veri_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)
# Cikti
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 0.0006967016kestirim = kestirim
gercek = veri_1$maddepa
hata <- function(kestirim, gercek) {
result <- data.frame(parametreler = c("a", "b", "c"),
bias = sapply(1L:3L, function(i) mean((kestirim[, i] - gercek[,i]))),
rmse = sapply(1L:3L, function(i) sqrt(mean((kestirim[, i] - gercek[,i])^2))),
korelasyon = sapply(1L:3L, function(i) cor(kestirim[, i], gercek[,i])))
return(result)
}## parametreler bias rmse korelasyon
## 1 a 0.79534558 1.8606784 0.8141316
## 2 b 0.08642950 0.3085654 0.9782335
## 3 c -0.01476499 0.1326092 0.4511526## Zorunlu paket yükleniyor: foreach## Zorunlu paket yükleniyor: iterators## Zorunlu paket yükleniyor: parallelcl <- makeCluster(2)
registerDoParallel(cl)
tekrar = 4
seed = sample.int(10000, 100)
maddesay = 10 # 10, 15, 20, or 25
bireysay = 1000 # 250, 500, 750, or 1000
simulasyon <- foreach(i=1:4,
.packages = c("mirt", "doParallel"),
.combine = rbind) %dopar% {
# Adım 1 madde parametrelerini ve veri setini üretme
adim1 <- veri_uretimi(maddesay =maddesay,
bireysay =bireysay, seed=seed[i])
# Adım 2 üretilen veri seti üzerinden ketsirim yapma
adim2 <- kestirilen_par(adim1$cevaplar)
# adim 3 raporlama
hata(adim2, adim1$maddepar)
}## parametreler bias rmse korelasyon
## 1 a 0.176202606 0.59144333 0.5959353
## 2 b 0.075402188 0.18504993 0.9592602
## 3 c 0.021128989 0.08024795 0.7522811
## 4 a 0.215034436 0.47319014 0.6894718
## 5 b -0.043119536 0.11252452 0.9926606
## 6 c -0.008863236 0.06222017 0.4317777
## 7 a 0.101699688 0.61720308 0.5958915
## 8 b -0.036914238 0.23091960 0.9842471
## 9 c -0.040769414 0.10582158 -0.1052242
## 10 a 0.523289357 1.46317361 0.3151747
## 11 b -0.007129032 0.28665003 0.9455948
## 12 c -0.012527911 0.12375238 0.2392146## Hata değerlerini hesaplayarak farklı üretilen veri setlerinin aslında genel olarak ne kadar iyi çalıştığını test ediyoruz.
## ── 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()
## ✖ 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()## parametreler bias rmse korelasyon maddesay bireysay
## 1 a 0.254 0.786 0.549 10 1000
## 2 b -0.003 0.204 0.970 10 1000
## 3 c -0.010 0.093 0.330 10 1000tekrar = 1;seed = sample.int(10000, 100)
maddesay = c(10, 20 ,40)
bireysay = c(250, 500, 1000)
# kumeler
cl <- makeCluster(6);registerDoParallel(cl)
# İc ice foreachler
sonuc <- foreach(i=1:tekrar,
.packages = c("mirt", "doParallel", "dplyr"),
.combine = rbind) %:%
foreach(j=maddesay,
.packages = c("mirt", "doParallel", "dplyr"),
.combine = rbind) %:%
foreach(k=bireysay,
.packages = c("mirt", "doParallel", "dplyr"),
.combine = rbind) %dopar% {
adim1 <- veri_uretimi(maddesay=j, bireysay=k, seed=seed[i])
adim2 <- kestirilen_par(adim1$cevaplar)
adim3 <- hata(adim2, adim1$maddepar)
adim3 %>%
group_by(parametreler) %>%
summarise(bias = round(mean(bias),3),
rmse = round(mean(rmse),3),
korelasyon = round(mean(korelasyon),3)) %>%
mutate(maddesay = j, bireysay = k,
) %>% as.data.frame()
}
stopCluster(cl)
sonuc## parametreler bias rmse korelasyon maddesay bireysay
## 1 a 2.954 5.532 0.701 10 250
## 2 b -0.002 0.304 0.946 10 250
## 3 c 0.034 0.129 0.145 10 250
## 4 a 1.175 2.621 0.347 10 500
## 5 b 0.104 0.218 0.975 10 500
## 6 c 0.051 0.127 -0.400 10 500
## 7 a 0.074 0.486 0.738 10 1000
## 8 b -0.020 0.137 0.987 10 1000
## 9 c -0.016 0.060 0.691 10 1000
## 10 a 0.466 1.333 0.461 20 250
## 11 b -0.069 0.205 0.957 20 250
## 12 c 0.021 0.093 0.356 20 250
## 13 a -0.029 0.293 0.826 20 500
## 14 b -0.003 0.166 0.970 20 500
## 15 c -0.018 0.062 0.768 20 500
## 16 a 0.113 0.359 0.714 20 1000
## 17 b -0.034 0.121 0.985 20 1000
## 18 c -0.007 0.056 0.637 20 1000
## 19 a 0.640 2.561 0.115 40 250
## 20 b -0.098 0.268 0.959 40 250
## 21 c -0.026 0.119 0.239 40 250
## 22 a 0.111 0.482 0.606 40 500
## 23 b 0.033 0.171 0.980 40 500
## 24 c 0.005 0.064 0.606 40 500
## 25 a 0.064 0.457 0.685 40 1000
## 26 b -0.041 0.135 0.988 40 1000
## 27 c -0.008 0.069 0.476 40 1000iterations = 4 ; seed = sample.int(10000, 100)
maddesay = 10 ;bireysay = 1000 #250, 500, 750, or 1000
