# Load Library dan Data
library(readxl)
library(mirt)
## Warning: package 'mirt' was built under R version 4.4.3
## Loading required package: stats4
## Loading required package: lattice
datasampel <- read_excel("C:/Users/ASUS/Documents/UNY/MySta/SEM 4/Statistika Pendidikan/UTS_Statpen/Dataset_Lana.xlsx", sheet = 4)
datasampel
## # A tibble: 900 × 37
## b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 1 0 0 0 1 1 0 0 0 1 0 1
## 2 1 1 1 0 0 0 1 0 1 1 0 0 0
## 3 1 0 1 1 1 0 1 0 1 1 0 0 0
## 4 1 0 0 0 0 0 0 1 0 0 0 0 0
## 5 1 0 0 1 1 0 0 0 0 0 1 0 0
## 6 1 0 0 0 0 0 0 1 1 1 1 1 0
## 7 1 1 0 1 0 1 1 1 1 0 0 1 0
## 8 1 1 1 1 1 1 1 1 1 1 1 1 1
## 9 1 1 1 1 1 1 1 1 1 1 1 1 1
## 10 1 1 1 1 1 1 1 1 1 1 0 1 1
## # ℹ 890 more rows
## # ℹ 24 more variables: b14 <dbl>, b15 <dbl>, b16 <dbl>, b17 <dbl>, b18 <dbl>,
## # b19 <dbl>, b20 <dbl>, b21 <dbl>, b22 <dbl>, b23 <dbl>, b24 <dbl>,
## # b25 <dbl>, b26 <dbl>, b27 <dbl>, b28 <dbl>, b29 <dbl>, b30 <dbl>,
## # b31 <dbl>, b32 <dbl>, b33 <dbl>, b34 <dbl>, b35 <dbl>, b36 <dbl>, b37 <dbl>
# Estimasi Model Rasch, 1PL, 2PL, 3PL, 4PL
# Model Rasch
mod_rasch <- mirt(datasampel, 1, itemtype = "Rasch", SE = TRUE)
## Iteration: 1, Log-Lik: -18234.057, Max-Change: 0.44424Iteration: 2, Log-Lik: -18180.942, Max-Change: 0.22401Iteration: 3, Log-Lik: -18173.188, Max-Change: 0.08937Iteration: 4, Log-Lik: -18172.000, Max-Change: 0.03228Iteration: 5, Log-Lik: -18171.674, Max-Change: 0.01122Iteration: 6, Log-Lik: -18171.480, Max-Change: 0.00583Iteration: 7, Log-Lik: -18170.949, Max-Change: 0.00444Iteration: 8, Log-Lik: -18170.875, Max-Change: 0.00340Iteration: 9, Log-Lik: -18170.813, Max-Change: 0.00314Iteration: 10, Log-Lik: -18170.563, Max-Change: 0.00167Iteration: 11, Log-Lik: -18170.548, Max-Change: 0.00158Iteration: 12, Log-Lik: -18170.536, Max-Change: 0.00143Iteration: 13, Log-Lik: -18170.486, Max-Change: 0.00090Iteration: 14, Log-Lik: -18170.483, Max-Change: 0.00072Iteration: 15, Log-Lik: -18170.480, Max-Change: 0.00064Iteration: 16, Log-Lik: -18170.470, Max-Change: 0.00047Iteration: 17, Log-Lik: -18170.469, Max-Change: 0.00035Iteration: 18, Log-Lik: -18170.469, Max-Change: 0.00029Iteration: 19, Log-Lik: -18170.467, Max-Change: 0.00025Iteration: 20, Log-Lik: -18170.467, Max-Change: 0.00018Iteration: 21, Log-Lik: -18170.467, Max-Change: 0.00013Iteration: 22, Log-Lik: -18170.466, Max-Change: 0.00014Iteration: 23, Log-Lik: -18170.466, Max-Change: 0.00011Iteration: 24, Log-Lik: -18170.466, Max-Change: 0.00006
