Temel çalışmalar
## Zorunlu paket yükleniyor: sm## Package 'sm', version 2.2-6.0: type help(sm) for summary information## Zorunlu paket yükleniyor: ltm## Zorunlu paket yükleniyor: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:sm':
##
## muscle## Zorunlu paket yükleniyor: msm## Zorunlu paket yükleniyor: polycor## Zorunlu paket yükleniyor: stats4## Zorunlu paket yükleniyor: lattice##
## Attaching package: 'mirt'## The following object is masked from 'package:ltm':
##
## Science# 2. Madde parametreleri oluştur
set.seed(54)
madde <- 10
maddepar <- cbind(
rnorm(madde, mean=0, sd=0.75)*1.702, # a
rnorm(madde, mean=0.30, sd=0.51)*1.702, # b
rnorm(madde, mean=0.16, sd=0.05) # c
)
# 3. Birey yetenek düzeylerini üret
bireypar <- rnorm(1000, 0, 1)
# 4. Cevap verisi üret
veri <- sim(maddepar, bireypar)
colnames(veri) <- paste("madde", 1:madde, sep="")
# 5. 3PL modeli kur
model3pl <- mirt(veri, 1, itemtype="3PL", technical=list(NCYCLES=1000))## Iteration: 1, Log-Lik: -6386.039, Max-Change: 0.75651Iteration: 2, Log-Lik: -6199.075, Max-Change: 0.78547Iteration: 3, Log-Lik: -6130.739, Max-Change: 0.49289Iteration: 4, Log-Lik: -6063.065, Max-Change: 0.59295Iteration: 5, Log-Lik: -6011.860, Max-Change: 0.51753Iteration: 6, Log-Lik: -5986.461, Max-Change: 0.41227Iteration: 7, Log-Lik: -5976.442, Max-Change: 0.27906Iteration: 8, Log-Lik: -5972.464, Max-Change: 0.24638Iteration: 9, Log-Lik: -5970.777, Max-Change: 0.22075Iteration: 10, Log-Lik: -5969.420, Max-Change: 0.08303Iteration: 11, Log-Lik: -5969.076, Max-Change: 2.49966Iteration: 12, Log-Lik: -5968.943, Max-Change: 0.03496Iteration: 13, Log-Lik: -5968.941, Max-Change: 0.04670Iteration: 14, Log-Lik: -5968.902, Max-Change: 0.03836Iteration: 15, Log-Lik: -5968.864, Max-Change: 0.03208Iteration: 16, Log-Lik: -5968.796, Max-Change: 0.02344Iteration: 17, Log-Lik: -5968.783, Max-Change: 0.01693Iteration: 18, 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0.00017Iteration: 164, Log-Lik: -5968.691, Max-Change: 0.00085Iteration: 165, Log-Lik: -5968.691, Max-Change: 0.00036Iteration: 166, Log-Lik: -5968.691, Max-Change: 0.00017Iteration: 167, Log-Lik: -5968.691, Max-Change: 0.00085Iteration: 168, Log-Lik: -5968.691, Max-Change: 0.00035Iteration: 169, Log-Lik: -5968.691, Max-Change: 0.00017Iteration: 170, Log-Lik: -5968.691, Max-Change: 0.00085Iteration: 171, Log-Lik: -5968.691, Max-Change: 0.00033Iteration: 172, Log-Lik: -5968.691, Max-Change: 0.00017Iteration: 173, Log-Lik: -5968.691, Max-Change: 0.00084Iteration: 174, Log-Lik: -5968.691, Max-Change: 0.00035Iteration: 175, Log-Lik: -5968.691, Max-Change: 0.00017## a b g u
## madde1 1.46527657 2.40728417 0.060956704 1
## madde2 0.40351618 -0.03208453 0.011871931 1
## madde3 -0.49865900 0.84048702 0.003104802 1
## madde4 1.83586631 1.16284994 0.237762309 1
## madde5 1.88916799 -0.83313569 0.434721463 1
## madde6 -1.91443271 -1.02346216 0.371462809 1
## madde7 0.03868613 8.94648158 0.236747483 1
## madde8 -1.57423372 0.30401644 0.016387278 1
## madde9 2.88287056 -0.06514307 0.194375141 1
## madde10 1.07663020 1.14319936 0.079042174 1veri_uretimi <- function(maddesay, bireysay, seed) {
# seed ayaralanır
set.seed(seed)
# madde parametreleri üretilir.
maddepar <- cbind(
rnorm(maddesay, mean = 1.13, sd = 0.25)*1.702, #a
rnorm(maddesay, mean = 0.21, sd = 0.51)*1.702, #b
rnorm(maddesay, mean = 0.16, sd = 0.05)) #c
# yetenek parametreleri üretilir
yetenek <- rnorm(bireysay, mean = 0, sd = 1)
# 3PL modele göre veri uretimi
cevaplar <- irtoys::sim(ip = maddepar, x = yetenek)
colnames(cevaplar) <- paste0("madde", 1:maddesay)
# Parametrelerin ve ciktinin nesnede toplanması
veri <- list(maddepar = maddepar,
yetenek = yetenek,
seed = seed,
cevaplar = cevaplar)
return(veri)
}## [1] 0.03057126 -1.48227491 -1.12664844 -1.76384329 -1.06261908 -1.34299924## [,1] [,2] [,3]
## [1,] 2.243794 -1.198281 0.2029150
## [2,] 2.780368 0.320935 0.1772450
## [3,] 1.772150 2.223700 0.1308774## madde1 madde2 madde3 madde4 madde5 madde6 madde7 madde8
## [1,] 1 1 0 1 1 1 0 0
## [2,] 0 0 0 0 1 0 1 0
## [3,] 1 0 0 1 0 1 0 1kestirilen_par <- function(veri, par=3){
if(par==3){
model <- mirt::mirt(veri, # cevap matrisi
1, # tek boyutlu model
itemtype = "3PL", # 3PL
verbose = FALSE,
technical = list(NCYCLES = 1000,
message = FALSE))
}else {
model <- mirt::mirt(veri, # cevap matrisi
1, # tek boyutlu model
itemtype = "2PL", # 2pl
verbose = FALSE,
technical = list(NCYCLES = 1000,
message = FALSE))
}
# Madde parametreleri
kestirim <- as.data.frame(mirt::coef(model, IRTpars = TRUE,
simplify = TRUE)$item[,1:3])
kestirim
}
kestirim <- kestirilen_par(veri_1$cevaplar)## Warning: EM cycles terminated after 1000 iterations.## a b g
## madde1 2.205493 -1.3787942 0.0013807796
## madde2 5.469459 0.4080018 0.2028277926
## madde3 1.048859 2.7996412 0.0859692109
## madde4 7.197095 -0.7353701 0.4387559242
## madde5 1.474044 1.1473398 0.2242418125
## madde6 2.184943 -1.2724474 0.0006967016veri setinin kontrolü
kestirim = kestirim
gercek = veri_1$maddepar
hata <- function(kestirim, gercek) {
result <- data.frame(parametreler = c("a", "b", "c"),
bias = sapply(1L:3L, function(i) mean((kestirim[, i] - gercek[,i]))),
rmse = sapply(1L:3L, function(i) sqrt(mean((kestirim[, i] - gercek[,i])^2))),
korelasyon = sapply(1L:3L, function(i) cor(kestirim[, i], gercek[,i])))
return(result)
}
hata(kestirim,veri_1$maddepar)## parametreler bias rmse korelasyon
## 1 a 0.79534558 1.8606784 0.8141316
## 2 b 0.08642950 0.3085654 0.9782335
## 3 c -0.01476499 0.1326092 0.4511526# Değerler 1 kez yaptığımız için kötü, deneme sayısını arttırarak değerleri düzelteceğiz.