library("doSNOW")## Zorunlu paket yükleniyor: snow##
## Attaching package: 'snow'## The following objects are masked from 'package:parallel':
##
## closeNode, clusterApply, clusterApplyLB, clusterCall, clusterEvalQ,
## clusterExport, clusterMap, clusterSplit, makeCluster, parApply,
## parCapply, parLapply, parRapply, parSapply, recvData, recvOneData,
## sendData, splitIndices, stopCluster## | | | 0%progress <- function(n) {setTxtProgressBar(pb, n)}
opts <- list(progress = progress)
sonuc1 <- foreach(i = 1:iterations,
.packages = c("mirt", "doSNOW", "dplyr"),
.options.snow = opts,
.combine = rbind) %dopar% {
adim1 <- veri_uretimi(maddesay, bireysay, seed = seed[i])
adim2 <- kestirilen_par(adim1$cevaplar)
adim3 <- hata(adim2, adim1$maddepar)
adim3 %>%
group_by(parametreler) %>%
summarise(bias = round(mean(bias), 3),
rmse = round(mean(rmse), 3),
korelasyon = round(mean(korelasyon), 3)) %>%
mutate(maddesay = maddesay, bireysay = bireysay) %>%
as.data.frame()
}## | |================== | 25% | |=================================== | 50% | |==================================================== | 75% | |======================================================================| 100%sonuc1.1 <- sonuc1 %>%
group_by(parametreler) %>%
summarise(bias = round(mean(bias),3),
rmse = round(mean(rmse),3),
korelasyon = round(mean(korelasyon),3)) %>%
mutate(maddesay = maddesay,
bireysay = bireysay) %>%
as.data.frame()## parametreler bias rmse korelasyon maddesay bireysay
## 1 a 0.188 0.650 0.544 10 1000
## 2 b -0.007 0.186 0.967 10 1000
## 3 c -0.009 0.090 0.383 10 1000iterations = 20 ; seed = sample.int(10000, 100)
maddesay = 10 ;bireysay = 1000 #250, 500, 750, or 1000
library("doSNOW")
cl1 <- makeCluster(2);registerDoSNOW(cl)
pb1 <- txtProgressBar(max = iterations, style = 3) ## | | | 0%progress1 <- function(n) {setTxtProgressBar(pb, n)}
opts1 <- list(progress = progress)
sonuc2 <- foreach(i = 1:iterations,
.packages = c("mirt", "doSNOW", "dplyr"),
.options.snow = opts,
.combine = rbind) %dopar% {
adim1.2 <- veri_uretimi(maddesay, bireysay, seed = seed[i])
adim2.2 <- kestirilen_par(adim1.2$cevaplar)
adim3.2 <- hata(adim2.2, adim1.2$maddepar)
adim3.2 %>%
group_by(parametreler) %>%
summarise(bias = round(mean(bias), 3),
rmse = round(mean(rmse), 3),
korelasyon = round(mean(korelasyon), 3)) %>%
mutate(maddesay = maddesay, bireysay = bireysay) %>%
as.data.frame()
}## | |================== | 25% | |=================================== | 50% | |==================================================== | 75% | |======================================================================| 100%sonuc2.20 <- sonuc2 %>%
group_by(parametreler) %>%
summarise(bias = round(mean(bias),3),
rmse = round(mean(rmse),3),
korelasyon = round(mean(korelasyon),3)) %>%
mutate(maddesay = maddesay,
bireysay = bireysay) %>%
as.data.frame()
sonuc2.20## parametreler bias rmse korelasyon maddesay bireysay
## 1 a 0.119 0.651 0.496 10 1000
## 2 b -0.082 0.456 0.879 10 1000
## 3 c -0.011 0.100 0.333 10 1000iterations = 50 ; seed = sample.int(10000, 100)
maddesay = 10 ;bireysay = 1000 #250, 500, 750, or 1000
library("doSNOW")
cl50 <- makeCluster(2);registerDoSNOW(cl)
pb50 <- txtProgressBar(max = iterations, style = 3) ## | | | 0%progress50 <- function(n) {setTxtProgressBar(pb, n)}
opts50 <- list(progress = progress)
sonuc50 <- foreach(i = 1:iterations,
.packages = c("mirt", "doSNOW", "dplyr"),
.options.snow = opts,
.combine = rbind) %dopar% {
adim1.3 <- veri_uretimi(maddesay, bireysay, seed = seed[i])
adim2.3 <- kestirilen_par(adim1.3$cevaplar)
adim3.3 <- hata(adim2.3, adim1.3$maddepar)
adim3.3 %>%
group_by(parametreler) %>%
summarise(bias = round(mean(bias), 3),
