data.melab.RdThis 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).
data(data.melab)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
Simulated data according to Li (2011).
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.
if (FALSE) {
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
}