veri_uretimi <- function(maddesay, bireysay, seed = NULL){
if(!is.null(seed)) {
set.seed(seed)}
else {
seed <- sample.int(10000, 1)
set.seed(seed)
cat("atanan seed = ", seed, "\n")
}
# madde parametreleri üretilir.
print("Madde parametresi uretme")
maddepar <- cbind(
rnorm(maddesay, mean = 1.13, sd = 0.25)*1.702, #a
rnorm(maddesay, mean = 0.21, sd = 0.51)*1.702, #b
rnorm(maddesay, mean = 0.16, sd = 0.05)) #c
# yetenek parametreleri üretilir
yetenek <- rnorm(bireysay, mean = 0, sd = 1)
# 3PL modele göre veri uretimi
print("Üretilen veri")
cevaplar <- irtoys::sim(ip = maddepar, x = yetenek)
colnames(cevaplar) <- paste0("madde", 1:maddesay)
# Parametrelerin ve ciktinin nesnede toplanması
print("Cıktıların birleştirilmesi")
veri <- list(maddepar = maddepar,
yetenek = yetenek,
seed = seed,
cevaplar = cevaplar)
# Cikti
return(veri)
}
temp2 <- veri_uretimi(maddesay = 10, bireysay = 1000)## atanan seed = 5593
## [1] "Madde parametresi uretme"
## [1] "Üretilen veri"
## [1] "Cıktıların birleştirilmesi"Tekrar Yöntemleri
## atanan seed = 7116
## [1] "Madde parametresi uretme"
## [1] "Üretilen veri"
## [1] "Cıktıların birleştirilmesi"
## atanan seed = 727
## [1] "Madde parametresi uretme"
## [1] "Üretilen veri"
## [1] "Cıktıların birleştirilmesi"
## atanan seed = 6970
## [1] "Madde parametresi uretme"
## [1] "Üretilen veri"
## [1] "Cıktıların birleştirilmesi"
## atanan seed = 4875
## [1] "Madde parametresi uretme"
## [1] "Üretilen veri"
## [1] "Cıktıların birleştirilmesi"
## atanan seed = 789
## [1] "Madde parametresi uretme"
## [1] "Üretilen veri"
## [1] "Cıktıların birleştirilmesi"## [[1]]
## [[1]]$maddepar
## [,1] [,2] [,3]
## [1,] 2.631254 -0.56996324 0.07520040
## [2,] 1.526717 0.06496369 0.18591439
## [3,] 1.265881 1.79755521 0.09939258
## [4,] 1.933478 2.32519222 0.19499314
## [5,] 2.362765 0.46074478 0.17566472
## [6,] 1.811836 0.82676319 0.18402382
## [7,] 2.260861 1.66795725 0.17728033
## [8,] 2.209573 0.17005423 0.14707589
## [9,] 2.460813 0.39180866 0.12776329
## [10,] 2.226531 0.37027774 0.16224585
##
##
## [[2]]
## [[2]]$maddepar
## [,1] [,2] [,3]
## [1,] 2.447188 0.94649343 0.21677913
## [2,] 1.924426 -0.91779189 0.19144033
## [3,] 1.813827 1.79259458 0.16927400
## [4,] 2.442280 -0.03696677 0.15831661
## [5,] 2.206052 0.93846942 0.19297008
## [6,] 1.770319 0.58215082 0.13535119
## [7,] 2.702847 0.72900406 0.16199978
## [8,] 2.195806 0.65673183 0.18471641
## [9,] 1.368156 -0.64558779 0.06431211
## [10,] 2.322501 0.27513934 0.23550202
##
##
## [[3]]
## [[3]]$maddepar
## [,1] [,2] [,3]
## [1,] 0.9529722 -0.9018162 0.15268493
## [2,] 1.6286945 1.1330071 0.12380312
## [3,] 1.9831582 0.6882311 0.20817723
## [4,] 2.3410654 -0.0603129 0.10285817
## [5,] 1.8155239 -0.1820915 0.06276859
## [6,] 0.8768784 0.2848566 0.11363667
## [7,] 2.0677440 0.6827309 0.16393405
## [8,] 2.1324429 1.7466449 0.16872661
## [9,] 1.9582909 0.5840565 0.17504181
## [10,] 1.6224441 -0.8963797 0.07685384
##
##
## [[4]]
## [[4]]$maddepar
## [,1] [,2] [,3]
## [1,] 1.664395 0.53977544 0.20156906
## [2,] 2.058941 -0.10366945 0.16521822
## [3,] 1.905575 -0.00870757 0.18055743
## [4,] 1.728602 1.60843166 0.14354715
## [5,] 2.064747 -0.50557761 0.03481295
## [6,] 1.176560 -0.59864146 0.14340471
## [7,] 2.248764 2.52694851 0.07244728
## [8,] 2.117758 2.02580788 0.15013590
## [9,] 2.164247 0.15750146 0.16432428
## [10,] 1.896558 0.06026242 0.24020693
##
##
## [[5]]
## [[5]]$maddepar
## [,1] [,2] [,3]
## [1,] 2.1462632 0.00821876 0.1248975
## [2,] 0.9613033 -0.51301338 0.1941735
## [3,] 1.9148863 0.20315617 0.1171156
## [4,] 2.0011860 -0.06608658 0.1783880
## [5,] 1.7695049 1.16286217 0.0885154
## [6,] 1.7171121 -0.31479658 0.1343838
## [7,] 1.6397438 0.72448059 0.1465945
## [8,] 1.8490233 -0.16943636 0.1500384
## [9,] 1.4930967 0.53916167 0.2028287
## [10,] 2.2380007 -0.31732423 0.1516605## $maddepar
## [,1] [,2] [,3]
## [1,] 2.631254 -0.56996324 0.07520040
## [2,] 1.526717 0.06496369 0.18591439
## [3,] 1.265881 1.79755521 0.09939258
## [4,] 1.933478 2.32519222 0.19499314
## [5,] 2.362765 0.46074478 0.17566472
## [6,] 1.811836 0.82676319 0.18402382
## [7,] 2.260861 1.66795725 0.17728033
## [8,] 2.209573 0.17005423 0.14707589
## [9,] 2.460813 0.39180866 0.12776329
## [10,] 2.226531 0.37027774 0.16224585
##
## $maddepar
## [,1] [,2] [,3]
## [1,] 2.447188 0.94649343 0.21677913
## [2,] 1.924426 -0.91779189 0.19144033
## [3,] 1.813827 1.79259458 0.16927400
## [4,] 2.442280 -0.03696677 0.15831661
## [5,] 2.206052 0.93846942 0.19297008
## [6,] 1.770319 0.58215082 0.13535119
## [7,] 2.702847 0.72900406 0.16199978
## [8,] 2.195806 0.65673183 0.18471641
## [9,] 1.368156 -0.64558779 0.06431211
## [10,] 2.322501 0.27513934 0.23550202
##
## $maddepar
## [,1] [,2] [,3]
## [1,] 0.9529722 -0.9018162 0.15268493
## [2,] 1.6286945 1.1330071 0.12380312
## [3,] 1.9831582 0.6882311 0.20817723
## [4,] 2.3410654 -0.0603129 0.10285817
## [5,] 1.8155239 -0.1820915 0.06276859
## [6,] 0.8768784 0.2848566 0.11363667
## [7,] 2.0677440 0.6827309 0.16393405
## [8,] 2.1324429 1.7466449 0.16872661
## [9,] 1.9582909 0.5840565 0.17504181
## [10,] 1.6224441 -0.8963797 0.07685384
##
## $maddepar
## [,1] [,2] [,3]
## [1,] 1.664395 0.53977544 0.20156906
## [2,] 2.058941 -0.10366945 0.16521822
## [3,] 1.905575 -0.00870757 0.18055743
## [4,] 1.728602 1.60843166 0.14354715
## [5,] 2.064747 -0.50557761 0.03481295
## [6,] 1.176560 -0.59864146 0.14340471
## [7,] 2.248764 2.52694851 0.07244728
## [8,] 2.117758 2.02580788 0.15013590
## [9,] 2.164247 0.15750146 0.16432428
## [10,] 1.896558 0.06026242 0.24020693
##
## $maddepar
## [,1] [,2] [,3]
## [1,] 2.1462632 0.00821876 0.1248975
## [2,] 0.9613033 -0.51301338 0.1941735
## [3,] 1.9148863 0.20315617 0.1171156
## [4,] 2.0011860 -0.06608658 0.1783880
## [5,] 1.7695049 1.16286217 0.0885154
## [6,] 1.7171121 -0.31479658 0.1343838
## [7,] 1.6397438 0.72448059 0.1465945
## [8,] 1.8490233 -0.16943636 0.1500384
## [9,] 1.4930967 0.53916167 0.2028287
## [10,] 2.2380007 -0.31732423 0.1516605Doparallel
library(doParallel) #çekirdekleri ayrı ayrı kullanır. detectCores() cl <- makeCluster(4) # en fazla n-2 registerDoParallel(cl) # burada kod stopCluster(cl)
