data.melab {CDM}

MELAB Data (Li, 2011)

Description

This is a simulated dataset according to the MELAB reading study (Li, 2011; Li & Suen, 2013). Li (2011) investigated the Fusion model (RUM model) for calibrating this dataset. The dataset in this package is simulated assuming the reduced RUM model (RRUM).

Usage

data(data.melab)

Format

The format of the dataset is:

List of 3
$ data : num [1:2019, 1:20] 0 1 0 1 1 0 0 0 1 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:20] "I1" "I2" "I3" "I4" ...
$ q.matrix :'data.frame':
..$ skill1: int [1:20] 1 1 0 0 1 1 0 1 0 1 ...
..$ skill2: int [1:20] 0 0 0 0 0 0 0 0 0 0 ...
..$ skill3: int [1:20] 0 0 0 1 0 1 1 0 1 0 ...
..$ skill4: int [1:20] 1 0 1 0 1 0 0 1 0 1 ...
$ skill.labels:'data.frame':
..$ skill : Factor w/ 4 levels "skill1","skill2",..: 1 2 3 4
..$ skill.label: Factor w/ 4 levels "connecting and synthesizing",..: 4 3 2 1

Source

Simulated data according to Li (2011).

References

Li, H. (2011). A cognitive diagnostic analysis of the MELAB reading test. Spaan Fellow, 9, 17-46.

Li, H., & Suen, H. K. (2013). Constructing and validating a Q-matrix for cognitive diagnostic analyses of a reading test. Educational Assessment, 18, 1-25.

Examples

## Not run: 
data(data.melab, package="CDM")

data <- data.melab$data
q.matrix <- data.melab$q.matrix

#*** Model 1: Reduced RUM model
mod1 <- CDM::gdina( data, q.matrix, rule="RRUM" )
summary(mod1)

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

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

#*** Model 4: 2PL model
mod4 <- CDM::gdm( data, theta.k=seq(-6,6,len=21), center )
summary(mod4)

#----
# Model comparisons

#*** RRUM vs. GDINA
anova(mod1,mod2)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df       p
  ##   1 Model 1 -20252.74 40505.48    69 40643.48 41030.60 30.88801 18 0.02966
  ##   2 Model 2 -20237.30 40474.59    87 40648.59 41136.69       NA NA      NA

  ##  -> GDINA is not superior to RRUM (according to AIC and BIC)

#*** DINA vs. RRUM
anova(mod1,mod3)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -20332.52 40665.04    55 40775.04 41083.61 159.5566 14  0
  ##   1 Model 1 -20252.74 40505.48    69 40643.48 41030.60       NA NA NA

  ##  -> RRUM fits the data significantly better than the DINA model

#*** RRUM vs. 2PL (use only AIC and BIC for comparison)
anova(mod1,mod4)
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   2 Model 2 -20390.19 40780.38    43 40866.38 41107.62 274.8962 26  0
  ##   1 Model 1 -20252.74 40505.48    69 40643.48 41030.60       NA NA NA

  ## -> RRUM fits the data better than 2PL

#----
# Model fit statistics

# RRUM
fmod1 <- CDM::modelfit.cor.din( mod1, jkunits=0)
summary(fmod1)
  ##   Test of Global Model Fit
  ##          type    value       p
  ##   1   max(X2) 10.10408 0.28109
  ##   2 abs(fcor)  0.06726 0.24023
  ##
  ##   Fit Statistics
  ##                       est
  ##   MADcor          0.01708
  ##   SRMSR           0.02158
  ##   MX2             0.96590
  ##   100*MADRESIDCOV 0.27269
  ##   MADQ3           0.02781

  ##  -> not a significant misfit of the RRUM model

# GDINA
fmod2 <- CDM::modelfit.cor.din( mod2, jkunits=0)
summary(fmod2)
  ##   Test of Global Model Fit
  ##          type    value       p
  ##   1   max(X2) 10.40294 0.23905
  ##   2 abs(fcor)  0.06817 0.20964
  ##
  ##   Fit Statistics
  ##                       est
  ##   MADcor          0.01703
  ##   SRMSR           0.02151
  ##   MX2             0.94468
  ##   100*MADRESIDCOV 0.27105
  ##   MADQ3           0.02713

## End(Not run)