DTMR Fraction Data (Bradshaw et al., 2014)

This is a simulated dataset of the DTMR fraction data described in Bradshaw, Izsak, Templin and Jacobson (2014).

data(data.dtmr)

Format

The format is:

List of 5
$ data : num [1:5000, 1:27] 0 0 0 0 0 1 0 0 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:27] "M1" "M2" "M3" "M4" ...
$ q.matrix :'data.frame': 27 obs. of 4 variables:
..$ RU : int [1:27] 1 0 0 1 1 0 1 0 0 0 ...
..$ PI : int [1:27] 0 0 1 0 0 1 0 0 0 0 ...
..$ APP: int [1:27] 0 1 0 0 0 0 0 1 1 1 ...
..$ MC : int [1:27] 0 0 0 0 0 0 0 0 0 0 ...
$ skill.distribution:'data.frame': 16 obs. of 5 variables:
..$ RU : int [1:16] 0 0 0 0 0 0 0 0 1 1 ...
..$ PI : int [1:16] 0 0 0 0 1 1 1 1 0 0 ...
..$ APP : int [1:16] 0 0 1 1 0 0 1 1 0 0 ...
..$ MC : int [1:16] 0 1 0 1 0 1 0 1 0 1 ...
..$ freq: int [1:16] 1064 350 280 406 196 126 238 770 14 28 ...
$ itempars :'data.frame': 27 obs. of 7 variables:
..$ item : chr [1:27] "M1" "M2" "M3" "M4" ...
..$ lam0 : num [1:27] -1.12 0.59 -2.07 -1.19 -1.67 -3.81 -0.73 -0.62 -0.09 0.28 ...
..$ RU : num [1:27] 2.24 0 0 0.65 1.52 0 1.2 0 0 0 ...
..$ PI : num [1:27] 0 0 1.7 0 0 2.08 0 0 0 0 ...
..$ APP : num [1:27] 0 1.27 0 0 0 0 0 4.25 2.16 0.87 ...
..$ MC : num [1:27] 0 0 0 0 0 0 0 0 0 0 ...
..$ RU.PI: num [1:27] 0 0 0 0 0 0 0 0 0 0 ...
$ sim_data :function (N, skill.distribution, itempars)
..- attr(*, "srcref")='srcref' int [1:8] 1 13 20 1 13 1 1 20
.. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x00000000298a8ed0>

The attribute definition are as follows

RU: Referent units

PI: Partitioning and iterating attribute

APP: Appropriateness attribute

MC: Multiplicative Comparison attribute

Source

Simulated dataset according to Bradshaw et al. (2014).

References

Bradshaw, L., Izsak, A., Templin, J., & Jacobson, E. (2014). Diagnosing teachers' understandings of rational numbers: Building a multidimensional test within the diagnostic classification framework. Educational Measurement: Issues and Practice, 33, 2-14.

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: Model comparisons data.dtmr
#############################################################################

data(data.dtmr, package="CDM")
data <- data.dtmr$data
q.matrix <- data.dtmr$q.matrix
I <- ncol(data)

#*** Model 1: LCDM
# define item wise rules
rule <- rep( "ACDM", I )
names(rule) <- colnames(data)
rule[ c("M14","M17") ] <- "GDINA2"
# estimate model
mod1 <- CDM::gdina( data, q.matrix, linkfct="logit", rule=rule)
summary(mod1)

#*** Model 2: DINA model
mod2 <- CDM::gdina( data, q.matrix, rule="DINA" )
summary(mod2)

#*** Model 3: RRUM model
mod3 <- CDM::gdina( data, q.matrix, rule="RRUM" )
summary(mod3)

#--- model comparisons

# LCDM vs. DINA
anova(mod1,mod2)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -76570.89 153141.8    69 153279.8 153729.5 1726.645 10  0
  ##   1 Model 1 -75707.57 151415.1    79 151573.1 152088.0       NA NA NA

# LCDM vs. RRUM
anova(mod1,mod3)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -75746.13 151492.3    77 151646.3 152148.1 77.10994  2  0
  ##   1 Model 1 -75707.57 151415.1    79 151573.1 152088.0       NA NA NA

#--- model fit
summary( CDM::modelfit.cor.din( mod1 ) )
  ##   Test of Global Model Fit
  ##          type   value       p
  ##   1   max(X2) 7.74382 1.00000
  ##   2 abs(fcor) 0.04056 0.72707
  ##
  ##   Fit Statistics
  ##                       est
  ##   MADcor          0.00959
  ##   SRMSR           0.01217
  ##   MX2             0.75696
  ##   100*MADRESIDCOV 0.20283
  ##   MADQ3           0.02220

#############################################################################
# EXAMPLE 2: Simulating data of structure data.dtmr
#############################################################################

data(data.dtmr, package="CDM")

# draw sample of N=200
set.seed(87)
data.dtmr$sim_data(N=200, skill.distribution=data.dtmr$skill.distribution,
             itempars=data.dtmr$itempars)
}