# 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 = 1)
datasampel
## # A tibble: 50 × 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 0 0 0 0 0 1 1 0 1 0 1 0 0
## 2 0 1 0 1 0 1 1 0 1 0 1 0 0
## 3 1 0 0 0 0 1 0 1 0 1 1 0 0
## 4 1 0 0 0 0 1 0 1 1 0 0 1 1
## 5 1 0 1 0 0 0 0 0 1 0 1 0 0
## 6 0 0 0 0 0 0 0 1 0 0 0 0 0
## 7 0 0 0 1 0 0 1 1 1 1 1 0 1
## 8 1 1 1 1 1 1 1 0 1 1 0 1 0
## 9 0 1 1 0 0 0 0 0 0 0 0 0 0
## 10 1 1 0 1 1 0 1 0 1 0 0 0 0
## # ℹ 40 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: -1133.418, Max-Change: 0.26501Iteration: 2, Log-Lik: -1131.695, Max-Change: 0.07582Iteration: 3, Log-Lik: -1131.481, Max-Change: 0.02680Iteration: 4, Log-Lik: -1131.448, Max-Change: 0.01010Iteration: 5, Log-Lik: -1131.439, Max-Change: 0.00430Iteration: 6, Log-Lik: -1131.437, Max-Change: 0.00227Iteration: 7, Log-Lik: -1131.433, Max-Change: 0.00176Iteration: 8, Log-Lik: -1131.433, Max-Change: 0.00083Iteration: 9, Log-Lik: -1131.433, Max-Change: 0.00062Iteration: 10, Log-Lik: -1131.432, Max-Change: 0.00049Iteration: 11, Log-Lik: -1131.432, Max-Change: 0.00013Iteration: 12, Log-Lik: -1131.432, Max-Change: 0.00011Iteration: 13, Log-Lik: -1131.432, Max-Change: 0.00004
##
## 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: -1132.004, Max-Change: 0.12676Iteration: 2, Log-Lik: -1131.515, Max-Change: 0.01256Iteration: 3, Log-Lik: -1131.473, Max-Change: 0.00853Iteration: 4, Log-Lik: -1131.438, Max-Change: 0.00256Iteration: 5, Log-Lik: -1131.436, Max-Change: 0.00256Iteration: 6, Log-Lik: -1131.434, Max-Change: 0.00165Iteration: 7, Log-Lik: -1131.433, Max-Change: 0.00016Iteration: 8, Log-Lik: -1131.432, Max-Change: 0.00014Iteration: 9, Log-Lik: -1131.432, Max-Change: 0.00011Iteration: 10, Log-Lik: -1131.432, Max-Change: 0.00045Iteration: 11, Log-Lik: -1131.432, Max-Change: 0.00026Iteration: 12, Log-Lik: -1131.432, Max-Change: 0.00025Iteration: 13, Log-Lik: -1131.432, Max-Change: 0.00010Iteration: 14, Log-Lik: -1131.432, Max-Change: 0.00009
##
## Calculating information matrix...
# Model 2PL
mod_2pl <- mirt(datasampel, 1, itemtype = "2PL", SE = TRUE)
## Iteration: 1, Log-Lik: -1132.004, Max-Change: 1.19215Iteration: 2, Log-Lik: -1098.901, Max-Change: 0.41397Iteration: 3, Log-Lik: -1096.596, Max-Change: 0.17296Iteration: 4, Log-Lik: -1096.410, Max-Change: 0.12166Iteration: 5, Log-Lik: -1096.278, Max-Change: 0.06172Iteration: 6, Log-Lik: -1096.243, Max-Change: 0.03418Iteration: 7, Log-Lik: -1096.226, Max-Change: 0.01481Iteration: 8, Log-Lik: -1096.221, Max-Change: 0.01058Iteration: 9, Log-Lik: -1096.218, Max-Change: 0.00742Iteration: 10, Log-Lik: -1096.215, Max-Change: 0.00240Iteration: 11, Log-Lik: -1096.214, Max-Change: 0.00254Iteration: 12, Log-Lik: -1096.214, Max-Change: 0.00234Iteration: 13, Log-Lik: -1096.213, Max-Change: 0.00152Iteration: 14, Log-Lik: -1096.213, Max-Change: 0.00100Iteration: 15, Log-Lik: -1096.213, Max-Change: 0.00125Iteration: 16, Log-Lik: -1096.213, Max-Change: 0.00025Iteration: 17, Log-Lik: -1096.213, Max-Change: 0.00074Iteration: 18, Log-Lik: -1096.213, Max-Change: 0.00020Iteration: 19, Log-Lik: -1096.213, Max-Change: 0.00091Iteration: 20, Log-Lik: -1096.213, Max-Change: 0.00025Iteration: 21, Log-Lik: -1096.213, Max-Change: 0.00061Iteration: 22, Log-Lik: -1096.213, Max-Change: 0.00031Iteration: 23, Log-Lik: -1096.213, Max-Change: 0.00016Iteration: 24, Log-Lik: -1096.213, Max-Change: 0.00042Iteration: 25, Log-Lik: -1096.213, Max-Change: 0.00018Iteration: 26, Log-Lik: -1096.213, Max-Change: 0.00009
