data.fraction.RdContains different sub-datasets of the fraction subtraction data of Tatsuoka with different Q-matrix specifications.
The dataset data.fraction1 is the fraction subtraction data set with
536 students and 15 items. The Q-matrix was defined in de la Torre (2009).
This dataset is a list with the dataset (data) and
the Q-matrix as entries.
The format is:
List of 2 $ data :'data.frame': ..$ T01: int [1:536] 0 1 1 1 0 0 0 0 0 0 ... ..$ T02: int [1:536] 1 1 1 1 1 0 0 1 0 0 ... ..$ T03: int [1:536] 0 1 1 1 1 1 0 0 0 0 ... ..$ T04: int [1:536] 1 1 1 0 0 0 0 0 0 0 ... ..$ T05: int [1:536] 0 1 0 0 0 1 1 0 1 1 ... ..$ T06: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ T07: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ T08: int [1:536] 1 1 0 1 1 0 0 0 1 1 ... ..$ T09: int [1:536] 1 1 1 1 0 1 0 0 1 0 ... ..$ T10: int [1:536] 1 1 1 0 0 0 0 0 0 0 ... ..$ T11: int [1:536] 1 1 1 1 0 0 0 0 0 0 ... ..$ T12: int [1:536] 0 1 0 0 0 0 0 0 0 0 ... ..$ T13: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ T14: int [1:536] 1 1 0 0 0 0 0 0 0 0 ... ..$ T15: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... $ q.matrix: int [1:15, 1:5] 1 1 1 1 0 1 1 1 1 1 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : chr [1:15] "T01" "T02" "T03" "T04" ... .. ..$ : chr [1:5] "QT1" "QT2" "QT3" "QT4" ...
The dataset data.fraction2 is the fraction subtraction data set
with 536 students and 11 items. For this data set, several \(Q\) matrices are
available. The data is a list. The first entry data
contains the data frame. The entry q.matrix1 contains
the Q-matrix of Henson, Templin and Willse (2009).
The third entry q.matrix2 is an alternative
Q-matrix of de la Torre (2009). The fourth entry is a
modified Q-matrix of q.matrix1.
The format is:
$ data :'data.frame': ..$ H01: int [1:536] 1 1 1 1 1 0 0 1 0 0 ... ..$ H02: int [1:536] 1 1 1 0 0 0 0 0 0 0 ... ..$ H03: int [1:536] 0 1 0 0 0 1 1 0 1 1 ... ..$ H04: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ H05: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ H06: int [1:536] 1 1 0 1 1 0 0 0 1 1 ... ..$ H08: int [1:536] 1 1 1 0 0 0 0 0 0 0 ... ..$ H09: int [1:536] 1 1 1 1 0 0 0 0 0 0 ... ..$ H10: int [1:536] 0 1 0 0 0 0 0 0 0 0 ... ..$ H11: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ H13: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... $ q.matrix1: int [1:11, 1:3] 1 1 1 1 1 1 1 1 1 1 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : chr [1:11] "H01" "H02" "H03" "H04" ... .. ..$ : chr [1:3] "QH1" "QH2" "QH3" $ q.matrix2: int [1:11, 1:5] 1 1 0 1 1 1 1 1 1 1 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : chr [1:11] "H01" "H02" "H03" "H04" ... .. ..$ : chr [1:5] "QT1" "QT2" "QT3" "QT4" ... $ q.matrix3: num [1:11, 1:3] 0 0 0 1 0 0 0 0 1 1 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : chr [1:11] "H01" "H02" "H03" "H04" ... .. ..$ : chr [1:3] "Dim1" "Dim2" "Dim3"
The dataset data.fraction3 contains 12 items and was
used in de la Torre (2011).
List of 2 $ data :'data.frame': 536 obs. of 12 variables: ..$ B01: int [1:536] 0 1 1 1 0 0 0 0 0 0 ... ..$ B02: int [1:536] 1 1 1 1 1 0 0 1 0 0 ... ..$ B03: int [1:536] 0 1 1 1 1 1 0 0 0 0 ... ..$ B04: int [1:536] 0 1 0 0 0 1 1 0 1 1 ... ..$ B05: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ B06: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ B07: int [1:536] 1 1 0 1 1 0 0 0 1 1 ... ..$ B08: int [1:536] 1 1 1 1 0 1 0 0 1 0 ... ..$ B09: int [1:536] 1 1 1 1 0 0 0 0 0 0 ... ..$ B10: int [1:536] 0 1 0 0 0 0 0 0 0 0 ... ..$ B11: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ B12: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... $ q.matrix:'data.frame': 12 obs. of 5 variables: ..$ item: Factor w/ 13 levels "","B01","B02",..: 2 3 4 5 6 7 8 9 10 11 ... ..$ QA1 : int [1:12] 1 1 1 1 1 1 1 1 1 1 ... ..$ QA2 : int [1:12] 0 1 0 0 1 1 1 0 0 0 ... ..$ QA3 : int [1:12] 0 1 0 1 1 1 0 1 1 1 ... ..$ QA4 : int [1:12] 0 1 0 0 1 1 0 0 0 1 ...
The dataset data.fraction4 contains 17 items and was
used in de la Torre and Douglas (2004) and Chen, Liu, Xu and Ying (2015).