## Zorunlu paket yükleniyor: foreach## Zorunlu paket yükleniyor: iterators## Zorunlu paket yükleniyor: parallelcl <- makeCluster(2)
registerDoParallel(cl)
tekrar = 4
seed = sample.int(10000, 100)
maddesay = 10 # 10, 15, 20, or 25
bireysay = 1000 # 250, 500, 750, or 1000
simulasyon <- foreach(i=1:4,
.packages = c("mirt", "doParallel"),
.combine = rbind) %dopar% {
# Adım 1 madde parametrelerini ve veri setini üretme
adim1 <- veri_uretimi(maddesay =maddesay,
bireysay =bireysay, seed=seed[i])
# Adım 2 üretilen veri seti üzerinden ketsirim yapma
adim2 <- kestirilen_par(adim1$cevaplar)
# adim 3 raporlama
hata(adim2, adim1$maddepar)
}
simulasyon## parametreler bias rmse korelasyon
## 1 a 0.117964991 0.48134347 0.25526597
## 2 b 0.058117956 0.31903309 0.94477735
## 3 c 0.007734476 0.15219601 0.09326600
## 4 a -0.023193677 0.31046880 0.80569733
## 5 b -0.025007282 0.23335019 0.93351742
## 6 c 0.014319537 0.10185641 0.50662488
## 7 a 0.043704632 0.72473806 0.20017255
## 8 b -0.102446922 0.20129189 0.98388695
## 9 c -0.014728611 0.05773816 0.06868250
## 10 a -0.138766758 0.86317780 0.11436649
## 11 b -1.884541922 5.90431824 -0.80830316
## 12 c -0.010804177 0.11707710 0.05341037## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.0.4
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ purrr::accumulate() masks foreach::accumulate()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ✖ dplyr::select() masks MASS::select()
## ✖ purrr::when() masks foreach::when()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorssimulasyon_v1 <- simulasyon %>%
group_by(parametreler) %>%
summarise(bias = round(mean(bias),3),
rmse = round(mean(rmse),3),
korelasyon = round(mean(korelasyon),3)) %>%
mutate(maddesay = maddesay,
bireysay = bireysay) %>%
as.data.frame()
simulasyon_v1## parametreler bias rmse korelasyon maddesay bireysay
## 1 a 0.000 0.595 0.344 10 1000
## 2 b -0.488 1.664 0.513 10 1000
## 3 c -0.001 0.107 0.180 10 1000Rasch Modeline Dayalı Veri Üretimi
b <- rnorm(20, 0, 1)
theta <- rnorm(1000, 0, 1)
madde_sayisi <- length(b)
kisi_sayisi <- length(theta)
replikasyon <- 10## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] -0.4210383 0.8469182 -1.473007 -0.5173531 -0.6558142 -0.7014217 -0.8240832
## [2,] -0.4210383 0.8469182 -1.473007 -0.5173531 -0.6558142 -0.7014217 -0.8240832
## [3,] -0.4210383 0.8469182 -1.473007 -0.5173531 -0.6558142 -0.7014217 -0.8240832
## [4,] -0.4210383 0.8469182 -1.473007 -0.5173531 -0.6558142 -0.7014217 -0.8240832
## [5,] -0.4210383 0.8469182 -1.473007 -0.5173531 -0.6558142 -0.7014217 -0.8240832
## [6,] -0.4210383 0.8469182 -1.473007 -0.5173531 -0.6558142 -0.7014217 -0.8240832
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 1.696775 0.1457323 -0.8355485 -0.6270315 1.590199 -1.469166 -0.532465
## [2,] 1.696775 0.1457323 -0.8355485 -0.6270315 1.590199 -1.469166 -0.532465
## [3,] 1.696775 0.1457323 -0.8355485 -0.6270315 1.590199 -1.469166 -0.532465
## [4,] 1.696775 0.1457323 -0.8355485 -0.6270315 1.590199 -1.469166 -0.532465
## [5,] 1.696775 0.1457323 -0.8355485 -0.6270315 1.590199 -1.469166 -0.532465
## [6,] 1.696775 0.1457323 -0.8355485 -0.6270315 1.590199 -1.469166 -0.532465
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.07028761 -1.445848 0.0531036 1.707013 -0.8290458 -0.7314925
## [2,] 0.07028761 -1.445848 0.0531036 1.707013 -0.8290458 -0.7314925
## [3,] 0.07028761 -1.445848 0.0531036 1.707013 -0.8290458 -0.7314925
## [4,] 0.07028761 -1.445848 0.0531036 1.707013 -0.8290458 -0.7314925
## [5,] 0.07028761 -1.445848 0.0531036 1.707013 -0.8290458 -0.7314925
## [6,] 0.07028761 -1.445848 0.0531036 1.707013 -0.8290458 -0.7314925theta.mat <- matrix(theta, kisi_sayisi, madde_sayisi)
head(theta.mat) # yukarıda tanımladığımız teta değerleri tabloda ## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1.0775472 1.0775472 1.0775472 1.0775472 1.0775472 1.0775472
## [2,] -1.2557011 -1.2557011 -1.2557011 -1.2557011 -1.2557011 -1.2557011
## [3,] -1.0936607 -1.0936607 -1.0936607 -1.0936607 -1.0936607 -1.0936607
## [4,] 0.9061701 0.9061701 0.9061701 0.9061701 0.9061701 0.9061701
## [5,] 1.5318050 1.5318050 1.5318050 1.5318050 1.5318050 1.5318050
## [6,] 1.4248174 1.4248174 1.4248174 1.4248174 1.4248174 1.4248174
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 1.0775472 1.0775472 1.0775472 1.0775472 1.0775472 1.0775472