rmse = round(mean(rmse), 3),
korelasyon = round(mean(korelasyon), 3)) %>%
mutate(maddesay = maddesay, bireysay = bireysay) %>%
as.data.frame()
}## | |================== | 25% | |=================================== | 50% | |==================================================== | 75% | |======================================================================| 100%sonuc50.1 <- sonuc50 %>%
group_by(parametreler) %>%
summarise(bias = round(mean(bias),3),
rmse = round(mean(rmse),3),
korelasyon = round(mean(korelasyon),3)) %>%
mutate(maddesay = maddesay,
bireysay = bireysay) %>%
as.data.frame()
sonuc50.1## parametreler bias rmse korelasyon maddesay bireysay
## 1 a 0.142 0.669 0.579 10 1000
## 2 b 0.002 0.211 0.968 10 1000
## 3 c -0.007 0.088 0.364 10 1000iterations = 50 ; seed = sample.int(10000, 100)
maddesay = 10 ;bireysay = 1000 #250, 500, 750, or 1000
library("doSNOW")
cl100 <- makeCluster(2);registerDoSNOW(cl)
pb100 <- txtProgressBar(max = iterations, style = 3) ## | | | 0%progress100 <- function(n) {setTxtProgressBar(pb, n)}
opts100 <- list(progress = progress)
sonuc100 <- foreach(i = 1:iterations,
.packages = c("mirt", "doSNOW", "dplyr"),
.options.snow = opts,
.combine = rbind) %dopar% {
adim1.4 <- veri_uretimi(maddesay, bireysay, seed = seed[i])
adim2.4 <- kestirilen_par(adim1.4$cevaplar)
adim3.4 <- hata(adim2.4, adim1.4$maddepar)
adim3.4 %>%
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()
}## | |================== | 25% | |=================================== | 50% | |==================================================== | 75% | |======================================================================| 100%sonuc100.1 <- sonuc100 %>%
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()
sonuc100.1## parametreler bias rmse korelasyon maddesay bireysay
## 1 a 0.156 0.682 0.551 10 1000
## 2 b 0.010 0.263 0.965 10 1000
## 3 c -0.006 0.097 0.371 10 1000# Farklı denemelerde değerlerin çoğu düşerken (korelasyonda yükselirke) bazı değerlerin istenilen seviyede olmadığını farkettim. Belki daha fazla iterasyon sayıları ile bütün değerlerin istenilen şekilde sonuçlanması sağlanabilir. Ama 50 tekrarda bütün parametrelerde neredeyse 1 2 tane hariç istenilen şekilde 0 yaklaştı ama korelasyon da düşmeler oldu.
b <- rnorm(20, 0, 1)
theta <- rnorm(1000, 0, 1)
madde_sayisi <- length(b)
kisi_sayisi <- length(theta)
replikasyon <- 10b.mat <- matrix(b, kisi_sayisi, madde_sayisi, byrow=T)
head(b.mat) # madde güçlükleri 1000 kişi için hesaplandı## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.9651624 -0.3228322 0.2527143 0.2047688 -0.2808158 0.3662255 0.3050855
## [2,] 0.9651624 -0.3228322 0.2527143 0.2047688 -0.2808158 0.3662255 0.3050855
## [3,] 0.9651624 -0.3228322 0.2527143 0.2047688 -0.2808158 0.3662255 0.3050855
## [4,] 0.9651624 -0.3228322 0.2527143 0.2047688 -0.2808158 0.3662255 0.3050855
## [5,] 0.9651624 -0.3228322 0.2527143 0.2047688 -0.2808158 0.3662255 0.3050855
## [6,] 0.9651624 -0.3228322 0.2527143 0.2047688 -0.2808158 0.3662255 0.3050855
## [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] -0.5631261 -0.003067096 0.7808752 1.13934 -1.375792 0.8461099 -1.400533
## [2,] -0.5631261 -0.003067096 0.7808752 1.13934 -1.375792 0.8461099 -1.400533
## [3,] -0.5631261 -0.003067096 0.7808752 1.13934 -1.375792 0.8461099 -1.400533
## [4,] -0.5631261 -0.003067096 0.7808752 1.13934 -1.375792 0.8461099 -1.400533
## [5,] -0.5631261 -0.003067096 0.7808752 1.13934 -1.375792 0.8461099 -1.400533
## [6,] -0.5631261 -0.003067096 0.7808752 1.13934 -1.375792 0.8461099 -1.400533
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0.5690497 0.3684318 0.04283965 -0.3729717 -1.048587 0.6879742
