IRT.compareModels(object, ...)

## S3 method for class 'IRT.compareModels'
summary(object, extended=TRUE, ...)

## Not run: 
#############################################################################
# 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

## End(Not run)