##
## Calculating information matrix...
# Model 3PL
mod_3pl <- mirt(datasampel, 1, itemtype = "3PL", SE = TRUE)
## Iteration: 1, Log-Lik: -1138.177, Max-Change: 4.06400Iteration: 2, Log-Lik: -1088.006, Max-Change: 4.01843Iteration: 3, Log-Lik: -1081.316, Max-Change: 3.88174Iteration: 4, Log-Lik: -1077.998, Max-Change: 2.52887Iteration: 5, Log-Lik: -1076.019, Max-Change: 2.81781Iteration: 6, Log-Lik: -1074.684, Max-Change: 1.52668Iteration: 7, Log-Lik: -1073.849, Max-Change: 3.11251Iteration: 8, Log-Lik: -1072.660, Max-Change: 1.60614Iteration: 9, Log-Lik: -1072.119, Max-Change: 5.15482Iteration: 10, Log-Lik: -1071.014, Max-Change: 0.90696Iteration: 11, Log-Lik: -1070.809, Max-Change: 10.60390Iteration: 12, Log-Lik: -1069.283, Max-Change: 0.42604Iteration: 13, Log-Lik: -1069.278, Max-Change: 19.07054Iteration: 14, Log-Lik: -1068.662, Max-Change: 0.54809Iteration: 15, Log-Lik: -1068.480, Max-Change: 4.74274Iteration: 16, Log-Lik: -1068.017, Max-Change: 4.08245Iteration: 17, Log-Lik: -1067.692, Max-Change: 6.15883Iteration: 18, Log-Lik: -1067.341, Max-Change: 1.85400Iteration: 19, Log-Lik: 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## Warning: EM cycles terminated after 500 iterations.
##
##
## Calculating information matrix...
# Model 4PL
mod_4pl <- mirt(datasampel, 1, itemtype = "4PL", SE = TRUE)
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Max-Change: 0.00086Iteration: 328, Log-Lik: -1051.818, Max-Change: 0.00049Iteration: 329, Log-Lik: -1051.818, Max-Change: 0.00065Iteration: 330, Log-Lik: -1051.818, Max-Change: 0.00086Iteration: 331, Log-Lik: -1051.818, Max-Change: 0.00049Iteration: 332, Log-Lik: -1051.818, Max-Change: 0.00065Iteration: 333, Log-Lik: -1051.818, Max-Change: 0.00086Iteration: 334, Log-Lik: -1051.818, Max-Change: 0.00049Iteration: 335, Log-Lik: -1051.818, Max-Change: 0.00065Iteration: 336, Log-Lik: -1051.818, Max-Change: 0.00086Iteration: 337, Log-Lik: -1051.818, Max-Change: 0.00049Iteration: 338, Log-Lik: -1051.818, Max-Change: 0.00064Iteration: 339, Log-Lik: -1051.818, Max-Change: 0.00085Iteration: 340, Log-Lik: -1051.818, Max-Change: 0.00049Iteration: 341, Log-Lik: -1051.818, Max-Change: 0.00064Iteration: 342, Log-Lik: -1051.818, Max-Change: 0.00085Iteration: 343, Log-Lik: -1051.818, Max-Change: 0.00048Iteration: 344, Log-Lik: -1051.818, Max-Change: 0.00064Iteration: 345, Log-Lik: -1051.818, Max-Change: 0.00085Iteration: 346, Log-Lik: -1051.818, Max-Change: 0.00048Iteration: 347, Log-Lik: -1051.818, Max-Change: 0.00064Iteration: 348, Log-Lik: -1051.818, Max-Change: 0.00085Iteration: 349, Log-Lik: -1051.818, Max-Change: 0.00048Iteration: 350, Log-Lik: -1051.818, Max-Change: 0.00064Iteration: 351, Log-Lik: -1051.818, Max-Change: 0.00085Iteration: 352, Log-Lik: -1051.818, Max-Change: 0.00048Iteration: 