## [2,] -1.2557011 -1.2557011 -1.2557011 -1.2557011 -1.2557011 -1.2557011
## [3,] -1.0936607 -1.0936607 -1.0936607 -1.0936607 -1.0936607 -1.0936607
## [4,] 0.9061701 0.9061701 0.9061701 0.9061701 0.9061701 0.9061701
## [5,] 1.5318050 1.5318050 1.5318050 1.5318050 1.5318050 1.5318050
## [6,] 1.4248174 1.4248174 1.4248174 1.4248174 1.4248174 1.4248174
## [,13] [,14] [,15] [,16] [,17] [,18]
## [1,] 1.0775472 1.0775472 1.0775472 1.0775472 1.0775472 1.0775472
## [2,] -1.2557011 -1.2557011 -1.2557011 -1.2557011 -1.2557011 -1.2557011
## [3,] -1.0936607 -1.0936607 -1.0936607 -1.0936607 -1.0936607 -1.0936607
## [4,] 0.9061701 0.9061701 0.9061701 0.9061701 0.9061701 0.9061701
## [5,] 1.5318050 1.5318050 1.5318050 1.5318050 1.5318050 1.5318050
## [6,] 1.4248174 1.4248174 1.4248174 1.4248174 1.4248174 1.4248174
## [,19] [,20]
## [1,] 1.0775472 1.0775472
## [2,] -1.2557011 -1.2557011
## [3,] -1.0936607 -1.0936607
## [4,] 0.9061701 0.9061701
## [5,] 1.5318050 1.5318050
## [6,] 1.4248174 1.4248174## Warning in dir.create("Rasch"): 'Rasch' zaten varfor (r in 1:replikasyon) {
logit <- (theta.mat - b.mat)
P <- 1 / (1 + exp(-logit))
print(head(P)) # çıktıyı görmek için print() kullan
}## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8173634 0.5574030 0.9276107 0.8313044 0.8498419 0.8555695 0.8700759
## [2,] 0.3026601 0.1088425 0.5541136 0.3233655 0.3543696 0.3648721 0.3937401
## [3,] 0.3379099 0.1255843 0.5937153 0.3597827 0.3922542 0.4031784 0.4330108
## [4,] 0.7903785 0.5148086 0.9152256 0.8058901 0.8266379 0.8330768 0.8494448
## [5,] 0.8757563 0.6648285 0.9527910 0.8858625 0.8991322 0.9031939 0.9134011
## [6,] 0.8636398 0.6405839 0.9477388 0.8745904 0.8890064 0.8934274 0.9045557
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0.34995705 0.7174433 0.8713665 0.8461318 0.37457209 0.9273524 0.8334131
## [2,] 0.04961961 0.1975888 0.3964802 0.3478123 0.05489364 0.5531644 0.3266808
## [3,] 0.05784320 0.2245417 0.4358278 0.3854144 0.06393251 0.5927885 0.3632709
## [4,] 0.31203875 0.6814488 0.8509052 0.8224743 0.33536269 0.9149271 0.8082432
## [5,] 0.45885073 0.7999645 0.9143037 0.8964916 0.48540566 0.9526180 0.8873816
## [6,] 0.43242652 0.7822940 0.9055409 0.8861343 0.45874859 0.9475482 0.8762385
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.7324835 0.9257657 0.7358372 0.34763169 0.8706359 0.8592458
## [2,] 0.2098237 0.5473939 0.2126869 0.04913904 0.3949253 0.3718686
## [3,] 0.2379506 0.5871478 0.2410806 0.05728779 0.4342296 0.4104348
## [4,] 0.6975973 0.9130945 0.7012100 0.30984526 0.8500784 0.8372166
## [5,] 0.8117646 0.9515543 0.8143764 0.45630974 0.9137929 0.9057914
## [6,] 0.7948692 0.9463771 0.7976569 0.42991560 0.9049832 0.8962569
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8173634 0.5574030 0.9276107 0.8313044 0.8498419 0.8555695 0.8700759
## [2,] 0.3026601 0.1088425 0.5541136 0.3233655 0.3543696 0.3648721 0.3937401
## [3,] 0.3379099 0.1255843 0.5937153 0.3597827 0.3922542 0.4031784 0.4330108
## [4,] 0.7903785 0.5148086 0.9152256 0.8058901 0.8266379 0.8330768 0.8494448
## [5,] 0.8757563 0.6648285 0.9527910 0.8858625 0.8991322 0.9031939 0.9134011
## [6,] 0.8636398 0.6405839 0.9477388 0.8745904 0.8890064 0.8934274 0.9045557
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0.34995705 0.7174433 0.8713665 0.8461318 0.37457209 0.9273524 0.8334131
## [2,] 0.04961961 0.1975888 0.3964802 0.3478123 0.05489364 0.5531644 0.3266808
## [3,] 0.05784320 0.2245417 0.4358278 0.3854144 0.06393251 0.5927885 0.3632709
## [4,] 0.31203875 0.6814488 0.8509052 0.8224743 0.33536269 0.9149271 0.8082432
## [5,] 0.45885073 0.7999645 0.9143037 0.8964916 0.48540566 0.9526180 0.8873816
## [6,] 0.43242652 0.7822940 0.9055409 0.8861343 0.45874859 0.9475482 0.8762385
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.7324835 0.9257657 0.7358372 0.34763169 0.8706359 0.8592458
## [2,] 0.2098237 0.5473939 0.2126869 0.04913904 0.3949253 0.3718686
## [3,] 0.2379506 0.5871478 0.2410806 0.05728779 0.4342296 0.4104348
## [4,] 0.6975973 0.9130945 0.7012100 0.30984526 0.8500784 0.8372166
## [5,] 0.8117646 0.9515543 0.8143764 0.45630974 0.9137929 0.9057914
## [6,] 0.7948692 0.9463771 0.7976569 0.42991560 0.9049832 0.8962569
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8173634 0.5574030 0.9276107 0.8313044 0.8498419 0.8555695 0.8700759
## [2,] 0.3026601 0.1088425 0.5541136 0.3233655 0.3543696 0.3648721 0.3937401
## [3,] 0.3379099 0.1255843 0.5937153 0.3597827 0.3922542 0.4031784 0.4330108
## [4,] 0.7903785 0.5148086 0.9152256 0.8058901 0.8266379 0.8330768 0.8494448
## [5,] 0.8757563 0.6648285 0.9527910 0.8858625 0.8991322 0.9031939 0.9134011
## [6,] 0.8636398 0.6405839 0.9477388 0.8745904 0.8890064 0.8934274 0.9045557
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0.34995705 0.7174433 0.8713665 0.8461318 0.37457209 0.9273524 0.8334131
## [2,] 0.04961961 0.1975888 0.3964802 0.3478123 0.05489364 0.5531644 0.3266808
## [3,] 0.05784320 0.2245417 0.4358278 0.3854144 0.06393251 0.5927885 0.3632709
## [4,] 0.31203875 0.6814488 0.8509052 0.8224743 0.33536269 0.9149271 0.8082432
## [5,] 0.45885073 0.7999645 0.9143037 0.8964916 0.48540566 0.9526180 0.8873816
## [6,] 0.43242652 0.7822940 0.9055409 0.8861343 0.45874859 0.9475482 0.8762385
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.7324835 0.9257657 0.7358372 0.34763169 0.8706359 0.8592458
## [2,] 0.2098237 0.5473939 0.2126869 0.04913904 0.3949253 0.3718686
## [3,] 0.2379506 0.5871478 0.2410806 0.05728779 0.4342296 0.4104348
## [4,] 0.6975973 0.9130945 0.7012100 0.30984526 0.8500784 0.8372166
## [5,] 0.8117646 0.9515543 0.8143764 0.45630974 0.9137929 0.9057914
## [6,] 0.7948692 0.9463771 0.7976569 0.42991560 0.9049832 0.8962569
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8173634 0.5574030 0.9276107 0.8313044 0.8498419 0.8555695 0.8700759