## [2,] 0.5690497 0.3684318 0.04283965 -0.3729717 -1.048587 0.6879742
## [3,] 0.5690497 0.3684318 0.04283965 -0.3729717 -1.048587 0.6879742
## [4,] 0.5690497 0.3684318 0.04283965 -0.3729717 -1.048587 0.6879742
## [5,] 0.5690497 0.3684318 0.04283965 -0.3729717 -1.048587 0.6879742
## [6,] 0.5690497 0.3684318 0.04283965 -0.3729717 -1.048587 0.6879742theta.mat <- matrix(theta, kisi_sayisi, madde_sayisi)
head(theta.mat) # birey yetenekleri 20 madde için yazıldı. Bireylerin yetenekleri sabit. ## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.8202497 0.8202497 0.8202497 0.8202497 0.8202497 0.8202497
## [2,] 0.3102407 0.3102407 0.3102407 0.3102407 0.3102407 0.3102407
## [3,] 0.1227299 0.1227299 0.1227299 0.1227299 0.1227299 0.1227299
## [4,] 0.3083173 0.3083173 0.3083173 0.3083173 0.3083173 0.3083173
## [5,] -0.5045297 -0.5045297 -0.5045297 -0.5045297 -0.5045297 -0.5045297
## [6,] -0.9474615 -0.9474615 -0.9474615 -0.9474615 -0.9474615 -0.9474615
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 0.8202497 0.8202497 0.8202497 0.8202497 0.8202497 0.8202497
## [2,] 0.3102407 0.3102407 0.3102407 0.3102407 0.3102407 0.3102407
## [3,] 0.1227299 0.1227299 0.1227299 0.1227299 0.1227299 0.1227299
## [4,] 0.3083173 0.3083173 0.3083173 0.3083173 0.3083173 0.3083173
## [5,] -0.5045297 -0.5045297 -0.5045297 -0.5045297 -0.5045297 -0.5045297
## [6,] -0.9474615 -0.9474615 -0.9474615 -0.9474615 -0.9474615 -0.9474615
## [,13] [,14] [,15] [,16] [,17] [,18]
## [1,] 0.8202497 0.8202497 0.8202497 0.8202497 0.8202497 0.8202497
## [2,] 0.3102407 0.3102407 0.3102407 0.3102407 0.3102407 0.3102407
## [3,] 0.1227299 0.1227299 0.1227299 0.1227299 0.1227299 0.1227299
## [4,] 0.3083173 0.3083173 0.3083173 0.3083173 0.3083173 0.3083173
## [5,] -0.5045297 -0.5045297 -0.5045297 -0.5045297 -0.5045297 -0.5045297
## [6,] -0.9474615 -0.9474615 -0.9474615 -0.9474615 -0.9474615 -0.9474615
## [,19] [,20]
## [1,] 0.8202497 0.8202497
## [2,] 0.3102407 0.3102407
## [3,] 0.1227299 0.1227299
## [4,] 0.3083173 0.3083173
## [5,] -0.5045297 -0.5045297
## [6,] -0.9474615 -0.9474615for (r in 1:replikasyon){
logit <- (theta.mat-b.mat)
P <- 1/(1+exp(-logit))
head(P) # bireylerin doğru cevaplama olasılıkları
rand <- matrix(runif(kisi_sayisi*madde_sayisi), kisi_sayisi, madde_sayisi)
res <- ifelse(P>rand, 1, 0)} #rastgele üretilen veri ile olasılıkları karşıl.
head(res)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
## [1,] 0 0 1 0 1 1 0 1 1 1 0 1 0 1
## [2,] 1 1 1 1 1 0 0 0 0 0 1 1 0 1
## [3,] 0 1 1 1 0 1 0 1 1 0 0 1 1 1
## [4,] 0 0 0 1 0 1 0 0 0 0 0 1 0 0
## [5,] 0 1 1 0 0 0 1 0 0 1 0 1 0 1
## [6,] 0 0 0 0 1 0 1 1 0 0 0 1 0 0
## [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0 0 1 1 1 0
## [2,] 1 0 0 1 1 0
## [3,] 1 0 1 1 1 0
## [4,] 1 0 1 0 0 0
## [5,] 0 0 0 0 1 0
## [6,] 1 1 0 0 1 0## Zorunlu paket yükleniyor: stats4## Zorunlu paket yükleniyor: latticecl <- makeCluster(2)
registerDoParallel(cl)
kisi_sayisi <- 1000
madde_sayisi <- 20
replikasyon <- 50
set.seed(123)
theta.vec <- rnorm(kisi_sayisi)
b.vec <- rnorm(madde_sayisi)
theta.mat <- matrix(theta.vec, nrow = kisi_sayisi, ncol = madde_sayisi)
b.mat <- matrix(b.vec, nrow = kisi_sayisi, ncol = madde_sayisi, byrow = TRUE)
# Rasch parametre tahmin fonksiyonu
rasch_kestirim <- function(cevaplar) {
if (is.null(colnames(cevaplar))) {
colnames(cevaplar) <- paste0("Item", 1:ncol(cevaplar))
}
mod <- mirt(cevaplar, 1, itemtype = "Rasch", verbose = FALSE)
b_kestirim <- coef(mod, IRTpars = TRUE, simplify = TRUE)$items[, "b"]
return(b_kestirim)
}
# Hata hesaplama fonksiyonu
hata_hesapla <- function(b_kest, b_gercek) {
bias <- mean(b_kest - b_gercek)
rmse <- sqrt(mean((b_kest - b_gercek)^2))
korelasyon <- cor(b_kest, b_gercek)
return(c(bias = bias, rmse = rmse, korelasyon = korelasyon))
}
# Paralel simülasyon ve analiz
hata_listesi <- foreach(r = 1:replikasyon, .combine = rbind, .packages = "mirt") %dopar% {
logit <- theta.mat - b.mat
P <- 1 / (1 + exp(-logit))
rand <- matrix(runif(kisi_sayisi * madde_sayisi), kisi_sayisi, madde_sayisi)
cevaplar <- ifelse(P > rand, 1, 0) # çıktıları inceledim 50 farklı veri setini gördüm sonra kodu sildim.