353, Log-Lik: -1051.818, Max-Change: 0.00064Iteration: 354, Log-Lik: -1051.818, Max-Change: 0.00084Iteration: 355, Log-Lik: -1051.818, Max-Change: 0.00048Iteration: 356, Log-Lik: -1051.818, Max-Change: 0.00064Iteration: 357, Log-Lik: -1051.818, Max-Change: 0.00084Iteration: 358, Log-Lik: -1051.818, Max-Change: 0.00048Iteration: 359, Log-Lik: -1051.818, Max-Change: 0.00064Iteration: 360, Log-Lik: -1051.818, Max-Change: 0.00084Iteration: 361, Log-Lik: -1051.818, Max-Change: 0.00048Iteration: 362, Log-Lik: -1051.818, Max-Change: 0.00063Iteration: 363, Log-Lik: -1051.818, Max-Change: 0.00084Iteration: 364, Log-Lik: -1051.818, Max-Change: 0.00048Iteration: 365, Log-Lik: -1051.818, Max-Change: 0.00063Iteration: 366, Log-Lik: -1051.818, Max-Change: 0.00084Iteration: 367, Log-Lik: -1051.818, Max-Change: 0.00048Iteration: 368, Log-Lik: -1051.818, Max-Change: 0.00063Iteration: 369, Log-Lik: -1051.818, Max-Change: 0.00084Iteration: 370, Log-Lik: -1051.818, Max-Change: 0.00048Iteration: 371, Log-Lik: -1051.818, Max-Change: 0.00063Iteration: 372, Log-Lik: -1051.818, Max-Change: 0.00083Iteration: 373, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 374, Log-Lik: -1051.818, Max-Change: 0.00063Iteration: 375, Log-Lik: -1051.818, Max-Change: 0.00083Iteration: 376, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 377, Log-Lik: -1051.818, Max-Change: 0.00063Iteration: 378, Log-Lik: -1051.818, Max-Change: 0.00083Iteration: 379, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 380, Log-Lik: -1051.818, Max-Change: 0.00063Iteration: 381, Log-Lik: -1051.818, Max-Change: 0.00083Iteration: 382, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 383, Log-Lik: -1051.818, Max-Change: 0.00063Iteration: 384, Log-Lik: -1051.818, Max-Change: 0.00083Iteration: 385, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 386, Log-Lik: -1051.818, Max-Change: 0.00062Iteration: 387, Log-Lik: -1051.818, Max-Change: 0.00083Iteration: 388, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 389, Log-Lik: -1051.818, Max-Change: 0.00062Iteration: 390, Log-Lik: -1051.818, Max-Change: 0.00082Iteration: 391, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 392, Log-Lik: -1051.818, Max-Change: 0.00062Iteration: 393, Log-Lik: -1051.818, Max-Change: 0.00082Iteration: 394, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 395, Log-Lik: -1051.818, Max-Change: 0.00062Iteration: 396, Log-Lik: -1051.818, Max-Change: 0.00082Iteration: 397, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 398, Log-Lik: -1051.818, Max-Change: 0.00062Iteration: 399, Log-Lik: -1051.818, Max-Change: 0.00082Iteration: 400, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 401, Log-Lik: -1051.818, Max-Change: 0.00062Iteration: 402, Log-Lik: -1051.818, Max-Change: 0.00082Iteration: 