##
## Calculating information matrix...
# Model 1PL (manual constraint)
model_1pl <- '
F1 = 1-37
CONSTRAIN = (1-37, a1)
'
mod_1pl <- mirt(datasampel, model_1pl, itemtype = "2PL", SE = TRUE)
## Iteration: 1, Log-Lik: -18319.671, Max-Change: 0.24172Iteration: 2, Log-Lik: -18242.038, Max-Change: 0.08368Iteration: 3, Log-Lik: -18209.273, Max-Change: 0.06300Iteration: 4, Log-Lik: -18192.359, Max-Change: 0.04806Iteration: 5, Log-Lik: -18183.294, Max-Change: 0.03747Iteration: 6, Log-Lik: -18178.142, Max-Change: 0.02845Iteration: 7, Log-Lik: -18175.219, Max-Change: 0.02284Iteration: 8, Log-Lik: -18173.429, Max-Change: 0.01799Iteration: 9, Log-Lik: -18172.348, Max-Change: 0.01420Iteration: 10, Log-Lik: -18170.701, Max-Change: 0.00339Iteration: 11, Log-Lik: -18170.647, Max-Change: 0.00274Iteration: 12, Log-Lik: -18170.609, Max-Change: 0.00221Iteration: 13, Log-Lik: -18170.514, Max-Change: 0.00128Iteration: 14, Log-Lik: -18170.508, Max-Change: 0.00098Iteration: 15, Log-Lik: -18170.503, Max-Change: 0.00135Iteration: 16, Log-Lik: -18170.483, Max-Change: 0.00203Iteration: 17, Log-Lik: -18170.479, Max-Change: 0.00095Iteration: 18, Log-Lik: -18170.477, Max-Change: 0.00070Iteration: 19, Log-Lik: -18170.469, Max-Change: 0.00025Iteration: 20, Log-Lik: -18170.468, Max-Change: 0.00019Iteration: 21, Log-Lik: -18170.468, Max-Change: 0.00015Iteration: 22, Log-Lik: -18170.468, Max-Change: 0.00016Iteration: 23, Log-Lik: -18170.468, Max-Change: 0.00046Iteration: 24, Log-Lik: -18170.467, Max-Change: 0.00007
##
## Calculating information matrix...
# Model 2PL
mod_2pl <- mirt(datasampel, 1, itemtype = "2PL", SE = TRUE)
## Iteration: 1, Log-Lik: -18319.671, Max-Change: 0.70071Iteration: 2, Log-Lik: -17912.865, Max-Change: 0.36257Iteration: 3, Log-Lik: -17864.078, Max-Change: 0.21282Iteration: 4, Log-Lik: -17843.138, Max-Change: 0.14133Iteration: 5, Log-Lik: -17831.360, Max-Change: 0.09471Iteration: 6, Log-Lik: -17824.587, Max-Change: 0.07651Iteration: 7, Log-Lik: -17820.672, Max-Change: 0.06362Iteration: 8, Log-Lik: -17818.257, Max-Change: 0.05088Iteration: 9, Log-Lik: -17816.758, Max-Change: 0.04041Iteration: 10, Log-Lik: -17814.210, Max-Change: 0.01092Iteration: 11, Log-Lik: -17814.113, Max-Change: 0.00738Iteration: 12, Log-Lik: -17814.042, Max-Change: 0.00628Iteration: 13, Log-Lik: -17813.889, Max-Change: 0.00394Iteration: 14, Log-Lik: -17813.856, Max-Change: 0.00229Iteration: 15, Log-Lik: -17813.831, Max-Change: 0.00274Iteration: 16, Log-Lik: -17813.764, Max-Change: 0.00328Iteration: 17, Log-Lik: -17813.751, Max-Change: 0.00316Iteration: 18, Log-Lik: -17813.737, Max-Change: 0.00186Iteration: 19, Log-Lik: -17813.717, Max-Change: 0.00216Iteration: 20, Log-Lik: -17813.709, Max-Change: 0.00172Iteration: 21, Log-Lik: -17813.701, Max-Change: 0.00186Iteration: 22, Log-Lik: -17813.678, Max-Change: 0.00205Iteration: 23, Log-Lik: -17813.674, Max-Change: 0.00112Iteration: 24, Log-Lik: -17813.671, Max-Change: 0.00106Iteration: 25, Log-Lik: -17813.656, Max-Change: 0.00087Iteration: 26, Log-Lik: -17813.655, Max-Change: 0.00079Iteration: 27, Log-Lik: -17813.654, Max-Change: 0.00075Iteration: 28, Log-Lik: -17813.649, Max-Change: 0.00055Iteration: 29, Log-Lik: -17813.648, Max-Change: 0.00094Iteration: 30, Log-Lik: -17813.647, Max-Change: 0.00058Iteration: 31, Log-Lik: -17813.647, Max-Change: 0.00053Iteration: 32, Log-Lik: -17813.646, Max-Change: 0.00047Iteration: 33, Log-Lik: -17813.646, Max-Change: 0.00041Iteration: 34, Log-Lik: -17813.645, Max-Change: 0.00055Iteration: 35, Log-Lik: -17813.645, Max-Change: 0.00052Iteration: 36, Log-Lik: -17813.645, Max-Change: 0.00032Iteration: 37, Log-Lik: -17813.644, Max-Change: 0.00041Iteration: 38, Log-Lik: -17813.644, Max-Change: 0.00027Iteration: 39, Log-Lik: -17813.644, Max-Change: 0.00025Iteration: 40, Log-Lik: -17813.644, Max-Change: 0.00030Iteration: 41, Log-Lik: -17813.644, Max-Change: 0.00029Iteration: 42, Log-Lik: -17813.644, Max-Change: 0.00020Iteration: 43, Log-Lik: -17813.644, Max-Change: 0.00028Iteration: 44, Log-Lik: -17813.644, Max-Change: 0.00017Iteration: 45, Log-Lik: -17813.644, Max-Change: 0.00016Iteration: 46, Log-Lik: -17813.644, Max-Change: 0.00018Iteration: 47, Log-Lik: -17813.644, Max-Change: 0.00017Iteration: 48, Log-Lik: -17813.644, Max-Change: 0.00013Iteration: 49, Log-Lik: -17813.644, Max-Change: 0.00018Iteration: 50, Log-Lik: -17813.644, Max-Change: 0.00011Iteration: 51, Log-Lik: -17813.644, Max-Change: 0.00011Iteration: 52, Log-Lik: -17813.644, Max-Change: 0.00011Iteration: 53, Log-Lik: -17813.644, Max-Change: 0.00011Iteration: 54, Log-Lik: -17813.644, Max-Change: 0.00009