## [2,] 0.3026601 0.1088425 0.5541136 0.3233655 0.3543696 0.3648721 0.3937401
## [3,] 0.3379099 0.1255843 0.5937153 0.3597827 0.3922542 0.4031784 0.4330108
## [4,] 0.7903785 0.5148086 0.9152256 0.8058901 0.8266379 0.8330768 0.8494448
## [5,] 0.8757563 0.6648285 0.9527910 0.8858625 0.8991322 0.9031939 0.9134011
## [6,] 0.8636398 0.6405839 0.9477388 0.8745904 0.8890064 0.8934274 0.9045557
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0.34995705 0.7174433 0.8713665 0.8461318 0.37457209 0.9273524 0.8334131
## [2,] 0.04961961 0.1975888 0.3964802 0.3478123 0.05489364 0.5531644 0.3266808
## [3,] 0.05784320 0.2245417 0.4358278 0.3854144 0.06393251 0.5927885 0.3632709
## [4,] 0.31203875 0.6814488 0.8509052 0.8224743 0.33536269 0.9149271 0.8082432
## [5,] 0.45885073 0.7999645 0.9143037 0.8964916 0.48540566 0.9526180 0.8873816
## [6,] 0.43242652 0.7822940 0.9055409 0.8861343 0.45874859 0.9475482 0.8762385
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.7324835 0.9257657 0.7358372 0.34763169 0.8706359 0.8592458
## [2,] 0.2098237 0.5473939 0.2126869 0.04913904 0.3949253 0.3718686
## [3,] 0.2379506 0.5871478 0.2410806 0.05728779 0.4342296 0.4104348
## [4,] 0.6975973 0.9130945 0.7012100 0.30984526 0.8500784 0.8372166
## [5,] 0.8117646 0.9515543 0.8143764 0.45630974 0.9137929 0.9057914
## [6,] 0.7948692 0.9463771 0.7976569 0.42991560 0.9049832 0.8962569
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8173634 0.5574030 0.9276107 0.8313044 0.8498419 0.8555695 0.8700759
## [2,] 0.3026601 0.1088425 0.5541136 0.3233655 0.3543696 0.3648721 0.3937401
## [3,] 0.3379099 0.1255843 0.5937153 0.3597827 0.3922542 0.4031784 0.4330108
## [4,] 0.7903785 0.5148086 0.9152256 0.8058901 0.8266379 0.8330768 0.8494448
## [5,] 0.8757563 0.6648285 0.9527910 0.8858625 0.8991322 0.9031939 0.9134011
## [6,] 0.8636398 0.6405839 0.9477388 0.8745904 0.8890064 0.8934274 0.9045557
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0.34995705 0.7174433 0.8713665 0.8461318 0.37457209 0.9273524 0.8334131
## [2,] 0.04961961 0.1975888 0.3964802 0.3478123 0.05489364 0.5531644 0.3266808
## [3,] 0.05784320 0.2245417 0.4358278 0.3854144 0.06393251 0.5927885 0.3632709
## [4,] 0.31203875 0.6814488 0.8509052 0.8224743 0.33536269 0.9149271 0.8082432
## [5,] 0.45885073 0.7999645 0.9143037 0.8964916 0.48540566 0.9526180 0.8873816
## [6,] 0.43242652 0.7822940 0.9055409 0.8861343 0.45874859 0.9475482 0.8762385
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.7324835 0.9257657 0.7358372 0.34763169 0.8706359 0.8592458
## [2,] 0.2098237 0.5473939 0.2126869 0.04913904 0.3949253 0.3718686
## [3,] 0.2379506 0.5871478 0.2410806 0.05728779 0.4342296 0.4104348
## [4,] 0.6975973 0.9130945 0.7012100 0.30984526 0.8500784 0.8372166
## [5,] 0.8117646 0.9515543 0.8143764 0.45630974 0.9137929 0.9057914
## [6,] 0.7948692 0.9463771 0.7976569 0.42991560 0.9049832 0.8962569
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8173634 0.5574030 0.9276107 0.8313044 0.8498419 0.8555695 0.8700759
## [2,] 0.3026601 0.1088425 0.5541136 0.3233655 0.3543696 0.3648721 0.3937401
## [3,] 0.3379099 0.1255843 0.5937153 0.3597827 0.3922542 0.4031784 0.4330108
## [4,] 0.7903785 0.5148086 0.9152256 0.8058901 0.8266379 0.8330768 0.8494448
## [5,] 0.8757563 0.6648285 0.9527910 0.8858625 0.8991322 0.9031939 0.9134011
## [6,] 0.8636398 0.6405839 0.9477388 0.8745904 0.8890064 0.8934274 0.9045557
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0.34995705 0.7174433 0.8713665 0.8461318 0.37457209 0.9273524 0.8334131
## [2,] 0.04961961 0.1975888 0.3964802 0.3478123 0.05489364 0.5531644 0.3266808
## [3,] 0.05784320 0.2245417 0.4358278 0.3854144 0.06393251 0.5927885 0.3632709
## [4,] 0.31203875 0.6814488 0.8509052 0.8224743 0.33536269 0.9149271 0.8082432
## [5,] 0.45885073 0.7999645 0.9143037 0.8964916 0.48540566 0.9526180 0.8873816
## [6,] 0.43242652 0.7822940 0.9055409 0.8861343 0.45874859 0.9475482 0.8762385
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.7324835 0.9257657 0.7358372 0.34763169 0.8706359 0.8592458
## [2,] 0.2098237 0.5473939 0.2126869 0.04913904 0.3949253 0.3718686
## [3,] 0.2379506 0.5871478 0.2410806 0.05728779 0.4342296 0.4104348
## [4,] 0.6975973 0.9130945 0.7012100 0.30984526 0.8500784 0.8372166
## [5,] 0.8117646 0.9515543 0.8143764 0.45630974 0.9137929 0.9057914
## [6,] 0.7948692 0.9463771 0.7976569 0.42991560 0.9049832 0.8962569
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8173634 0.5574030 0.9276107 0.8313044 0.8498419 0.8555695 0.8700759
## [2,] 0.3026601 0.1088425 0.5541136 0.3233655 0.3543696 0.3648721 0.3937401
## [3,] 0.3379099 0.1255843 0.5937153 0.3597827 0.3922542 0.4031784 0.4330108
## [4,] 0.7903785 0.5148086 0.9152256 0.8058901 0.8266379 0.8330768 0.8494448
## [5,] 0.8757563 0.6648285 0.9527910 0.8858625 0.8991322 0.9031939 0.9134011
## [6,] 0.8636398 0.6405839 0.9477388 0.8745904 0.8890064 0.8934274 0.9045557
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0.34995705 0.7174433 0.8713665 0.8461318 0.37457209 0.9273524 0.8334131
## [2,] 0.04961961 0.1975888 0.3964802 0.3478123 0.05489364 0.5531644 0.3266808
## [3,] 0.05784320 0.2245417 0.4358278 0.3854144 0.06393251 0.5927885 0.3632709
## [4,] 0.31203875 0.6814488 0.8509052 0.8224743 0.33536269 0.9149271 0.8082432
## [5,] 0.45885073 0.7999645 0.9143037 0.8964916 0.48540566 0.9526180 0.8873816
## [6,] 0.43242652 0.7822940 0.9055409 0.8861343 0.45874859 0.9475482 0.8762385
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.7324835 0.9257657 0.7358372 0.34763169 0.8706359 0.8592458
