TIMSS 2003 Mathematics 8th Grade (Su et al., 2013)

This is a dataset with a subset of 23 Mathematics items from TIMSS 2003 items used in Su, Choi, Lee, Choi and McAninch (2013).

data(data.timss03.G8.su)

Format

The data contains scored item responses (data), the Q-matrix (q.matrix) and further item informations (iteminfo).

The format is

List of 3
$ data :'data.frame':
..$ idstud : num [1:757] 1e+07 1e+07 1e+07 1e+07 1e+07 ...
..$ idbook : num [1:757] 1 1 1 1 1 1 1 1 1 1 ...
..$ M012001 : num [1:757] 0 1 0 0 1 0 1 0 0 0 ...
..$ M012002 : num [1:757] 1 1 0 1 0 0 1 1 1 1 ...
..$ M012004 : num [1:757] 0 1 1 1 1 0 1 1 0 0 ...
[...]
..$ M022234B: num [1:757] 0 0 0 0 0 0 0 0 0 0 ...
..$ M022251 : num [1:757] 0 0 0 0 0 0 0 0 0 0 ...
..$ M032570 : num [1:757] 1 1 0 1 0 0 1 1 1 1 ...
..$ M032643 : num [1:757] 1 0 0 0 0 0 1 1 0 0 ...
$ q.matrix: int [1:23, 1:13] 1 0 0 0 0 0 1 0 0 0 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:23] "M012001" "M012002" "M012004" "M012016" ...
.. ..$ : chr [1:13] "S1" "S2" "S3" "S4" ...
$ iteminfo: chr [1:23, 1:9] "M012001" "M012002" "M012004" "M012016" ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:9] "item" "ItemType" "reporting_category" "content" ...

For a detailed description of skills S1, S2, ..., S15 see Su et al. (2013, Table 2).

See also

The TIMSS 2003 dataset for 8th graders (with a larger number of items) was also analyzed in Skaggs, Wilkins and Hein (2016).

Source

Subset of US 8th graders (Booklet 1) in the TIMSS 2003 mathematics study

References

Skaggs, G., Wilkins, J. L. M., & Hein, S. F. (2016). Grain size and parameter recovery with TIMSS and the general diagnostic model. International Journal of Testing, 16(4), 310-330.

Su, Y.-L., Choi, K. M., Lee, W.-C., Choi, T., & McAninch, M. (2013). Hierarchical cognitive diagnostic analysis for TIMSS 2003 mathematics. CASMA Research Report 35. Center for Advanced Studies in Measurement and Assessment (CASMA), University of Iowa.

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: Data Su et al. (2013)
#############################################################################

data(data.timss03.G8.su, package="CDM")
data <- data.timss03.G8.su$data[,-c(1,2)]
q.matrix <- data.timss03.G8.su$q.matrix

#*** Model 1: DINA model with complete skill space of 2^13=8192 skill classes
mod1 <- CDM::din( data, q.matrix )

#*** Model 2: Skill space approximation with 3000 skill classes instead of
#    2^13=8192 classes as in Model 1
ss2 <- CDM::skillspace.approximation( L=3000, K=ncol(q.matrix) )
mod2 <- CDM::din( data, q.matrix, skillclasses=ss2 )

#*** Model 3: DINA model with a hierarchical skill space
#   see Su et al. (2013): Fig. 6
B <- "S1 > S2 > S7 > S8
      S15 > S9
      S3 > S9
      S13 > S4 > S9
      S14 > S5 > S6 > S11"
# Note that S10 and S12 are not included in the dataset contained in this package
skill.names <- colnames(q.matrix)
ss3 <- CDM::skillspace.hierarchy(B=B, skill.names=skill.names)
# The reduced skill space "only" contains 325 skill classes
mod3 <- CDM::din( data, q.matrix, skillclasses=ss3$skillspace.reduced )
}