# Sütun isimlerini ekle
colnames(cevaplar) <- paste0("Item", 1:ncol(cevaplar))
b_kest <- rasch_kestirim(cevaplar)
hata_hesapla(b_kest, b.vec)
}
stopCluster(cl)
# Ortalama hata değerleri
ortalama_hata <- colMeans(hata_listesi)
print(ortalama_hata)## bias rmse korelasyon
## -0.01571813 0.08395774 0.99842301set.seed(21)
a <- round(rlnorm(20, meanlog=0.000, sdlog=0.200), 3)
b <- round(rnorm(20, mean=0.000, sd=1.000), 3)
k <- length(b)
set.seed(41)
birey <- rnorm(400, mean=0.500, sd=0.750)
n <- length(birey)theta <- rep(birey, k)
aa <- rep(a, each=n)
bb <- rep(b, each=n)
p <- 1/(1+exp(-((aa)*(theta-bb))))
head(round(p, 3))## [1] 0.361 0.574 0.732 0.779 0.715 0.636## [1] 0.339 0.154 0.363 0.315 0.627 0.177## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 1 0 0 0 1 1 1 1 1 1 0 1 0
## [2,] 1 0 1 1 1 1 0 1 1 1 1 1 1
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## [301,] 0 1 1 1 1 1 1 1 1 1 1 1 0
## [302,] 1 1 1 1 0 0 1 1 1 1 1 1 1
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## [307,] 1 1 1 1 1 0 0 1 1 1 1 1 1
## [308,] 1 1 1 1 1 0 1 1 1 1 0 0 1
## [309,] 0 1 1 1 0 0 1 1 1 1 1 1 1
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## [311,] 0 1 1 0 0 0 1 0 0 0 1 1 1
## [312,] 1 1 1 1 0 1 1 1 1 0 1 0 1
## [313,] 1 1 0 1 1 1 0 1 0 1 1 1 1
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## [316,] 0 0 1 1 1 0 1 1 1 1 1 1 1
## [317,] 0 1 1 0 1 0 0 1 1 1 1 1 0
## [318,] 1 1 1 1 0 0 1 1 1 1 1 0 1
## [319,] 0 1 1 1 0 0 0 1 1 1 1 1 0
## [320,] 1 0 1 1 0 0 1 1 0 1 1 0 1
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## [323,] 0 1 1 0 1 0 0 1 1 1 0 0 0
## [324,] 1 1 1 1 1 0 1 0 1 0 1 0 0
## [325,] 0 0 1 0 1 0 0 0 0 1 1 0 0
## [326,] 0 0 1 0 0 1 1 0 0 1 1 0 1
## [327,] 1 0 1 1 1 1 1 1 0 0 1 1 0
## [328,] 1 1 1 1 1 1 1 1 1 1 1 1 1
## [329,] 1 1 1 1 1 1 1 1 0 1 1 1 1
## [330,] 1 0 1 1 1 1 0 0 1 1 1 1 1
## [331,] 0 0 1 1 0 0 1 1 0 1 1 0 0
## [332,] 0 1 1 1 1 1 0 1 1 1 1 1 1
## [333,] 1 1 1 1 1 1 1 1 1 1 1 1 0
## [334,] 1 1 1 1 1 0 1 1 1 1 1 1 1
## [335,] 0 0 1 1 1 0 1 0 0 1 1 1 1
## [336,] 0 1 1 1 1 0 0 1 1 1 1 1 1
## [337,] 1 1 1 1 0 0 1 0 1 1 1 1 0
## [338,] 0 0 0 1 0 1 1 0 1 1 0 1 1
## [339,] 0 0 1 1 0 0 0 1 1 1 1 1 0
## [340,] 1 1 1 1 1 0 1 1 0 1 0 0 1
## [341,] 1 0 1 0 1 1 1 1 1 0 1 1 1
## [342,] 1 1 1 1 1 0 0 1 0 1 1 1 1
## [343,] 1 1 1 1 0 0 1 0 1 1 1 1 1
## [344,] 0 0 0 0 0 0 0 0 1 1 1 0 0
## [345,] 1 1 1 1 1 0 1 1 1 1 1 1 0
## [346,] 0 0 1 1 0 0 0 0 1 0 1 1 1
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## [348,] 0 0 1 1 0 0 0 1 1 1 0 1 1