##
## Calculating information matrix...
# Model 3PL
mod_3pl <- mirt(datasampel, 1, itemtype = "3PL", SE = TRUE)
## Iteration: 1, Log-Lik: -18466.198, Max-Change: 1.33901Iteration: 2, Log-Lik: -17833.579, Max-Change: 1.04865Iteration: 3, Log-Lik: -17722.932, Max-Change: 1.00107Iteration: 4, Log-Lik: -17668.865, Max-Change: 1.06276Iteration: 5, Log-Lik: -17636.884, Max-Change: 0.79878Iteration: 6, Log-Lik: -17616.663, Max-Change: 0.52681Iteration: 7, Log-Lik: -17604.003, Max-Change: 0.34090Iteration: 8, Log-Lik: -17595.859, Max-Change: 0.29281Iteration: 9, Log-Lik: -17590.653, Max-Change: 0.13529Iteration: 10, Log-Lik: -17587.336, Max-Change: 0.12865Iteration: 11, Log-Lik: -17585.030, Max-Change: 0.11517Iteration: 12, Log-Lik: -17583.369, Max-Change: 0.09447Iteration: 13, Log-Lik: -17579.430, Max-Change: 0.06327Iteration: 14, Log-Lik: -17579.068, Max-Change: 0.07337Iteration: 15, Log-Lik: -17578.809, Max-Change: 0.02336Iteration: 16, Log-Lik: -17578.659, Max-Change: 0.03832Iteration: 17, Log-Lik: -17578.449, Max-Change: 0.42498Iteration: 18, Log-Lik: -17578.226, Max-Change: 0.01934Iteration: 19, 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0.00016Iteration: 500, Log-Lik: -17576.381, Max-Change: 0.00059
## Warning: EM cycles terminated after 500 iterations.
##
##
## Calculating information matrix...
# Model 4PL
mod_4pl <- mirt(datasampel, 1, itemtype = "4PL", SE = TRUE)
## Iteration: 1, Log-Lik: -19196.843, Max-Change: 6.64923Iteration: 2, Log-Lik: -17930.852, Max-Change: 3.29767Iteration: 3, Log-Lik: -17731.804, Max-Change: 1.56366Iteration: 4, Log-Lik: -17655.953, Max-Change: 1.09116Iteration: 5, Log-Lik: -17616.868, Max-Change: 0.79950Iteration: 6, Log-Lik: -17597.885, Max-Change: 0.68059Iteration: 7, Log-Lik: -17585.660, Max-Change: 0.57618Iteration: 8, Log-Lik: -17577.867, Max-Change: 0.37168Iteration: 9, Log-Lik: -17573.308, Max-Change: 0.36597Iteration: 10, Log-Lik: -17569.113, Max-Change: 0.46018Iteration: 11, Log-Lik: -17566.907, Max-Change: 1.16478Iteration: 12, Log-Lik: -17565.867, Max-Change: 0.54328Iteration: 13, Log-Lik: -17565.319, Max-Change: 0.26747Iteration: 14, Log-Lik: -17564.921, Max-Change: 0.30400Iteration: 15, Log-Lik: -17564.548, Max-Change: 0.14778Iteration: 16, Log-Lik: -17564.487, Max-Change: 1.05557Iteration: 17, Log-Lik: -17564.079, Max-Change: 0.13644Iteration: 18, Log-Lik: -17563.931, Max-Change: 0.07217Iteration: 19, Log-Lik: -17563.814, Max-Change: 0.03506Iteration: 20, Log-Lik: -17563.749, Max-Change: 0.04457Iteration: 21, Log-Lik: -17563.679, Max-Change: 0.04055Iteration: 22, Log-Lik: -17563.536, Max-Change: 0.02132Iteration: 23, Log-Lik: -17563.494, Max-Change: 0.01108Iteration: 24, Log-Lik: -17563.453, Max-Change: 0.01003Iteration: 25, Log-Lik: -17563.322, Max-Change: 0.00797Iteration: 26, Log-Lik: -17563.300, Max-Change: 0.00624Iteration: 27, Log-Lik: -17563.279, Max-Change: 0.00672Iteration: 28, Log-Lik: -17563.182, Max-Change: 0.00883Iteration: 29, Log-Lik: -17563.170, Max-Change: 0.00348Iteration: 30, Log-Lik: -17563.162, Max-Change: 0.00554Iteration: 31, Log-Lik: -17563.145, Max-Change: 0.00590Iteration: 32, Log-Lik: -17563.133, Max-Change: 0.00440Iteration: 33, Log-Lik: -17563.127, Max-Change: 0.00592Iteration: 34, Log-Lik: -17563.111, Max-Change: 0.00268Iteration: 35, Log-Lik: -17563.102, Max-Change: 0.00348Iteration: 36, Log-Lik: -17563.099, Max-Change: 0.00472Iteration: 37, Log-Lik: -17563.091, Max-Change: 0.00283Iteration: 38, Log-Lik: -17563.086, Max-Change: 0.00145Iteration: 39, Log-Lik: -17563.083, Max-Change: 0.00356Iteration: 40, Log-Lik: -17563.080, Max-Change: 0.00340Iteration: 41, Log-Lik: -17563.076, Max-Change: 0.00225Iteration: 42, Log-Lik: -17563.074, Max-Change: 0.00145Iteration: 43, Log-Lik: -17563.071, Max-Change: 0.00220Iteration: 44, Log-Lik: -17563.069, Max-Change: 0.00306Iteration: 45, Log-Lik: -17563.067, Max-Change: 0.00122Iteration: 46, Log-Lik: -17563.066, Max-Change: 0.00143Iteration: 47, Log-Lik: -17563.064, Max-Change: 0.00339Iteration: 48, Log-Lik: -17563.062, Max-Change: 0.00112Iteration: 49, Log-Lik: -17563.061, Max-Change: 0.00126Iteration: 50, Log-Lik: -17563.060, Max-Change: 0.00307Iteration: 51, Log-Lik: -17563.059, Max-Change: 0.00225Iteration: 52, Log-Lik: -17563.055, Max-Change: 0.00311Iteration: 53, Log-Lik: -17563.054, Max-Change: 0.00219Iteration: 54, Log-Lik: -17563.052, Max-Change: 0.00477Iteration: 55, Log-Lik: -17563.050, Max-Change: 0.00108Iteration: 56, Log-Lik: -17563.049, Max-Change: 0.00119Iteration: 57, Log-Lik: -17563.048, Max-Change: 0.00130Iteration: 58, Log-Lik: -17563.047, Max-Change: 0.00206Iteration: 59, Log-Lik: -17563.046, Max-Change: 0.00164Iteration: 60, Log-Lik: -17563.045, Max-Change: 0.00038Iteration: 61, Log-Lik: -17563.045, Max-Change: 0.00034Iteration: 62, Log-Lik: -17563.045, Max-Change: 0.00144Iteration: 63, Log-Lik: -17563.044, Max-Change: 0.00032Iteration: 64, Log-Lik: -17563.044, Max-Change: 0.00144Iteration: 65, Log-Lik: -17563.044, Max-Change: 0.00181Iteration: 66, Log-Lik: -17563.043, Max-Change: 0.00035Iteration: 67, Log-Lik: -17563.043, Max-Change: 0.00029Iteration: 68, Log-Lik: -17563.043, Max-Change: 0.00115Iteration: 69, Log-Lik: -17563.042, Max-Change: 0.00050Iteration: 70, Log-Lik: -17563.042, Max-Change: 0.00030Iteration: 71, Log-Lik: -17563.042, Max-Change: 0.00114Iteration: 72, Log-Lik: -17563.042, Max-Change: 0.00054Iteration: 73, Log-Lik: 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Log-Lik: -17563.037, Max-Change: 0.00025Iteration: 128, Log-Lik: -17563.037, Max-Change: 0.00052Iteration: 129, Log-Lik: -17563.037, Max-Change: 0.00046Iteration: 130, Log-Lik: -17563.037, Max-Change: 0.00024Iteration: 131, Log-Lik: -17563.037, Max-Change: 0.00052Iteration: 132, Log-Lik: -17563.037, Max-Change: 0.00046Iteration: 133, Log-Lik: -17563.037, Max-Change: 0.00024Iteration: 134, Log-Lik: -17563.037, Max-Change: 0.00051Iteration: 135, Log-Lik: -17563.037, Max-Change: 0.00045Iteration: 136, Log-Lik: -17563.037, Max-Change: 0.00023Iteration: 137, Log-Lik: -17563.037, Max-Change: 0.00051Iteration: 138, Log-Lik: -17563.037, Max-Change: 0.00044Iteration: 139, Log-Lik: -17563.037, Max-Change: 0.00023Iteration: 140, Log-Lik: -17563.037, Max-Change: 0.00050Iteration: 141, Log-Lik: -17563.036, Max-Change: 0.00043Iteration: 142, Log-Lik: -17563.036, Max-Change: 0.00023Iteration: 143, Log-Lik: -17563.036, Max-Change: 0.00050Iteration: 144, Log-Lik: -17563.036, Max-Change: 0.00043Iteration: 145, Log-Lik: -17563.036, Max-Change: 0.00022