403, Log-Lik: -1051.818, Max-Change: 0.00047Iteration: 404, Log-Lik: -1051.818, Max-Change: 0.00062Iteration: 405, Log-Lik: -1051.818, Max-Change: 0.00082Iteration: 406, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 407, Log-Lik: -1051.818, Max-Change: 0.00062Iteration: 408, Log-Lik: -1051.818, Max-Change: 0.00082Iteration: 409, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 410, Log-Lik: -1051.818, Max-Change: 0.00061Iteration: 411, Log-Lik: -1051.818, Max-Change: 0.00081Iteration: 412, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 413, Log-Lik: -1051.818, Max-Change: 0.00061Iteration: 414, Log-Lik: -1051.818, Max-Change: 0.00081Iteration: 415, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 416, Log-Lik: -1051.818, Max-Change: 0.00061Iteration: 417, Log-Lik: -1051.818, Max-Change: 0.00081Iteration: 418, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 419, Log-Lik: -1051.818, Max-Change: 0.00061Iteration: 420, Log-Lik: -1051.818, Max-Change: 0.00081Iteration: 421, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 422, Log-Lik: -1051.818, Max-Change: 0.00061Iteration: 423, Log-Lik: -1051.818, Max-Change: 0.00081Iteration: 424, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 425, Log-Lik: -1051.818, Max-Change: 0.00061Iteration: 426, Log-Lik: -1051.818, Max-Change: 0.00081Iteration: 427, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 428, Log-Lik: -1051.818, Max-Change: 0.00061Iteration: 429, Log-Lik: -1051.818, Max-Change: 0.00081Iteration: 430, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 431, Log-Lik: -1051.818, Max-Change: 0.00061Iteration: 432, Log-Lik: -1051.818, Max-Change: 0.00080Iteration: 433, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 434, Log-Lik: -1051.818, Max-Change: 0.00061Iteration: 435, Log-Lik: -1051.818, Max-Change: 0.00080Iteration: 436, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 437, Log-Lik: -1051.818, Max-Change: 0.00061Iteration: 438, Log-Lik: -1051.818, Max-Change: 0.00080Iteration: 439, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 440, Log-Lik: -1051.818, Max-Change: 0.00060Iteration: 441, Log-Lik: -1051.818, Max-Change: 0.00080Iteration: 442, Log-Lik: -1051.818, Max-Change: 0.00046Iteration: 443, Log-Lik: -1051.818, Max-Change: 0.00060Iteration: 444, Log-Lik: -1051.818, Max-Change: 0.00080Iteration: 445, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 446, Log-Lik: -1051.818, Max-Change: 0.00060Iteration: 447, Log-Lik: -1051.818, Max-Change: 0.00080Iteration: 448, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 449, Log-Lik: -1051.818, Max-Change: 0.00060Iteration: 450, Log-Lik: -1051.818, Max-Change: 0.00080Iteration: 451, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 452, Log-Lik: -1051.818, Max-Change: 