## [349,] 0 0 1 1 1 0 0 0 1 0 1 1 0
## [350,] 0 1 1 1 1 0 0 1 1 1 1 1 0
## [351,] 1 0 1 1 1 1 0 1 1 0 1 1 0
## [352,] 1 1 1 0 0 0 1 0 1 1 1 1 1
## [353,] 1 1 1 1 1 1 0 1 1 1 1 1 1
## [354,] 1 1 1 1 1 0 1 1 1 0 0 1 0
## [355,] 1 0 1 1 1 0 1 0 1 1 1 1 1
## [356,] 0 1 1 0 0 0 1 1 1 1 1 1 1
## [357,] 0 1 1 1 0 0 1 0 1 1 1 1 1
## [358,] 0 1 1 1 1 0 0 1 1 1 1 1 0
## [359,] 0 1 1 1 0 0 0 0 1 0 1 0 0
## [360,] 1 1 1 1 1 1 1 1 1 1 1 0 1
## [361,] 1 1 1 1 1 0 0 1 1 1 1 0 1
## [362,] 1 1 1 0 1 1 0 1 1 1 1 1 1
## [363,] 0 1 0 1 1 0 1 1 0 1 1 0 0
## [364,] 1 1 1 0 1 1 1 1 1 1 1 1 0
## [365,] 0 1 1 1 1 1 1 0 1 1 1 1 1
## [366,] 1 1 1 1 1 1 1 1 1 1 1 1 1
## [367,] 0 0 1 1 1 1 0 1 0 1 1 1 1
## [368,] 1 1 1 1 0 0 0 0 1 0 1 1 0
## [369,] 1 1 1 0 0 1 1 1 1 1 1 1 0
## [370,] 0 0 1 1 0 0 1 1 0 1 0 1 1
## [371,] 0 0 1 1 0 0 0 1 1 1 1 0 0
## [372,] 0 1 1 1 1 0 1 1 1 1 1 1 1
## [373,] 0 1 1 1 1 0 1 1 1 1 1 1 1
## [374,] 0 1 0 1 1 0 1 1 0 0 1 0 0
## [375,] 0 1 1 1 0 0 1 0 1 0 1 1 1
## [376,] 1 1 0 1 0 0 1 0 1 0 1 1 0
## [377,] 0 0 1 0 0 1 1 1 1 1 0 0 0
## [378,] 1 1 1 1 1 1 1 1 1 0 1 1 1
## [379,] 0 1 1 1 1 1 1 1 1 1 1 1 1
## [380,] 0 1 1 1 1 0 0 1 1 1 1 1 1
## [381,] 1 1 1 1 1 1 1 1 1 1 1 1 1
## [382,] 0 1 1 1 1 1 0 1 0 0 0 1 1
## [383,] 1 1 1 1 1 1 1 1 1 1 1 1 1
## [384,] 1 1 1 1 1 1 1 1 0 1 1 1 1
## [385,] 0 1 1 1 1 1 1 1 1 1 1 1 1
## [386,] 0 1 0 0 1 0 0 1 1 1 0 0 0
## [387,] 1 1 1 0 1 1 1 1 1 1 1 1 1
## [388,] 0 1 1 1 1 1 0 1 1 1 1 1 0
## [389,] 1 0 1 1 1 0 1 0 1 1 1 1 1
## [390,] 1 0 1 0 1 1 0 1 1 0 1 0 0
## [391,] 1 0 1 1 1 0 1 1 1 1 0 1 1
## [392,] 0 1 1 1 1 1 0 1 0 1 1 1 0
## [393,] 1 0 1 1 1 1 1 0 0 1 1 1 0
## [394,] 0 0 1 1 1 1 1 1 0 1 1 0 1
## [395,] 1 0 0 1 0 0 0 1 0 1 0 0 0
## [396,] 1 0 1 1 1 1 1 1 1 1 1 1 0
## [397,] 0 1 1 0 0 1 0 1 1 1 1 1 1
## [398,] 0 0 1 1 1 1 0 1 1 1 0 1 0
## [399,] 0 0 1 1 1 0 0 1 1 1 0 1 1
## [400,] 1 1 1 1 1 0 0 1 1 0 1 1 0
## [,14] [,15] [,16] [,17] [,18] [,19] [,20]
## [1,] 0 0 1 1 0 1 0
## [2,] 1 0 0 1 1 0 0
## [3,] 0 0 1 0 1 0 1
## [4,] 0 0 1 0 1 1 1
## [5,] 1 1 0 0 0 1 0
## [6,] 0 0 0 1 1 0 0
## [7,] 0 1 1 0 1 0 1
## [8,] 0 0 1 0 0 0 0
## [9,] 1 0 1 1 1 0 0
## [10,] 1 1 1 0 1 0 0
## [11,] 0 1 0 0 0 0 0
## [12,] 0 0 0 0 1 0 0
## [13,] 0 0 1 0 1 1 0
## [14,] 1 1 0 1 1 0 0
## [15,] 0 0 0 0 1 0 0
## [16,] 1 1 1 1 1 1 1
## [17,] 0 0 1 1 1 0 0
## [18,] 0 0 1 0 1 1 0
## [19,] 0 1 1 0 1 1 0
## [20,] 1 1 1 1 1 0 1
## [21,] 0 0 0 0 0 0 0
## [22,] 1 0 1 0 0 1 1
## [23,] 0 0 1 0 0 0 0
## [24,] 1 1 1 0 0 0 0
## [25,] 0 0 1 1 1 0 1
## [26,] 1 0 1 0 1 0 0
## [27,] 0 0 1 0 0 0 0
## [28,] 0 0 0 0 0 0 0
## [29,] 1 0 1 0 1 0 0
## [30,] 0 