Estimating Polytomous IRT GPCM Using R
Mr. Osama Alwusaidi
9/7/2019
Abstract
Comparison of the parameters of the items estimated according to Partial and Generalized Partial Credit Models: a simulation study By: Osama AbdulAziz Alwusaidi
Contents
- Basic descriptive statistics
- Partial Credit Models (PCM)
- Generalized Partial Credit Models (GPCM)
Basic descriptive statistics
summary(Data_OAlwusaidi_GPCM)## Item01 Item02 Item03 Item04
## Min. :0.000 Min. :0.00 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:1.00 1st Qu.:1.000 1st Qu.:1.000
## Median :2.000 Median :2.00 Median :2.000 Median :2.000
## Mean :2.082 Mean :1.94 Mean :2.151 Mean :2.305
## 3rd Qu.:3.000 3rd Qu.:3.00 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.00 Max. :4.000 Max. :4.000
## Item05 Item06 Item07 Item08
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.00
## 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.00
## Median :2.000 Median :2.000 Median :2.000 Median :1.00
## Mean :2.409 Mean :2.019 Mean :1.937 Mean :1.38
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:2.00
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.00
## Item09 Item10 Item11 Item12
## Min. :0.00 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.00 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:0.000
## Median :2.00 Median :3.000 Median :2.000 Median :1.000
## Mean :1.99 Mean :2.389 Mean :2.074 Mean :1.578
## 3rd Qu.:3.00 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.00 Max. :4.000 Max. :4.000 Max. :4.000
## Item13 Item14 Item15 Item16
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:0.000
## Median :2.000 Median :2.000 Median :2.000 Median :1.000
## Mean :2.462 Mean :1.836 Mean :1.811 Mean :1.303
## 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:2.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item17 Item18 Item19 Item20
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:0.000
## Median :2.000 Median :3.000 Median :1.000 Median :1.000
## Mean :2.018 Mean :2.449 Mean :1.427 Mean :1.577
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item21 Item22 Item23 Item24
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:3.000 1st Qu.:1.000 1st Qu.:2.000
## Median :3.000 Median :4.000 Median :3.000 Median :3.000
## Mean :2.499 Mean :3.167 Mean :2.393 Mean :2.697
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item25 Item26 Item27 Item28
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:1.000
## Median :2.000 Median :2.000 Median :3.000 Median :2.000
## Mean :2.172 Mean :2.018 Mean :2.744 Mean :2.099
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item29 Item30 Item31 Item32
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:1.000 1st Qu.:0.000
## Median :2.000 Median :1.000 Median :2.000 Median :1.000
## Mean :1.938 Mean :1.597 Mean :2.208 Mean :1.576
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item33 Item34 Item35 Item36
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:2.000
## Median :1.000 Median :3.000 Median :2.000 Median :3.000
## Mean :1.713 Mean :2.503 Mean :1.873 Mean :2.505
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item37 Item38 Item39 Item40
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000
## Median :2.000 Median :2.000 Median :1.000 Median :2.000
## Mean :2.451 Mean :1.784 Mean :1.939 Mean :2.095
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item41 Item42 Item43 Item44
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:0.000 1st Qu.:1.000
## Median :2.000 Median :1.000 Median :2.000 Median :3.000
## Mean :2.047 Mean :1.349 Mean :1.603 Mean :2.296
## 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.:3.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000
## Item45 Item46 Item47 Item48
## Min. :0.000 Min. :0.000 Min. :0.00 Min. :0.000
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:0.00 1st Qu.:1.000
## Median :3.000 Median :1.000 Median :1.00 Median :2.000
## Mean :2.289 Mean :1.723 Mean :1.49 Mean :2.112
## 3rd Qu.:4.000 3rd Qu.:2.000 3rd Qu.:3.00 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.00 Max. :4.000
## Item49 Item50 Item51 Item52
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.00
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:1.00
## Median :1.000 Median :2.000 Median :3.000 Median :3.00
## Mean :1.988 Mean :1.793 Mean :2.459 Mean :2.47
## 3rd Qu.:4.000 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:4.00
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.00
## Item53 Item54 Item55 Item56
## Min. :0.0000 Min. :0.00 Min. :0.000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.00 1st Qu.:0.000 1st Qu.:1.000
## Median :1.0000 Median :1.00 Median :1.000 Median :2.000
## Mean :0.9477 Mean :1.01 Mean :1.392 Mean :2.007
## 3rd Qu.:2.0000 3rd Qu.:2.00 3rd Qu.:2.000 3rd Qu.:4.000
## Max. :4.0000 Max. :4.00 Max. :4.000 Max. :4.000
## Item57 Item58 Item59 Item60
## Min. :0.000 Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:0.000 1st Qu.:2.000 1st Qu.:1.000
## Median :2.000 Median :1.000 Median :3.000 Median :2.000
## Mean :1.925 Mean :1.755 Mean :2.519 Mean :1.864
## 3rd Qu.:3.000 3rd Qu.:3.000 3rd Qu.:4.000 3rd Qu.:3.000
## Max. :4.000 Max. :4.000 Max. :4.000 Max. :4.000Partial Credit Models (PCM) with R Output
##
## Call:
## mirt(data = Data_OAlwusaidi_GPCM, model = model.pcm, itemtype = "Rasch",
## SE = TRUE, verbose = FALSE)
##
## Full-information item factor analysis with 1 factor(s).
## Converged within 1e-04 tolerance after 37 EM iterations.
## mirt version: 1.30
## M-step optimizer: nlminb
## EM acceleration: Ramsay
## Number of rectangular quadrature: 61
## Latent density type: Gaussian
##
## Information matrix estimated with method: Oakes
## Condition number of information matrix = 1135.934
## Second-order test: model is a possible local maximum
##
## Log-likelihood = -761541.2
## Estimated parameters: 241
## AIC = 1523564; AICc = 1523576
## BIC = 1525302; SABIC = 1524536
## G2 (1e+10) = 1338876, p = 1
## RMSEA = 0, CFI = NaN, TLI = NaNPartial Credit Models (GPCM) with R Output
##
## Call:
## mirt(data = Data_OAlwusaidi_GPCM, model = model.gpcm, itemtype = "gpcm",
## SE = TRUE, verbose = FALSE)
##
## Full-information item factor analysis with 1 factor(s).
## Converged within 1e-04 tolerance after 145 EM iterations.
## mirt version: 1.30
## M-step optimizer: BFGS
## EM acceleration: Ramsay
## Number of rectangular quadrature: 61
## Latent density type: Gaussian
##
## Information matrix estimated with method: Oakes
## Condition number of information matrix = 8432.643
## Second-order test: model is a possible local maximum
##
## Log-likelihood = -723068.2
## Estimated parameters: 300
## AIC = 1446736; AICc = 1446755
## BIC = 1448899; SABIC = 1447946
## G2 (1e+10) = 1261930, p = 1
## RMSEA = 0, CFI = NaN, TLI = NaNVisualizing Polytomous IRT Models PCM
## Visualizing Polytomous IRT Models GPCM