0.00060Iteration: 453, Log-Lik: -1051.818, Max-Change: 0.00079Iteration: 454, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 455, Log-Lik: -1051.818, Max-Change: 0.00060Iteration: 456, Log-Lik: -1051.818, Max-Change: 0.00079Iteration: 457, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 458, Log-Lik: -1051.818, Max-Change: 0.00060Iteration: 459, Log-Lik: -1051.818, Max-Change: 0.00079Iteration: 460, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 461, Log-Lik: -1051.818, Max-Change: 0.00060Iteration: 462, Log-Lik: -1051.818, Max-Change: 0.00079Iteration: 463, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 464, Log-Lik: -1051.818, Max-Change: 0.00060Iteration: 465, Log-Lik: -1051.818, Max-Change: 0.00079Iteration: 466, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 467, Log-Lik: -1051.818, Max-Change: 0.00060Iteration: 468, Log-Lik: -1051.818, Max-Change: 0.00079Iteration: 469, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 470, Log-Lik: -1051.818, Max-Change: 0.00059Iteration: 471, Log-Lik: -1051.818, Max-Change: 0.00079Iteration: 472, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 473, Log-Lik: -1051.818, Max-Change: 0.00059Iteration: 474, Log-Lik: -1051.818, Max-Change: 0.00079Iteration: 475, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 476, Log-Lik: -1051.818, Max-Change: 0.00059Iteration: 477, Log-Lik: -1051.818, Max-Change: 0.00078Iteration: 478, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 479, Log-Lik: -1051.818, Max-Change: 0.00059Iteration: 480, Log-Lik: -1051.818, Max-Change: 0.00078Iteration: 481, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 482, Log-Lik: -1051.818, Max-Change: 0.00059Iteration: 483, Log-Lik: -1051.818, Max-Change: 0.00078Iteration: 484, Log-Lik: -1051.818, Max-Change: 0.00045Iteration: 485, Log-Lik: -1051.818, Max-Change: 0.00059Iteration: 486, Log-Lik: -1051.818, Max-Change: 0.00078Iteration: 487, Log-Lik: -1051.818, Max-Change: 0.00044Iteration: 488, Log-Lik: -1051.818, Max-Change: 0.00059Iteration: 489, Log-Lik: -1051.818, Max-Change: 0.00078Iteration: 490, Log-Lik: -1051.818, Max-Change: 0.00044Iteration: 491, Log-Lik: -1051.818, Max-Change: 0.00059Iteration: 492, Log-Lik: -1051.818, Max-Change: 0.00078Iteration: 493, Log-Lik: -1051.818, Max-Change: 0.00044Iteration: 494, Log-Lik: -1051.818, Max-Change: 0.00059Iteration: 495, Log-Lik: -1051.818, Max-Change: 0.00078Iteration: 496, Log-Lik: -1051.818, Max-Change: 0.00044Iteration: 497, Log-Lik: -1051.818, Max-Change: 0.00059Iteration: 498, Log-Lik: -1051.818, Max-Change: 0.00078Iteration: 499, Log-Lik: -1051.818, Max-Change: 0.00044Iteration: 500, Log-Lik: -1051.818, Max-Change: 0.00059