0 0 0 0 0 0
## [31,] 0 0 1 0 0 1 1
## [32,] 0 1 0 0 0 0 1
## [33,] 0 0 1 1 1 1 1
## [34,] 1 0 1 0 1 0 0
## [35,] 0 0 0 0 0 0 0
## [36,] 0 0 1 0 1 1 0
## [37,] 1 1 0 1 0 0 0
## [38,] 0 0 0 1 1 0 1
## [39,] 1 0 1 1 0 0 1
## [40,] 0 0 0 0 1 0 1
## [41,] 1 1 1 0 0 0 0
## [42,] 0 1 1 0 1 0 0
## [43,] 0 0 0 0 1 0 0
## [44,] 0 1 1 1 1 1 1
## [45,] 1 1 1 1 1 0 0
## [46,] 0 0 1 0 1 1 0
## [47,] 0 0 0 0 1 0 0
## [48,] 0 0 1 0 0 0 0
## [49,] 0 1 1 0 0 0 0
## [50,] 0 1 1 0 1 0 1
## [51,] 0 0 1 0 1 1 1
## [52,] 1 0 1 0 1 0 0
## [53,] 1 0 1 1 0 1 1
## [54,] 1 1 1 0 0 0 0
## [55,] 1 0 1 0 1 1 0
## [56,] 0 1 0 0 0 0 0
## [57,] 0 0 0 0 0 0 0
## [58,] 1 0 1 0 1 0 1
## [59,] 1 0 1 0 1 0 1
## [60,] 1 0 1 0 1 0 0
## [61,] 1 0 0 0 1 0 1
## [62,] 1 0 1 1 1 0 0
## [63,] 1 1 0 1 1 1 0
## [64,] 1 0 0 0 1 0 1
## [65,] 0 0 0 1 0 0 1
## [66,] 1 0 1 0 1 1 1
## [67,] 1 1 1 0 0 0 1
## [68,] 0 1 1 0 1 1 0
## [69,] 1 1 1 1 1 1 1
## [70,] 0 0 0 0 0 0 1
## [71,] 0 0 0 0 1 0 0
## [72,] 0 0 1 0 0 1 0
## [73,] 0 0 1 0 1 0 0
## [74,] 1 0 1 0 1 1 1
## [75,] 0 0 1 0 0 0 1
## [76,] 1 0 1 1 1 1 1
## [77,] 0 0 1 0 0 0 0
## [78,] 0 0 1 0 0 1 0
## [79,] 0 0 0 0 0 0 0
## [80,] 0 0 0 0 1 0 0
## [81,] 1 1 1 0 1 0 1
## [82,] 1 0 0 0 1 0 1
## [83,] 1 0 1 0 0 1 0
## [84,] 0 0 0 0 1 0 0
## [85,] 1 0 1 0 1 0 0
## [86,] 0 1 1 0 1 0 1
## [87,] 1 0 1 0 1 0 0
## [88,] 0 0 0 0 1 0 0
## [89,] 1 0 0 0 1 0 0
## [90,] 0 0 0 0 1 0 1
## [91,] 1 1 0 0 1 0 1
## [92,] 0 1 0 0 0 0 1
## [93,] 0 0 1 0 1 1 1
## [94,] 1 0 1 1 1 1 0
## [95,] 0 0 1 1 1 0 1
## [96,] 0 1 1 0 0 0 1
## [97,] 0 0 1 1 1 0 0
## [98,] 1 0 0 0 0 1 0
## [99,] 0 1 1 1 1 1 0
## [100,] 1 0 0 0 1 1 1
## [101,] 1 0 1 0 1 0 0
## [102,] 1 0 1 0 1 1 0
## [103,] 0 0 0 0 1 0 0
## [104,] 1 1 1 0 0 0 1
## [105,] 0 0 1 0 1 0 0
## [106,] 1 0 1 0 1 1 0
## [107,] 0 0 0 0 1 0 0
## [108,] 0 0 1 1 0 0 0
## [109,] 1 1 1 0 1 0 0
## [110,] 0 1 1 0 1 0 0
## [111,] 0 0 0 0 0 0 0
## [112,] 0 1 0 0 0 0 0
## [113,] 1 0 1 1 0 1 0
## [114,] 1 0 1 0 0 0 0
## [115,] 1 0 1 1 1 1 0
## [116,] 0 0 1 0 1 1 0
## [117,] 0 1 1 0 0 0 0
## [118,] 0 1 1 0 0 0 0
## [119,] 0 1 1 1 1 0 0
## [120,] 1 0 1 1 1 0 1
## [121,] 1 1 0 0 0 0 0
## [122,] 1 0 0 0 0 0 0
## [123,] 1 0 1 1 1 1 1
## [124,] 0 0 0 1 0 0 0
## [125,] 1 1 0 0 0 0 1
## [126,] 0 0 1 1 1 0 1
## [127,] 0 1 1 1 1 0 0
## [128,] 0 0 1 1 1 0 0
## [129,] 0 1 1 0 1 0 0
## [130,] 0 0 1 0 0 1 0
## [131,] 1 0 0 0 0 0 0
## [132,] 1 0 1 0 1 1 0
## [133,] 0 0 0 1 1 1 0
## [134,] 0 0 0 1 1 1 0
## [135,] 0 0 1 0 1 1 0
## [136,] 0 0 0 0 0 0 0
## [137,] 1 0 1 0 1 0 1
## [138,] 1 0 1 0 1 1 0
## [139,] 1 0 