##
## Calculating information matrix...
# Uji Kecocokan Item (Item Fit) dan Tabel Keputusan
# Rasch
fit_rasch <- itemfit(mod_rasch, fit_stats = "S_X2")
fit_rasch_df <- data.frame(
Butir = fit_rasch$item,
Chi = round(fit_rasch$S_X2, 2),
pvalue = round(fit_rasch$p.S_X2, 2),
Keputusan = ifelse(fit_rasch$p.S_X2 >= 0.05, "Cocok", "Tidak Cocok")
)
print(fit_rasch_df)
## Butir Chi pvalue Keputusan
## 1 b1 33.91 0.17 Cocok
## 2 b2 87.63 0.00 Tidak Cocok
## 3 b3 57.87 0.00 Tidak Cocok
## 4 b4 28.84 0.37 Cocok
## 5 b5 27.40 0.44 Cocok
## 6 b6 47.20 0.01 Tidak Cocok
## 7 b7 18.93 0.87 Cocok
## 8 b8 31.94 0.23 Cocok
## 9 b9 38.64 0.07 Cocok
## 10 b10 58.44 0.00 Tidak Cocok
## 11 b11 31.44 0.25 Cocok
## 12 b12 63.16 0.00 Tidak Cocok
## 13 b13 42.13 0.04 Tidak Cocok
## 14 b14 58.67 0.00 Tidak Cocok
## 15 b15 175.26 0.00 Tidak Cocok
## 16 b16 77.00 0.00 Tidak Cocok
## 17 b17 43.33 0.02 Tidak Cocok
## 18 b18 63.86 0.00 Tidak Cocok
## 19 b19 45.37 0.01 Tidak Cocok
## 20 b20 40.24 0.05 Tidak Cocok
## 21 b21 117.69 0.00 Tidak Cocok
## 22 b22 51.49 0.00 Tidak Cocok
## 23 b23 66.19 0.00 Tidak Cocok
## 24 b24 59.48 0.00 Tidak Cocok
## 25 b25 24.23 0.56 Cocok
## 26 b26 40.00 0.07 Cocok
## 27 b27 40.88 0.04 Tidak Cocok
## 28 b28 34.47 0.19 Cocok
## 29 b29 28.89 0.07 Cocok
## 30 b30 29.90 0.32 Cocok
## 31 b31 32.60 0.21 Cocok
## 32 b32 18.84 0.90 Cocok
## 33 b33 17.44 0.90 Cocok
## 34 b34 168.59 0.00 Tidak Cocok
## 35 b35 54.82 0.00 Tidak Cocok
## 36 b36 35.91 0.12 Cocok
## 37 b37 63.42 0.00 Tidak Cocok
cat("Jumlah butir cocok/tidak cocok model Rasch:\n")
## Jumlah butir cocok/tidak cocok model Rasch:
print(table(fit_rasch_df$Keputusan))
##
## Cocok Tidak Cocok
## 16 21
# Model 1PL
fit_1PL <- itemfit(mod_1pl, fit_stats = "S_X2")
fit_1PL_df <- data.frame(
Butir = fit_1PL$item,
Chi = round(fit_1PL$S_X2, 2),
pvalue = round(fit_1PL$p.S_X2, 2),
Keputusan = ifelse(fit_1PL$p.S_X2 >= 0.05, "Cocok", "Tidak Cocok")
)
print(fit_1PL_df)
## Butir Chi pvalue Keputusan
## 1 b1 33.91 0.17 Cocok
## 2 b2 87.63 0.00 Tidak Cocok
## 3 b3 57.87 0.00 Tidak Cocok
## 4 b4 28.84 0.37 Cocok
## 5 b5 27.40 0.44 Cocok
## 6 b6 47.20 0.01 Tidak Cocok
## 7 b7 18.93 0.87 Cocok
## 8 b8 31.94 0.23 Cocok
## 9 b9 38.64 0.07 Cocok
## 10 b10 58.44 0.00 Tidak Cocok
## 11 b11 31.44 0.25 Cocok
## 12 b12 63.16 0.00 Tidak Cocok
## 13 b13 42.13 0.04 Tidak Cocok
## 14 b14 58.67 0.00 Tidak Cocok
## 15 b15 175.26 0.00 Tidak Cocok
## 16 b16 77.00 0.00 Tidak Cocok
## 17 b17 43.34 0.02 Tidak Cocok
## 18 b18 63.87 0.00 Tidak Cocok
## 19 b19 45.37 0.01 Tidak Cocok
## 20 b20 40.24 0.05 Tidak Cocok
## 21 b21 117.70 0.00 Tidak Cocok
## 22 b22 51.49 0.00 Tidak Cocok
## 23 b23 66.20 0.00 Tidak Cocok
## 24 b24 59.48 0.00 Tidak Cocok
## 25 b25 24.23 0.56 Cocok
## 26 b26 40.00 0.07 Cocok
## 27 b27 40.87 0.04 Tidak Cocok
## 28 b28 34.47 0.19 Cocok
## 29 b29 28.90 0.07 Cocok
## 30 b30 29.90 0.32 Cocok
## 31 b31 32.60 0.21 Cocok
## 32 b32 18.84 0.90 Cocok
## 33 b33 17.44 0.90 Cocok
## 34 b34 168.60 0.00 Tidak Cocok
## 35 b35 54.83 0.00 Tidak Cocok
## 36 b36 35.91 0.12 Cocok
## 37 b37 63.42 0.00 Tidak Cocok
cat("Jumlah butir cocok/tidak cocok model 1PL:\n")
