IRT.compareModels.RdPerforms model comparisons based on information criteria and likelihood
ratio test. This function allows all objects for which the
logLik (stats) S3 method is defined.
The output of IRT.modelfit can also be used as
input for this function.
IRT.compareModels(object, ...)
# S3 method for IRT.compareModels
summary(object, extended=TRUE, ...)Object
Optional logical indicating whether all or or only a subset of fit statistics should be printed.
Further objects to be passed.
A list with following entries
Data frame with information criteria
Data frame with all (useful) pairwise likelihood ratio tests
The function is based on IRT.IC.
For comparing two models see anova.din.
For computing absolute model fit see IRT.modelfit.
if (FALSE) {
#############################################################################
# EXAMPLE 1: Model comparison sim.dina dataset
#############################################################################
data(sim.dina, package="CDM")
data(sim.qmatrix, package="CDM")
dat <- sim.dina
q.matrix <- sim.qmatrix
#*** Model 0: DINA model with equal guessing and slipping parameters
mod0 <- CDM::din( dat, q.matrix, guess.equal=TRUE, slip.equal=TRUE )
summary(mod0)
#*** Model 1: DINA model
mod1 <- CDM::din( dat, q.matrix )
summary(mod1)
#*** Model 2: DINO model
mod2 <- CDM::din( dat, q.matrix, rule="DINO")
summary(mod2)
#*** Model 3: Additive GDINA model
mod3 <- CDM::gdina( dat, q.matrix, rule="ACDM")
summary(mod3)
#*** Model 4: GDINA model
mod4 <- CDM::gdina( dat, q.matrix, rule="GDINA")
summary(mod4)
# model comparisons
res <- CDM::IRT.compareModels( mod0, mod1, mod2, mod3, mod4 )
res
## > res
## $IC
## Model loglike Deviance Npars Nobs AIC BIC AIC3 AICc CAIC
## 1 mod0 -2176.482 4352.963 9 400 4370.963 4406.886 4379.963 4371.425 4415.886
## 2 mod1 -2042.378 4084.756 25 400 4134.756 4234.543 4159.756 4138.232 4259.543
## 3 mod2 -2086.805 4173.610 25 400 4223.610 4323.396 4248.610 4227.086 4348.396
## 4 mod3 -2048.233 4096.466 32 400 4160.466 4288.193 4192.466 4166.221 4320.193
## 5 mod4 -2026.633 4053.266 41 400 4135.266 4298.917 4176.266 4144.887 4339.917
##
# -> The DINA model (mod1) performed best in terms of AIC.
## $LRtest
## Model1 Model2 Chi2 df p
## 1 mod0 mod1 268.20713 16 0.000000e+00
## 2 mod0 mod2 179.35362 16 0.000000e+00
## 3 mod0 mod3 256.49745 23 0.000000e+00
## 4 mod0 mod4 299.69671 32 0.000000e+00
## 5 mod1 mod3 -11.70967 7 1.000000e+00
## 6 mod1 mod4 31.48959 16 1.164415e-02
## 7 mod2 mod3 77.14383 7 5.262457e-14
## 8 mod2 mod4 120.34309 16 0.000000e+00
## 9 mod3 mod4 43.19926 9 1.981445e-06
##
# -> The GDINA model (mod4) was superior to the other models in terms
# of the likelihood ratio test.
# get an overview with summary
summary(res)
summary(res,extended=FALSE)
#*******************
# applying model comparison for objects of class IRT.modelfit
# compute model fit statistics
fmod0 <- CDM::IRT.modelfit(mod0)
fmod1 <- CDM::IRT.modelfit(mod1)
fmod4 <- CDM::IRT.modelfit(mod4)
# model comparison
res <- CDM::IRT.compareModels( fmod0, fmod1, fmod4 )
res
## $IC
## Model loglike Deviance Npars Nobs AIC BIC AIC3
## mod0 mod0 -2176.482 4352.963 9 400 4370.963 4406.886 4379.963
## mod1 mod1 -2042.378 4084.756 25 400 4134.756 4234.543 4159.756
## mod4 mod4 -2026.633 4053.266 41 400 4135.266 4298.917 4176.266
## AICc CAIC maxX2 p_maxX2 MADcor SRMSR
## mod0 4371.425 4415.886 118.172707 0.0000000 0.09172287 0.10941300
## mod1 4138.232 4259.543 8.728248 0.1127943 0.03025354 0.03979948
## mod4 4144.887 4339.917 2.397241 1.0000000 0.02284029 0.02989669
## X100.MADRESIDCOV MADQ3 MADaQ3
## mod0 1.9749936 0.08840892 0.08353917
## mod1 0.6713952 0.06184332 0.05923058
## mod4 0.5148707 0.07477337 0.07145600
##
## $LRtest
## Model1 Model2 Chi2 df p
## 1 mod0 mod1 268.20713 16 0.00000000
## 2 mod0 mod4 299.69671 32 0.00000000
## 3 mod1 mod4 31.48959 16 0.01164415
}