## [2,] 0.2098237 0.5473939 0.2126869 0.04913904 0.3949253 0.3718686
## [3,] 0.2379506 0.5871478 0.2410806 0.05728779 0.4342296 0.4104348
## [4,] 0.6975973 0.9130945 0.7012100 0.30984526 0.8500784 0.8372166
## [5,] 0.8117646 0.9515543 0.8143764 0.45630974 0.9137929 0.9057914
## [6,] 0.7948692 0.9463771 0.7976569 0.42991560 0.9049832 0.8962569
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8173634 0.5574030 0.9276107 0.8313044 0.8498419 0.8555695 0.8700759
## [2,] 0.3026601 0.1088425 0.5541136 0.3233655 0.3543696 0.3648721 0.3937401
## [3,] 0.3379099 0.1255843 0.5937153 0.3597827 0.3922542 0.4031784 0.4330108
## [4,] 0.7903785 0.5148086 0.9152256 0.8058901 0.8266379 0.8330768 0.8494448
## [5,] 0.8757563 0.6648285 0.9527910 0.8858625 0.8991322 0.9031939 0.9134011
## [6,] 0.8636398 0.6405839 0.9477388 0.8745904 0.8890064 0.8934274 0.9045557
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0.34995705 0.7174433 0.8713665 0.8461318 0.37457209 0.9273524 0.8334131
## [2,] 0.04961961 0.1975888 0.3964802 0.3478123 0.05489364 0.5531644 0.3266808
## [3,] 0.05784320 0.2245417 0.4358278 0.3854144 0.06393251 0.5927885 0.3632709
## [4,] 0.31203875 0.6814488 0.8509052 0.8224743 0.33536269 0.9149271 0.8082432
## [5,] 0.45885073 0.7999645 0.9143037 0.8964916 0.48540566 0.9526180 0.8873816
## [6,] 0.43242652 0.7822940 0.9055409 0.8861343 0.45874859 0.9475482 0.8762385
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.7324835 0.9257657 0.7358372 0.34763169 0.8706359 0.8592458
## [2,] 0.2098237 0.5473939 0.2126869 0.04913904 0.3949253 0.3718686
## [3,] 0.2379506 0.5871478 0.2410806 0.05728779 0.4342296 0.4104348
## [4,] 0.6975973 0.9130945 0.7012100 0.30984526 0.8500784 0.8372166
## [5,] 0.8117646 0.9515543 0.8143764 0.45630974 0.9137929 0.9057914
## [6,] 0.7948692 0.9463771 0.7976569 0.42991560 0.9049832 0.8962569
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8173634 0.5574030 0.9276107 0.8313044 0.8498419 0.8555695 0.8700759
## [2,] 0.3026601 0.1088425 0.5541136 0.3233655 0.3543696 0.3648721 0.3937401
## [3,] 0.3379099 0.1255843 0.5937153 0.3597827 0.3922542 0.4031784 0.4330108
## [4,] 0.7903785 0.5148086 0.9152256 0.8058901 0.8266379 0.8330768 0.8494448
## [5,] 0.8757563 0.6648285 0.9527910 0.8858625 0.8991322 0.9031939 0.9134011
## [6,] 0.8636398 0.6405839 0.9477388 0.8745904 0.8890064 0.8934274 0.9045557
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0.34995705 0.7174433 0.8713665 0.8461318 0.37457209 0.9273524 0.8334131
## [2,] 0.04961961 0.1975888 0.3964802 0.3478123 0.05489364 0.5531644 0.3266808
## [3,] 0.05784320 0.2245417 0.4358278 0.3854144 0.06393251 0.5927885 0.3632709
## [4,] 0.31203875 0.6814488 0.8509052 0.8224743 0.33536269 0.9149271 0.8082432
## [5,] 0.45885073 0.7999645 0.9143037 0.8964916 0.48540566 0.9526180 0.8873816
## [6,] 0.43242652 0.7822940 0.9055409 0.8861343 0.45874859 0.9475482 0.8762385
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.7324835 0.9257657 0.7358372 0.34763169 0.8706359 0.8592458
## [2,] 0.2098237 0.5473939 0.2126869 0.04913904 0.3949253 0.3718686
## [3,] 0.2379506 0.5871478 0.2410806 0.05728779 0.4342296 0.4104348
## [4,] 0.6975973 0.9130945 0.7012100 0.30984526 0.8500784 0.8372166
## [5,] 0.8117646 0.9515543 0.8143764 0.45630974 0.9137929 0.9057914
## [6,] 0.7948692 0.9463771 0.7976569 0.42991560 0.9049832 0.8962569
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8173634 0.5574030 0.9276107 0.8313044 0.8498419 0.8555695 0.8700759
## [2,] 0.3026601 0.1088425 0.5541136 0.3233655 0.3543696 0.3648721 0.3937401
## [3,] 0.3379099 0.1255843 0.5937153 0.3597827 0.3922542 0.4031784 0.4330108
## [4,] 0.7903785 0.5148086 0.9152256 0.8058901 0.8266379 0.8330768 0.8494448
## [5,] 0.8757563 0.6648285 0.9527910 0.8858625 0.8991322 0.9031939 0.9134011
## [6,] 0.8636398 0.6405839 0.9477388 0.8745904 0.8890064 0.8934274 0.9045557
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0.34995705 0.7174433 0.8713665 0.8461318 0.37457209 0.9273524 0.8334131
## [2,] 0.04961961 0.1975888 0.3964802 0.3478123 0.05489364 0.5531644 0.3266808
## [3,] 0.05784320 0.2245417 0.4358278 0.3854144 0.06393251 0.5927885 0.3632709
## [4,] 0.31203875 0.6814488 0.8509052 0.8224743 0.33536269 0.9149271 0.8082432
## [5,] 0.45885073 0.7999645 0.9143037 0.8964916 0.48540566 0.9526180 0.8873816
## [6,] 0.43242652 0.7822940 0.9055409 0.8861343 0.45874859 0.9475482 0.8762385
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.7324835 0.9257657 0.7358372 0.34763169 0.8706359 0.8592458
## [2,] 0.2098237 0.5473939 0.2126869 0.04913904 0.3949253 0.3718686
## [3,] 0.2379506 0.5871478 0.2410806 0.05728779 0.4342296 0.4104348
## [4,] 0.6975973 0.9130945 0.7012100 0.30984526 0.8500784 0.8372166
## [5,] 0.8117646 0.9515543 0.8143764 0.45630974 0.9137929 0.9057914
## [6,] 0.7948692 0.9463771 0.7976569 0.42991560 0.9049832 0.8962569for (r in 1:replikasyon) {
# Lojit değerleri (theta - b)
logit <- theta.mat - b.mat
# Rasch modeli olasılıkları
P <- 1 / (1 + exp(-logit))
# Her kişi için her maddeye random 0-1 kararı (Monte Carlo simülasyonu)
rand <- matrix(runif(kisi_sayisi * madde_sayisi), kisi_sayisi, madde_sayisi)
res <- ifelse(P > rand, 1, 0)
# Simülasyon çıktısını dosyaya yaz
write.table(res,
file = paste("Rasch/Rasch_rep", r, ".txt", sep = ""),
sep = ",",
row.names = FALSE,
col.names = FALSE,
na = " ",
quote = FALSE)
}
# burada da rastgele veri oluşturuyoruz bizim rastgele verimizdeki
#doğru cevaplama oranı elde ettiğimiz değerden büyükse 0 bizim değerimiz
#büyükse 1 yazıyoruz. oluşan dosyalar Rasch klasöründe library(irtoys) #yukarıdaki işlemin aynısını elde etmek mümkün.