## Warning: EM cycles terminated after 500 iterations.
##
##
## 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 11.90 0.16 Cocok
## 2 b2 14.89 0.04 Tidak Cocok
## 3 b3 13.15 0.11 Cocok
## 4 b4 8.38 0.50 Cocok
## 5 b5 7.23 0.51 Cocok
## 6 b6 5.29 0.63 Cocok
## 7 b7 7.64 0.37 Cocok
## 8 b8 2.85 0.90 Cocok
## 9 b9 15.09 0.09 Cocok
## 10 b10 10.10 0.18 Cocok
## 11 b11 7.33 0.60 Cocok
## 12 b12 19.62 0.01 Tidak Cocok
## 13 b13 6.10 0.53 Cocok
## 14 b14 6.36 0.70 Cocok
## 15 b15 11.24 0.26 Cocok
## 16 b16 16.10 0.02 Tidak Cocok
## 17 b17 10.40 0.06 Cocok
## 18 b18 11.86 0.11 Cocok
## 19 b19 3.42 0.91 Cocok
## 20 b20 13.67 0.13 Cocok
## 21 b21 14.45 0.11 Cocok
## 22 b22 6.25 0.40 Cocok
## 23 b23 4.85 0.43 Cocok
## 24 b24 13.20 0.15 Cocok
## 25 b25 1.90 0.98 Cocok
## 26 b26 9.23 0.42 Cocok
## 27 b27 9.16 0.24 Cocok
## 28 b28 9.07 0.43 Cocok
## 29 b29 3.65 0.16 Cocok
## 30 b30 9.45 0.31 Cocok
## 31 b31 4.77 0.69 Cocok
## 32 b32 3.30 0.51 Cocok
## 33 b33 6.90 0.33 Cocok
## 34 b34 14.49 0.04 Tidak Cocok
## 35 b35 12.27 0.20 Cocok
## 36 b36 13.25 0.10 Cocok
## 37 b37 6.87 0.55 Cocok
cat("Jumlah butir cocok/tidak cocok model Rasch:\n")
## Jumlah butir cocok/tidak cocok model Rasch:
print(table(fit_rasch_df$Keputusan))
##
## Cocok Tidak Cocok
## 33 4
# Model 1PL
fit_1PL <- itemfit(mod_1pl, fit_stats = "S_X2")
fit_1PL_df <- data.frame(
Butir = fit_1PL$item,
Chi = round(fit_1PL$S_X2, 2),
pvalue = round(fit_1PL$p.S_X2, 2),
Keputusan = ifelse(fit_1PL$p.S_X2 >= 0.05, "Cocok", "Tidak Cocok")
)
print(fit_1PL_df)
## Butir Chi pvalue Keputusan
## 1 b1 11.90 0.16 Cocok
## 2 b2 14.89 0.04 Tidak Cocok
## 3 b3 13.15 0.11 Cocok
## 4 b4 8.38 0.50 Cocok
## 5 b5 7.23 0.51 Cocok
## 6 b6 5.29 0.62 Cocok
## 7 b7 7.64 0.37 Cocok
## 8 b8 2.85 0.90 Cocok
## 9 b9 15.09 0.09 Cocok
## 10 b10 10.10 0.18 Cocok
## 11 b11 7.33 0.60 Cocok
## 12 b12 19.62 0.01 Tidak Cocok
## 13 b13 6.10 0.53 Cocok
## 14 b14 6.36 0.70 Cocok
## 15 b15 11.24 0.26 Cocok
## 16 b16 16.10 0.02 Tidak Cocok
## 17 b17 10.40 0.06 Cocok
## 18 b18 11.86 0.11 Cocok
## 19 b19 3.42 0.91 Cocok
## 20 b20 13.67 0.13 Cocok
## 21 b21 14.45 0.11 Cocok
## 22 b22 6.25 0.40 Cocok
## 23 b23 4.85 0.43 Cocok
## 24 b24 13.20 0.15 Cocok
## 25 b25 1.90 0.98 Cocok
## 26 b26 9.23 0.42 Cocok
## 27 b27 9.16 0.24 Cocok
## 28 b28 9.07 0.43 Cocok
## 29 b29 3.65 0.16 Cocok
## 30 b30 9.45 0.31 Cocok
## 31 b31 4.77 0.69 Cocok
## 32 b32 3.30 0.51 Cocok
## 33 b33 6.90 0.33 Cocok
## 34 b34 14.49 0.04 Tidak Cocok
## 35 b35 12.27 0.20 Cocok
## 36 b36 13.25 0.10 Cocok
## 37 b37 6.87 0.55 Cocok
cat("Jumlah butir cocok/tidak cocok model 1PL:\n")
## Jumlah butir cocok/tidak cocok model 1PL:
print(table(fit_1PL_df$Keputusan))