## Jumlah butir cocok/tidak cocok model 1PL:
print(table(fit_1PL_df$Keputusan))
##
## Cocok Tidak Cocok
## 16 21
# Model 2PL
fit_2PL <- itemfit(mod_2pl, fit_stats = "S_X2")
fit_2PL_df <- data.frame(
Butir = fit_2PL$item,
Chi = round(fit_2PL$S_X2, 2),
pvalue = round(fit_2PL$p.S_X2, 2),
Keputusan = ifelse(fit_2PL$p.S_X2 >= 0.05, "Cocok", "Tidak Cocok")
)
print(fit_2PL_df)
## Butir Chi pvalue Keputusan
## 1 b1 30.10 0.22 Cocok
## 2 b2 25.25 0.67 Cocok
## 3 b3 21.35 0.38 Cocok
## 4 b4 19.26 0.78 Cocok
## 5 b5 12.81 0.98 Cocok
## 6 b6 39.29 0.05 Tidak Cocok
## 7 b7 12.29 0.98 Cocok
## 8 b8 25.20 0.51 Cocok
## 9 b9 27.41 0.29 Cocok
## 10 b10 46.48 0.01 Tidak Cocok
## 11 b11 27.03 0.41 Cocok
## 12 b12 46.60 0.01 Tidak Cocok
## 13 b13 41.75 0.03 Tidak Cocok
## 14 b14 39.00 0.03 Tidak Cocok
## 15 b15 25.68 0.64 Cocok
## 16 b16 27.10 0.51 Cocok
## 17 b17 23.39 0.71 Cocok
## 18 b18 44.67 0.02 Tidak Cocok
## 19 b19 26.85 0.26 Cocok
## 20 b20 30.77 0.33 Cocok
## 21 b21 28.00 0.52 Cocok
## 22 b22 51.36 0.00 Tidak Cocok
## 23 b23 50.53 0.01 Tidak Cocok
## 24 b24 49.45 0.00 Tidak Cocok
## 25 b25 23.15 0.62 Cocok
## 26 b26 33.78 0.17 Cocok
## 27 b27 22.27 0.56 Cocok
## 28 b28 28.26 0.35 Cocok
## 29 b29 33.12 0.03 Tidak Cocok
## 30 b30 20.73 0.65 Cocok
## 31 b31 28.62 0.38 Cocok
## 32 b32 14.03 0.97 Cocok
## 33 b33 16.91 0.91 Cocok
## 34 b34 32.50 0.30 Cocok
## 35 b35 27.90 0.52 Cocok
## 36 b36 30.62 0.17 Cocok
## 37 b37 51.35 0.00 Tidak Cocok
cat("Jumlah butir cocok/tidak cocok model 2PL:\n")
## Jumlah butir cocok/tidak cocok model 2PL:
print(table(fit_2PL_df$Keputusan))
##
## Cocok Tidak Cocok
## 26 11
# Model 3PL
fit_3PL <- itemfit(mod_3pl, fit_stats = "S_X2")
fit_3PL_df <- data.frame(
Butir = fit_3PL$item,
Chi = round(fit_3PL$S_X2, 2),
pvalue = round(fit_3PL$p.S_X2, 2),
Keputusan = ifelse(fit_3PL$p.S_X2 >= 0.05, "Cocok", "Tidak Cocok")
)
print(fit_3PL_df)
## Butir Chi pvalue Keputusan
## 1 b1 30.48 0.21 Cocok
## 2 b2 17.65 0.89 Cocok
## 3 b3 23.22 0.28 Cocok
## 4 b4 20.05 0.74 Cocok
## 5 b5 15.62 0.93 Cocok
## 6 b6 32.94 0.11 Cocok
## 7 b7 11.05 0.99 Cocok
## 8 b8 20.54 0.61 Cocok
## 9 b9 29.96 0.19 Cocok
## 10 b10 42.36 0.02 Tidak Cocok
## 11 b11 21.16 0.63 Cocok
## 12 b12 23.35 0.44 Cocok
## 13 b13 29.43 0.25 Cocok
## 14 b14 22.52 0.37 Cocok
## 15 b15 21.31 0.81 Cocok
## 16 b16 14.80 0.96 Cocok
## 17 b17 21.11 0.78 Cocok
## 18 b18 41.88 0.03 Tidak Cocok
## 19 b19 21.81 0.47 Cocok
## 20 b20 26.90 0.47 Cocok
## 21 b21 18.85 0.90 Cocok
## 22 b22 43.52 0.02 Tidak Cocok
## 23 b23 35.75 0.10 Cocok
## 24 b24 37.67 0.03 Tidak Cocok
## 25 b25 22.99 0.58 Cocok
## 26 b26 29.76 0.28 Cocok
## 27 b27 20.09 0.69 Cocok
## 28 b28 26.64 0.37 Cocok
## 29 b29 28.31 0.08 Cocok
## 30 b30 17.14 0.76 Cocok
## 31 b31 19.30 0.78 Cocok
## 32 b32 15.91 0.94 Cocok
## 33 b33 13.85 0.97 Cocok
## 34 b34 25.81 0.58 Cocok
## 35 b35 26.71 0.53 Cocok
## 36 b36 20.58 0.66 Cocok
## 37 b37 34.00 0.20 Cocok
cat("Jumlah butir cocok/tidak cocok model 3PL:\n")
