
alpha4: find a common denominator,
alpha5: borrow from whole number part,
alpha6: column borrow to subtract the second numerator from the first,
alpha7: subtract numerators,
alpha8: reduce answers to simplest form.

Details

This Q-matrix can be found in DeCarlo (2011). It is the same used by de la Torre and Douglas (2004).

References

de la Torre, J. and Douglas, J. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333--353.

Tatsuoka, C. (2002). Data analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society, Series C, Applied Statistics, 51, 337--350.