fraction.subtraction.qmatrix {CDM} | R Documentation |

## Fraction Subtraction Q-Matrix

### Description

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

### Usage

```
data(fraction.subtraction.qmatrix)
```

### 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).

### Source

DeCarlo, L. T. (2011). On the analysis of fraction subtraction data:
The DINA Model, classification, latent class sizes, and the Q-Matrix.
*Applied Psychological Measurement*, **35**, 8–26.

### 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.

Tatsuoka, K. (1984) *Analysis of errors in fraction addition and subtraction
problems*. Final Report for NIE-G-81-0002, University of Illinois, Urbana-Champaign.

*CDM*version 8.2-6 Index]