CDM (version 8.2-6)

IRT.compareModels: Comparisons of Several Models

Description

Performs 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.

Usage

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

Value

A list with following entries

IC

Data frame with information criteria

LRtest

Data frame with all (useful) pairwise likelihood ratio tests

Arguments

object

Object

extended

Optional logical indicating whether all or or only a subset of fit statistics should be printed.

...

Further objects to be passed.

See Also

The function is based on IRT.IC.

For comparing two models see anova.din.

For computing absolute model fit see IRT.modelfit.

Examples

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
}