## Jumlah butir cocok/tidak cocok model 3PL:
print(table(fit_3PL_df$Keputusan))
##
## Cocok Tidak Cocok
## 33 4
# Model 4PL
fit_4PL <- itemfit(mod_4pl, fit_stats = "S_X2")
fit_4PL_df <- data.frame(
Butir = fit_4PL$item,
Chi = round(fit_4PL$S_X2, 2),
pvalue = round(fit_4PL$p.S_X2, 2),
Keputusan = ifelse(fit_4PL$p.S_X2 >= 0.05, "Cocok", "Tidak Cocok")
)
print(fit_4PL_df)
## Butir Chi pvalue Keputusan
## 1 b1 27.30 0.29 Cocok
## 2 b2 17.23 0.87 Cocok
## 3 b3 22.69 0.25 Cocok
## 4 b4 19.28 0.74 Cocok
## 5 b5 13.05 0.95 Cocok
## 6 b6 32.85 0.08 Cocok
## 7 b7 10.99 0.98 Cocok
## 8 b8 20.10 0.58 Cocok
## 9 b9 28.95 0.18 Cocok
## 10 b10 40.29 0.03 Tidak Cocok
## 11 b11 20.18 0.69 Cocok
## 12 b12 23.46 0.38 Cocok
## 13 b13 29.90 0.19 Cocok
## 14 b14 20.38 0.50 Cocok
## 15 b15 21.91 0.74 Cocok
## 16 b16 15.76 0.92 Cocok
## 17 b17 21.70 0.70 Cocok
## 18 b18 36.64 0.08 Cocok
## 19 b19 20.61 0.42 Cocok
## 20 b20 26.45 0.44 Cocok
## 21 b21 20.35 0.82 Cocok
## 22 b22 42.99 0.01 Tidak Cocok
## 23 b23 35.83 0.07 Cocok
## 24 b24 36.67 0.06 Cocok
## 25 b25 22.46 0.55 Cocok
## 26 b26 29.51 0.20 Cocok
## 27 b27 19.55 0.67 Cocok
## 28 b28 25.98 0.35 Cocok
## 29 b29 27.96 0.06 Cocok
## 30 b30 18.75 0.66 Cocok
## 31 b31 18.72 0.77 Cocok
## 32 b32 14.95 0.94 Cocok
## 33 b33 13.50 0.98 Cocok
## 34 b34 25.66 0.54 Cocok
## 35 b35 26.07 0.46 Cocok
## 36 b36 19.88 0.65 Cocok
## 37 b37 32.25 0.22 Cocok
cat("Jumlah butir cocok/tidak cocok model 4PL:\n")
## Jumlah butir cocok/tidak cocok model 4PL:
print(table(fit_4PL_df$Keputusan))
##
## Cocok Tidak Cocok
## 35 2
# Plot Empirical untuk Butir ke-9 pada Setiap Model
itemfit(mod_rasch, 'S_X2', empirical.plot = 9)
itemfit(mod_1pl, 'S_X2', empirical.plot = 9)
itemfit(mod_2pl, 'S_X2', empirical.plot = 9)
itemfit(mod_3pl, 'S_X2', empirical.plot = 9)
itemfit(mod_4pl, 'S_X2', empirical.plot = 9)
# Visualisasi Plot Semua Butir
for (coba in 1:nrow(fit_rasch_df)) {
print(itemfit(mod_rasch, 'S_X2', empirical.plot = coba))
}
# Step 6: Uji Kecocokan Model dengan ANOVA (AIC, BIC)
anova(mod_rasch, mod_1pl)
## AIC SABIC HQ BIC logLik X2 df p
## mod_rasch 36416.93 36478.74 36486.64 36599.42 -18170.47
## mod_1pl 36416.93 36478.74 36486.65 36599.43 -18170.47 -0.002 0 NaN
anova(mod_1pl, mod_2pl)
## AIC SABIC HQ BIC logLik X2 df p
## mod_1pl 36416.93 36478.74 36486.65 36599.43 -18170.47
## mod_2pl 35775.29 35895.65 35911.04 36130.66 -17813.64 713.647 36 0
anova(mod_2pl, mod_3pl)
## AIC SABIC HQ BIC logLik X2 df p
## mod_2pl 35775.29 35895.65 35911.04 36130.66 -17813.64
## mod_3pl 35374.76 35555.31 35578.40 35907.83 -17576.38 474.526 37 0
anova(mod_3pl, mod_4pl)
## AIC SABIC HQ BIC logLik X2 df p
## mod_3pl 35374.76 35555.31 35578.40 35907.83 -17576.38
## mod_4pl 35422.07 35662.80 35693.59 36132.83 -17563.04 26.689 37 0.895
library(mirt)
# Model null (baseline): item independen, satu iterasi
mod_null <- mirt(datasampel, 1, itemtype = 'Rasch', technical = list(NCYCLES = 1), SE = FALSE)