pa <- cbind(runif(20,.8,2), runif(20,-2.4,2.4), rep(0,50))## Warning in cbind(runif(20, 0.8, 2), runif(20, -2.4, 2.4), rep(0, 50)): number
## of rows of result is not a multiple of vector length (arg 1)## [,1] [,2] [,3]
## [1,] 1.3771243 -0.30416437 0
## [2,] 1.6242496 0.02520480 0
## [3,] 1.3834711 -1.40908589 0
## [4,] 1.8034839 1.34743977 0
## [5,] 1.8669113 -0.70620562 0
## [6,] 1.6167948 -0.12161805 0
## [7,] 1.4220566 -0.21610085 0
## [8,] 1.7523547 -0.76939139 0
## [9,] 0.9338350 -0.87534890 0
## [10,] 0.9787673 1.27712915 0
## [11,] 1.0814431 2.02750930 0
## [12,] 0.8359014 2.03753939 0
## [13,] 1.2061091 -0.19165938 0
## [14,] 1.0612400 0.07935722 0
## [15,] 1.0659210 -1.75169221 0
## [16,] 1.4760645 1.36405050 0
## [17,] 1.1813284 1.10258995 0
## [18,] 0.9002891 2.05151438 0
## [19,] 1.5463380 -2.06814964 0
## [20,] 1.7999300 -1.60897737 0
## [21,] 1.3771243 -0.30416437 0
## [22,] 1.6242496 0.02520480 0
## [23,] 1.3834711 -1.40908589 0
## [24,] 1.8034839 1.34743977 0
## [25,] 1.8669113 -0.70620562 0
## [26,] 1.6167948 -0.12161805 0
## [27,] 1.4220566 -0.21610085 0
## [28,] 1.7523547 -0.76939139 0
## [29,] 0.9338350 -0.87534890 0
## [30,] 0.9787673 1.27712915 0
## [31,] 1.0814431 2.02750930 0
## [32,] 0.8359014 2.03753939 0
## [33,] 1.2061091 -0.19165938 0
## [34,] 1.0612400 0.07935722 0
## [35,] 1.0659210 -1.75169221 0
## [36,] 1.4760645 1.36405050 0
## [37,] 1.1813284 1.10258995 0
## [38,] 0.9002891 2.05151438 0
## [39,] 1.5463380 -2.06814964 0
## [40,] 1.7999300 -1.60897737 0
## [41,] 1.3771243 -0.30416437 0
## [42,] 1.6242496 0.02520480 0
## [43,] 1.3834711 -1.40908589 0
## [44,] 1.8034839 1.34743977 0
## [45,] 1.8669113 -0.70620562 0
## [46,] 1.6167948 -0.12161805 0
## [47,] 1.4220566 -0.21610085 0
## [48,] 1.7523547 -0.76939139 0
## [49,] 0.9338350 -0.87534890 0
## [50,] 0.9787673 1.27712915 0## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
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## [76,] 1 1 1 1 1 1 1 1 1 0 0 1 1
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## [1000,] 0UYGULAMA
#1 ve 2 pl model için aynı yetenek düzeylerindeki öğrenciler de a parametresi öğrencilerin sırlamalarını değiştirmi bakmak istiyorum
library(irtoys)
# 1. Veri üretimi
set.seed(633)
n_madde <- 10
n_birey <- 1000
# Gerçek a, b parametreleri
a_gercek <- rlnorm(n_madde, 0, 0.2) # 2PL için #ort=0, std:0,2
b_gercek <- rnorm(n_madde, 0, 1) #ort=0, std:1
# 1PL modeline uygun: a = 1 sabit
a_1pl <- rep(1, n_madde)
# Yetenek düzeyleri
theta <- rnorm(n_birey, 0, 1) #ort=0 std=1
# Madde parametre matrisleri
par_1pl <- cbind(a_1pl, b_gercek, c = rep(0, n_madde))
par_2pl <- cbind(a_gercek, b_gercek, c = rep(0, n_madde))
# Yanıt simülasyonu (her iki model için aynı birey kullanılıyor)
cevaplar <- sim(par_2pl, theta) # Simülasyon hep gerçek a ile
# Cevap matrisini madde adlarıyla isimlendir
colnames(cevaplar) <- paste0("madde", 1:n_madde)
head(cevaplar)## madde1 madde2 madde3 madde4 madde5 madde6 madde7 madde8 madde9 madde10
## [1,] 1 1 1 1 0 1 1 1 1 1
## [2,] 1 1 0 1 0 0 0 1 1 1
## [3,] 1 1 1 1 1 1 1 0 1 1
## [4,] 1 0 0 0 0 1 1 1 1 1
## [5,] 1 1 0 1 0 1 0 0 1 0
## [6,] 1 1 1 1 0 1 0 1 1 1library(mirt)
# 1PL model tahmini (Rasch)
model_1pl <- mirt(cevaplar, 1, itemtype = "Rasch", verbose = FALSE)
# 2PL model tahmini
model_2pl <- mirt(cevaplar, 1, itemtype = "2PL", verbose = FALSE)
# Birey puan tahminleri
fs_1pl <- fscores(model_1pl, method = "EAP")
fs_2pl <- fscores(model_2pl, method = "EAP")
head(fs_1pl)## F1
## [1,] 1.2703440
## [2,] 0.0914867
## [3,] 1.2703440
## [4,] 0.0914867
## [5,] -0.2642850
## [6,] 0.8482151## F1
## [1,] 1.18302887
## [2,] 0.11455380
## [3,] 1.22788017
## [4,] 0.08551001
## [5,] -0.18663978
## [6,] 0.93625427## [1] 928.5 556.0 943.5 545.5 408.5 890.0## [1] 937.5 528.5 959.0 495.5 404.5 847.0## [1] 0.9831332#korelasyon çok yüksek her iki modelinde benzer sonuçlara ulaştığı söylenebilr.