##
## Cocok Tidak Cocok
## 33 4
# 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 11.51 0.17 Cocok
## 2 b2 12.59 0.25 Cocok
## 3 b3 6.25 0.28 Cocok
## 4 b4 9.04 0.53 Cocok
## 5 b5 7.49 0.59 Cocok
## 6 b6 2.70 0.75 Cocok
## 7 b7 11.66 0.31 Cocok
## 8 b8 3.12 0.87 Cocok
## 9 b9 14.84 0.10 Cocok
## 10 b10 9.24 0.10 Cocok
## 11 b11 4.19 0.52 Cocok
## 12 b12 12.51 0.05 Cocok
## 13 b13 3.95 0.79 Cocok
## 14 b14 6.10 0.64 Cocok
## 15 b15 9.12 0.52 Cocok
## 16 b16 12.42 0.26 Cocok
## 17 b17 4.85 0.77 Cocok
## 18 b18 11.44 0.18 Cocok
## 19 b19 3.11 0.87 Cocok
## 20 b20 10.63 0.06 Cocok
## 21 b21 9.84 0.45 Cocok
## 22 b22 4.97 0.42 Cocok
## 23 b23 3.68 0.82 Cocok
## 24 b24 9.68 0.05 Tidak Cocok
## 25 b25 2.01 0.98 Cocok
## 26 b26 8.98 0.44 Cocok
## 27 b27 13.16 0.04 Tidak Cocok
## 28 b28 6.21 0.40 Cocok
## 29 b29 3.57 0.17 Cocok
## 30 b30 6.92 0.33 Cocok
## 31 b31 4.75 0.69 Cocok
## 32 b32 2.99 0.56 Cocok
## 33 b33 7.07 0.42 Cocok
## 34 b34 14.56 0.04 Tidak Cocok
## 35 b35 8.48 0.58 Cocok
## 36 b36 8.27 0.14 Cocok
## 37 b37 2.78 0.99 Cocok
cat("Jumlah butir cocok/tidak cocok model 2PL:\n")
## Jumlah butir cocok/tidak cocok model 2PL:
print(table(fit_2PL_df$Keputusan))
##
## Cocok Tidak Cocok
## 34 3
# Model 3PL
fit_3PL <- itemfit(mod_3pl, fit_stats = "S_X2")
fit_3PL_df <- data.frame(
Butir = fit_3PL$item,
Chi = round(fit_3PL$S_X2, 2),
pvalue = round(fit_3PL$p.S_X2, 2),
Keputusan = ifelse(fit_3PL$p.S_X2 >= 0.05, "Cocok", "Tidak Cocok")
)
print(fit_3PL_df)
## Butir Chi pvalue Keputusan
## 1 b1 9.32 0.16 Cocok
## 2 b2 10.38 0.24 Cocok
## 3 b3 7.98 0.16 Cocok
## 4 b4 7.93 0.44 Cocok
## 5 b5 7.75 0.46 Cocok
## 6 b6 5.23 0.39 Cocok
## 7 b7 11.30 0.26 Cocok
## 8 b8 6.15 0.52 Cocok
## 9 b9 14.31 0.07 Cocok
## 10 b10 7.17 0.13 Cocok
## 11 b11 5.97 0.11 Cocok
## 12 b12 15.86 0.01 Tidak Cocok
## 13 b13 4.23 0.65 Cocok
## 14 b14 3.18 0.87 Cocok
## 15 b15 7.35 0.60 Cocok
## 16 b16 10.92 0.21 Cocok
## 17 b17 6.06 0.42 Cocok
## 18 b18 8.70 0.19 Cocok
## 19 b19 5.38 0.50 Cocok
## 20 b20 7.55 0.06 Cocok
## 21 b21 10.12 0.43 Cocok
## 22 b22 5.25 0.26 Cocok
## 23 b23 4.20 0.52 Cocok
## 24 b24 8.37 0.04 Tidak Cocok
## 25 b25 1.01 0.99 Cocok
## 26 b26 9.44 0.31 Cocok
## 27 b27 11.44 0.04 Tidak Cocok
## 28 b28 6.80 0.24 Cocok
## 29 b29 2.58 0.11 Cocok
## 30 b30 7.04 0.22 Cocok
## 31 b31 5.56 0.47 Cocok
## 32 b32 2.11 0.71 Cocok
## 33 b33 7.44 0.19 Cocok
## 34 b34 19.05 0.01 Tidak Cocok
## 35 b35 6.95 0.64 Cocok
## 36 b36 5.11 0.16 Cocok
## 37 b37 3.38 0.95 Cocok
cat("Jumlah butir cocok/tidak cocok model 3PL:\n")
## Jumlah butir cocok/tidak cocok model 3PL:
print(table(fit_3PL_df$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 9.80 0.20 Cocok