List of 2 $ data :'data.frame': 536 obs. of 17 variables: ..$ A01: int [1:536] 0 0 0 1 0 0 0 0 0 0 ... ..$ A02: int [1:536] 0 1 1 1 0 0 0 0 0 0 ... ..$ A03: int [1:536] 0 1 1 1 0 0 0 0 0 0 ... ..$ A04: int [1:536] 1 1 1 1 1 0 0 1 0 0 ... ..$ A05: int [1:536] 1 1 0 1 1 0 0 0 1 1 ... ..$ A06: int [1:536] 1 1 1 1 0 1 0 0 1 0 ... ..$ A07: int [1:536] 1 1 1 1 0 0 0 0 0 0 ... ..$ A08: int [1:536] 0 0 0 1 0 0 0 0 0 1 ... ..$ A09: int [1:536] 1 1 1 0 0 0 0 0 0 0 ... ..$ A10: int [1:536] 1 1 1 0 0 0 0 0 0 0 ... ..$ A11: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ A12: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ A13: int [1:536] 0 1 0 0 0 0 0 0 0 0 ... ..$ A14: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ A15: int [1:536] 1 1 0 0 0 0 0 0 0 0 ... ..$ A16: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ A17: int [1:536] 0 1 0 0 0 0 0 0 0 0 ... $ q.matrix:'data.frame': 17 obs. of 9 variables: ..$ item: Factor w/ 18 levels "","A01","A02",..: 2 3 4 5 6 7 8 9 10 11 ... ..$ QA1 : int [1:17] 0 0 0 0 0 0 0 0 1 0 ... ..$ QA2 : int [1:17] 0 0 0 1 0 1 1 1 1 1 ... ..$ QA3 : int [1:17] 0 0 0 1 0 0 0 0 0 0 ... ..$ QA4 : int [1:17] 1 1 1 0 0 0 0 1 0 0 ... ..$ QA5 : int [1:17] 0 0 0 1 0 0 1 0 0 1 ... ..$ QA6 : int [1:17] 1 0 0 0 0 0 1 0 0 0 ... ..$ QA7 : int [1:17] 1 1 1 1 1 1 1 1 1 1 ... ..$ QA8 : int [1:17] 0 0 0 0 1 0 0 1 0 0 ...
The dataset data.fraction5 contains 15 items and was
used as an example for the multiple strategy DINA model in
de la Torre and Douglas (2008) and Hou and de la Torre (2014).
The two Q-matrices for coding the multiple strategies are contained
in one matrix q.matrix by joining the columns of both matrices.
List of 2 $ data :'data.frame': 536 obs. of 15 variables: ..$ T01: int [1:536] 0 1 1 1 0 0 0 0 0 0 ... ..$ T02: int [1:536] 1 1 1 1 1 0 0 1 0 0 ... ..$ T03: int [1:536] 0 1 1 1 1 1 0 0 0 0 ... ..$ T04: int [1:536] 1 1 1 0 0 0 0 0 0 0 ... ..$ T05: int [1:536] 0 1 0 0 0 1 1 0 1 1 ... ..$ T06: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ T07: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ T08: int [1:536] 1 1 0 1 1 0 0 0 1 1 ... ..$ T09: int [1:536] 1 1 1 1 0 1 0 0 1 0 ... ..$ T10: int [1:536] 1 1 1 0 0 0 0 0 0 0 ... ..$ T11: int [1:536] 1 1 1 1 0 0 0 0 0 0 ... ..$ T12: int [1:536] 0 1 0 0 0 0 0 0 0 0 ... ..$ T13: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... ..$ T14: int [1:536] 1 1 0 0 0 0 0 0 0 0 ... ..$ T15: int [1:536] 1 1 0 1 0 0 0 0 0 0 ... $ q.matrix:'data.frame': 15 obs. of 15 variables: ..$ item: Factor w/ 16 levels "","T01","T02",..: 2 3 4 5 6 7 8 9 10 11 ... ..$ SA1 : int [1:15] 0 1 1 1 0 1 1 1 1 1 ... ..$ SA2 : int [1:15] 0 1 0 1 0 1 1 1 0 0 ... ..$ SA3 : int [1:15] 0 1 0 1 1 1 1 0 1 1 ... ..$ SA4 : int [1:15] 0 1 0 1 0 1 1 0 0 1 ... ..$ SA5 : int [1:15] 0 0 0 1 0 0 0 0 0 1 ... ..$ SA6 : int [1:15] 0 0 0 0 0 0 0 0 0 0 ... ..$ SA7 : int [1:15] 0 0 0 0 0 0 0 0 0 0 ... ..$ SB1 : int [1:15] 0 1 1 1 0 1 1 1 1 1 ... ..$ SB2 : int [1:15] 0 0 0 0 1 1 1 1 0 1 ... ..$ SB3 : int [1:15] 0 0 0 0 0 0 0 0 0 0 ... ..$ SB4 : int [1:15] 0 0 0 0 0 0 0 0 0 0 ... ..$ SB5 : int [1:15] 0 0 0 1 1 0 0 0 0 1 ... ..$ SB6 : int [1:15] 0 1 0 1 1 1 1 0 1 0 ... ..$ SB7 : int [1:15] 0 0 0 0 1 0 0 0 0 0 ...
See fraction.subtraction.data for more information
about the data source.
GDINA::frac20
Chen, Y., Liu, J., Xu, G. and Ying, Z. (2015). Statistical analysis of Q-matrix based diagnostic classification models. Journal of the American Statistical Association, 110(510), 850-866.
de la Torre, J. (2009). DINA model parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34, 115-130.
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179-199.
de la Torre, J., & Douglas, J. A. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333-353.
de la Torre, J., & Douglas, J. A. (2008). Model evaluation and multiple strategies in cognitive diagnosis: An analysis of fraction subtraction data. Psychometrika, 73, 595-624.
Henson, R. A., Templin, J. T., & Willse, J. T. (2009). Defining a family of cognitive diagnosis models using log-linear models with latent variables. Psychometrika, 74, 191-210.
Huo, Y., & de la Torre, J. (2014). Estimating a cognitive diagnostic model for multiple strategies via the EM algorithm. Applied Psychological Measurement, 38, 464-485.