## Iteration: 1, Log-Lik: -18234.057, Max-Change: 0.44424
## Warning: EM cycles terminated after 1 iterations.
logLik_null <- as.numeric(logLik(mod_null))
# Log-likelihood tiap model
logLik_rasch <- as.numeric(logLik(mod_rasch))
logLik_1pl <- as.numeric(logLik(mod_1pl))
logLik_2pl <- as.numeric(logLik(mod_2pl))
logLik_3pl <- as.numeric(logLik(mod_3pl))
logLik_4pl <- as.numeric(logLik(mod_4pl))
# Fungsi NFI
nfi <- function(logLik_null, logLik_model) {
return((logLik_null - logLik_model) / logLik_null)
}
# Hitung NFI masing-masing
nfi_rasch <- nfi(logLik_null, logLik_rasch)
nfi_1pl <- nfi(logLik_null, logLik_1pl)
nfi_2pl <- nfi(logLik_null, logLik_2pl)
nfi_3pl <- nfi(logLik_null, logLik_3pl)
nfi_4pl <- nfi(logLik_null, logLik_4pl)
# Hitung AIC dan BIC via anova
anova_rasch_1pl <- anova(mod_rasch, mod_1pl)
anova_1pl_2pl <- anova(mod_1pl, mod_2pl)
anova_2pl_3pl <- anova(mod_2pl, mod_3pl)
anova_3pl_4pl <- anova(mod_3pl, mod_4pl)
get_anova_ic <- function(anova_res, idx = 1) {
list(AIC = anova_res$AIC[idx], BIC = anova_res$BIC[idx])
}
AIC_rasch <- get_anova_ic(anova_rasch_1pl, 1)$AIC
BIC_rasch <- get_anova_ic(anova_rasch_1pl, 1)$BIC
AIC_1pl <- get_anova_ic(anova_rasch_1pl, 2)$AIC
BIC_1pl <- get_anova_ic(anova_rasch_1pl, 2)$BIC
AIC_2pl <- get_anova_ic(anova_1pl_2pl, 2)$AIC
BIC_2pl <- get_anova_ic(anova_1pl_2pl, 2)$BIC
AIC_3pl <- get_anova_ic(anova_2pl_3pl, 2)$AIC
BIC_3pl <- get_anova_ic(anova_2pl_3pl, 2)$BIC
AIC_4pl <- get_anova_ic(anova_3pl_4pl, 2)$AIC
BIC_4pl <- get_anova_ic(anova_3pl_4pl, 2)$BIC
# Fungsi jumlah cocok/tidak cocok
count_fit <- function(df) {
cocok <- sum(df$Keputusan == "Cocok", na.rm = TRUE)
tidak <- sum(df$Keputusan == "Tidak Cocok", na.rm = TRUE)
na <- sum(is.na(df$Keputusan))
return(c(cocok, tidak, na))
}
fit_counts <- rbind(
count_fit(fit_rasch_df),
count_fit(fit_1PL_df),
count_fit(fit_2PL_df),
count_fit(fit_3PL_df),
count_fit(fit_4PL_df)
)
# Rekapitulasi
n_sampel <- nrow(datasampel)
n_item <- ncol(datasampel)
rekap_model <- data.frame(
Model = c("Rasch", "1PL", "2PL", "3PL", "4PL"),
n = rep(n_sampel, 5),
AIC = c(AIC_rasch, AIC_1pl, AIC_2pl, AIC_3pl, AIC_4pl),
BIC = c(BIC_rasch, BIC_1pl, BIC_2pl, BIC_3pl, BIC_4pl),
Butir_Cocok = fit_counts[,1],
Butir_Tidak_Cocok = fit_counts[,2],
Butir_NA = fit_counts[,3],
Jumlah_Variabel = rep(n_item, 5),
NFI_maks = round(c(nfi_rasch, nfi_1pl, nfi_2pl, nfi_3pl, nfi_4pl), 4)
)
print(rekap_model)
## Model n AIC BIC Butir_Cocok Butir_Tidak_Cocok Butir_NA
## 1 Rasch 900 36416.93 36599.42 16 21 0
## 2 1PL 900 36416.93 36599.43 16 21 0
## 3 2PL 900 35775.29 36130.66 26 11 0
## 4 3PL 900 35374.76 35907.83 33 4 0
## 5 4PL 900 35422.07 36132.83 35 2 0
## Jumlah_Variabel NFI_maks
## 1 37 0.0006
## 2 37 0.0006
## 3 37 0.0202
## 4 37 0.0333
## 5 37 0.0340