## 2 b2 9.18 0.24 Cocok
## 3 b3 6.45 0.09 Cocok
## 4 b4 8.52 0.29 Cocok
## 5 b5 7.30 0.29 Cocok
## 6 b6 5.60 0.23 Cocok
## 7 b7 11.06 0.09 Cocok
## 8 b8 2.61 0.76 Cocok
## 9 b9 14.51 0.04 Tidak Cocok
## 10 b10 6.94 0.07 Cocok
## 11 b11 5.09 0.28 Cocok
## 12 b12 14.96 0.00 Tidak Cocok
## 13 b13 4.49 0.61 Cocok
## 14 b14 3.25 0.66 Cocok
## 15 b15 10.14 0.26 Cocok
## 16 b16 9.77 0.20 Cocok
## 17 b17 5.51 0.36 Cocok
## 18 b18 11.39 0.08 Cocok
## 19 b19 4.61 0.47 Cocok
## 20 b20 9.66 0.05 Tidak Cocok
## 21 b21 9.95 0.35 Cocok
## 22 b22 7.73 0.10 Cocok
## 23 b23 3.79 0.58 Cocok
## 24 b24 6.24 0.04 Tidak Cocok
## 25 b25 1.46 0.92 Cocok
## 26 b26 5.42 0.37 Cocok
## 27 b27 9.54 0.02 Tidak Cocok
## 28 b28 6.52 0.16 Cocok
## 29 b29 6.68 0.01 Tidak Cocok
## 30 b30 7.11 0.21 Cocok
## 31 b31 5.45 0.36 Cocok
## 32 b32 4.78 0.19 Cocok
## 33 b33 7.78 0.10 Cocok
## 34 b34 18.03 0.00 Tidak Cocok
## 35 b35 6.10 0.64 Cocok
## 36 b36 4.07 0.04 Tidak Cocok
## 37 b37 2.52 0.96 Cocok
cat("Jumlah butir cocok/tidak cocok model 4PL:\n")
## Jumlah butir cocok/tidak cocok model 4PL:
print(table(fit_4PL_df$Keputusan))
##
## Cocok Tidak Cocok
## 29 8
# Plot Empirical untuk Butir ke-9 pada Setiap Model
itemfit(mod_rasch, 'S_X2', empirical.plot = 9)
itemfit(mod_1pl, 'S_X2', empirical.plot = 9)
itemfit(mod_2pl, 'S_X2', empirical.plot = 9)
itemfit(mod_3pl, 'S_X2', empirical.plot = 9)
itemfit(mod_4pl, 'S_X2', empirical.plot = 9)
# Visualisasi Plot Semua Butir
for (coba in 1:nrow(fit_rasch_df)) {
print(itemfit(mod_rasch, 'S_X2', empirical.plot = coba))
}
# Step 6: Uji Kecocokan Model dengan ANOVA (AIC, BIC)
anova(mod_rasch, mod_1pl)
## AIC SABIC HQ BIC logLik X2 df p
## mod_rasch 2338.865 2292.246 2366.533 2411.522 -1131.432
## mod_1pl 2338.865 2292.246 2366.533 2411.522 -1131.432 0 0 NaN
anova(mod_1pl, mod_2pl)
## AIC SABIC HQ BIC logLik X2 df p
## mod_1pl 2338.865 2292.246 2366.533 2411.522 -1131.432
## mod_2pl 2340.426 2249.642 2394.306 2481.915 -1096.213 70.439 36 0.001
anova(mod_2pl, mod_3pl)
## AIC SABIC HQ BIC logLik X2 df p
## mod_2pl 2340.426 2249.642 2394.306 2481.915 -1096.213
## mod_3pl 2352.670 2216.494 2433.490 2564.905 -1065.335 61.755 37 0.007
anova(mod_3pl, mod_4pl)
## AIC SABIC HQ BIC logLik X2 df p
## mod_3pl 2352.670 2216.494 2433.490 2564.905 -1065.335
## mod_4pl 2399.636 2218.068 2507.396 2682.615 -1051.818 27.035 37 0.886
# Menghitung NFI (Normed Fit Index) untuk Setiap Model
get_fit_index <- function(mod) {
fit <- M2(mod)
return(c(CFI = fit$CFI, TLI = fit$TLI, RMSEA = fit$RMSEA))
}
fit_rasch <- get_fit_index(mod_rasch)
fit_1pl <- get_fit_index(mod_1pl)
fit_2pl <- get_fit_index(mod_2pl)
fit_3pl <- get_fit_index(mod_3pl)
fit_4pl <- get_fit_index(mod_4pl)
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: -1133.418, Max-Change: 0.26501
## 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 50 2338.865 2411.522 33 4 0
## 2 1PL 50 2338.865 2411.522 33 4 0
## 3 2PL 50 2340.426 2481.915 34 3 0
## 4 3PL 50 2352.670 2564.905 33 4 0
## 5 4PL 50 2399.636 2682.615 29 8 0
## Jumlah_Variabel NFI_maks
## 1 37 0.0002
## 2 37 0.0002
## 3 37 0.0314
## 4 37 0.0586
## 5 37 0.0706