# Sıralama farklarını görelim
siralama_farki <- rank_2pl - rank_1pl
# En çok değişen 10 birey
head(sort(abs(siralama_farki), decreasing = TRUE), 10)## [1] 158.5 151.0 147.5 143.0 143.0 143.0 143.0 143.0 141.5 140.5# Histogramla görelim
hist(siralama_farki, main = "2PL - 1PL Sıralama Farkları", xlab = "Sıra farkı", col = "lightblue")
Histogramın tepe noktası 0 civarında; bu da şu anlama gelir:
Çoğu bireyin sıralaması 1PL ve 2PL modellerinde benzer.
Ayırt edicilik parametresi (a) eklense bile genel sıralama çok değişmemiş
Histogram sağa ve sola doğru simetrik.
Bu, sıralama değişimlerinin yukarı ve aşağı yönlü olarak dengeli dağıldığını gösterir.
Yani bazı bireyler 2PL modelinde daha yukarıda sıralanmış, bazıları ise daha aşağıda.
En uç sıralama farkları ±150 civarında.
Bu bireylerin sıralamaları 2PL ile 1PL arasında önemli ölçüde değişmiş.
Fakat bu birey sayısı az (uçlardaki çubuklar kısa).
## [1] 55 177 214 296 332 381plot(rank_1pl, rank_2pl, main="1PL vs 2PL Sıralama Karşılaştırması",
xlab="1PL Sırası", ylab="2PL Sırası", pch=19, col="gray")
# Eşitlik çizgisi (y = x)
abline(a = 0, b = 1, col = "blue", lwd = 2, lty = 2)
# Sıralama farkı yüksek bireyler kırmızı ile
points(rank_1pl[fark_yuksek_bireyler], rank_2pl[fark_yuksek_bireyler],
col = "red", pch = 19)
legend("topleft", legend = c("Diğer bireyler", "Sıralama farkı yüksek", "Eşitlik çizgisi"),
col = c("gray", "red", "blue"), pch = c(19, 19, NA), lty = c(NA, NA, 2), lwd = c(NA, NA, 2))
# 1PL modeli (Rasch)
model_1pl <- mirt(cevaplar, 1, itemtype = "Rasch", verbose=FALSE)
theta_1pl_est <- fscores(model_1pl, method="EAP")
# 2PL modeli
model_2pl <- mirt(cevaplar, 1, itemtype = "2PL", verbose=FALSE)
theta_2pl_est <- fscores(model_2pl, method="EAP")
data.frame(
birey = fark_yuksek_bireyler,
theta_1pl = theta_1pl_est[fark_yuksek_bireyler],
theta_2pl = theta_2pl_est[fark_yuksek_bireyler],
fark = theta_2pl_est[fark_yuksek_bireyler] - theta_1pl_est[fark_yuksek_bireyler]
)## birey theta_1pl theta_2pl fark
## 1 55 0.8482151 0.99288881 0.14467373
## 2 177 0.4590732 0.56223757 0.10316441
## 3 214 0.0914867 0.26957646 0.17808976
## 4 296 0.4590732 0.65577993 0.19670676
## 5 332 0.8482151 0.99288881 0.14467373
## 6 381 0.8482151 0.87409671 0.02588164
## 7 384 0.4590732 0.65577993 0.19670676
## 8 395 -0.2642850 -0.09769890 0.16658608
## 9 460 0.8482151 0.87409671 0.02588164
## 10 488 -0.2642850 -0.10985838 0.15442660
## 11 603 0.0914867 0.28203481 0.19054811
## 12 623 -0.2642850 -0.08578348 0.17850150
## 13 656 0.8482151 0.87409671 0.02588164
## 14 680 0.8482151 0.82483356 -0.02338152
## 15 806 0.0914867 0.26957646 0.17808976
## 16 824 0.8482151 0.87409671 0.02588164
## 17 932 0.8482151 0.99288881 0.14467373
## 18 995 0.0914867 0.22493241 0.13344570# teta değerlerin en çok farklılaştığı bireyler
# Yüksek ayırıcılık eşiği (örnek: 1.1)
esik <- 1.1
yüksek_a_maddeler <- which(a_gercek > esik)
# Maddelerin isimleri
yüksek_a_madde_isimleri <- paste0("madde", yüksek_a_maddeler)
yüksek_a_madde_isimleri## [1] "madde1" "madde5" "madde6" "madde8"rank_1pl <- rank(theta_1pl_est)
rank_2pl <- rank(theta_2pl_est)
# Sıralama farkı yüksek bireylerin sıraları
birey_siralamalari <- data.frame(
birey = fark_yuksek_bireyler,
rank_1pl = rank_1pl[fark_yuksek_bireyler],
rank_2pl = rank_2pl[fark_yuksek_bireyler]
)
cevaplar_yuksek_a <- cevaplar[fark_yuksek_bireyler, yüksek_a_madde_isimleri]
# Cevaplar ve sıralamaları birleştir (satır bazında)
cevaplar_yuksek_a_df <- cbind(birey_siralamalari, cevaplar_yuksek_a)
cevaplar_yuksek_a_df## birey rank_1pl rank_2pl madde1 madde5 madde6 madde8
## 1 55 766.5 907.0 1 1 1 1
## 2 177 623.0 745.0 1 1 0 1
## 3 214 495.5 619.5 1 1 1 0
## 4 296 631.5 756.5 1 1 1 1
## 5 332 766.5 907.0 1 1 1 1
## 6 381 761.5 876.5 1 1 1 1
## 7 384 631.5 756.5 1 1 1 1
## 8 395 315.5 457.0 1 1 1 0
## 9 460 761.5 876.5 1 1 1 1
## 10 488 351.5 455.0 1 1 1 0
## 11 603 495.5 622.0 1 1 1 1
## 12 623 351.5 459.0 1 1 1 1
## 13 656 761.5 876.5 1 1 1 1
## 14 680 766.5 869.0 0 1 1 1
## 15 806 495.5 619.5 1 1 1 0
## 16 824 761.5 876.5 1 1 1 1
## 17 932 766.5 907.0 1 1 1 1
## 18 995 465.5 613.0 0 1 1 1# sıralama farkının en fazla olduğu bireyler incelendiğinde a değeri yüksek olan maddelere genellikle doğru cevap verdikleri görülmüş bence bu farklılık bu bireylerin bu maddeleri dopru cevaplamalarından kaynaklı. zaten 2pl teta değerleri sıralama farkı olan bireylerde daha yüksek