0 0 0 0 0
## [140,] 0 0 0 0 1 0 1
## [141,] 1 1 1 0 0 0 0
## [142,] 1 0 1 1 1 1 0
## [143,] 0 0 1 0 1 0 1
## [144,] 0 0 1 1 0 0 0
## [145,] 1 0 0 0 1 0 0
## [146,] 0 0 1 1 1 0 0
## [147,] 0 0 0 0 0 0 0
## [148,] 0 0 1 0 1 1 1
## [149,] 0 0 1 0 0 1 0
## [150,] 0 0 1 0 1 0 0
## [151,] 1 0 1 0 1 1 1
## [152,] 1 1 0 0 0 0 1
## [153,] 0 0 1 0 1 1 0
## [154,] 0 0 1 0 1 1 0
## [155,] 0 1 1 0 0 0 0
## [156,] 0 1 0 0 0 0 0
## [157,] 0 0 0 0 1 1 0
## [158,] 0 1 1 0 0 1 1
## [159,] 0 0 0 0 0 0 0
## [160,] 1 1 1 0 0 1 1
## [161,] 1 1 1 0 1 0 0
## [162,] 0 0 1 1 1 1 1
## [163,] 0 0 1 0 0 0 1
## [164,] 1 0 1 1 0 0 0
## [165,] 1 0 0 1 1 1 0
## [166,] 1 0 0 0 1 0 0
## [167,] 0 0 1 0 1 0 1
## [168,] 0 0 0 0 1 1 0
## [169,] 0 0 1 0 0 0 0
## [170,] 1 0 0 1 1 0 1
## [171,] 0 0 1 0 0 0 0
## [172,] 0 0 0 0 0 0 1
## [173,] 0 1 1 1 0 0 1
## [174,] 0 1 0 1 0 0 0
## [175,] 0 0 0 0 0 0 0
## [176,] 1 0 0 0 0 0 0
## [177,] 1 0 0 0 0 0 0
## [178,] 1 0 1 0 1 0 0
## [179,] 1 0 1 0 0 0 0
## [180,] 0 0 0 0 1 1 0
## [181,] 0 1 0 0 0 0 0
## [182,] 0 0 1 0 0 0 0
## [183,] 0 0 1 0 1 0 0
## [184,] 0 0 1 0 1 0 0
## [185,] 0 1 1 0 1 1 0
## [186,] 0 0 1 0 0 0 0
## [187,] 0 0 1 0 0 1 1
## [188,] 1 1 1 0 1 1 0
## [189,] 0 0 1 0 0 0 0
## [190,] 0 1 0 0 1 0 1
## [191,] 1 1 1 1 1 1 1
## [192,] 0 0 0 0 0 1 0
## [193,] 0 0 0 0 1 1 1
## [194,] 0 1 0 0 1 0 0
## [195,] 1 0 1 0 1 0 1
## [196,] 0 1 1 0 1 1 0
## [197,] 0 0 1 0 0 0 1
## [198,] 1 0 1 1 1 1 1
## [199,] 0 0 0 0 0 0 0
## [200,] 0 0 0 0 0 0 0
## [201,] 0 0 0 0 0 0 0
## [202,] 0 0 1 0 0 0 0
## [203,] 1 1 1 0 1 0 1
## [204,] 0 0 1 0 0 1 0
## [205,] 0 0 1 0 0 0 0
## [206,] 0 1 1 0 1 0 0
## [207,] 0 0 1 0 1 1 0
## [208,] 1 0 1 1 1 0 0
## [209,] 0 1 1 0 1 0 0
## [210,] 0 0 1 0 1 1 0
## [211,] 0 0 0 1 0 0 0
## [212,] 1 0 1 0 1 1 1
## [213,] 0 0 0 0 0 0 0
## [214,] 1 0 0 0 1 0 0
## [215,] 0 1 0 0 0 1 1
## [216,] 0 1 1 0 1 0 0
## [217,] 0 0 0 0 0 0 0
## [218,] 1 1 1 0 1 1 0
## [219,] 1 0 0 1 0 0 0
## [220,] 1 0 1 1 1 0 0
## [221,] 0 0 1 1 1 1 1
## [222,] 1 0 0 0 1 0 0
## [223,] 0 1 1 0 1 0 0
## [224,] 0 0 1 0 0 0 0
## [225,] 1 1 1 0 1 0 0
## [226,] 0 0 0 0 1 1 0
## [227,] 1 0 0 0 1 0 0
## [228,] 0 1 0 0 0 1 0
## [229,] 0 0 0 0 1 0 0
## [230,] 0 0 1 0 0 1 1
## [231,] 0 1 1 1 1 0 0
## [232,] 0 0 1 1 1 0 0
## [233,] 0 1 1 0 0 0 0
## [234,] 0 0 1 0 0 0 1
## [235,] 1 0 1 0 1 0 0
## [236,] 0 0 1 0 1 0 0
## [237,] 0 1 1 1 0 0 0
## [238,] 0 1 1 0 0 1 0
## [239,] 0 0 0 1 0 0 0
## [240,] 0 0 0 1 0 0 0
## [241,] 1 0 1 1 1 0 0
## [242,] 0 0 1 0 1 0 0
## [243,] 0 0 1 1 1 0 0
## [244,] 1 1 1 0 1 0 1
## [245,] 1 1 1 0 1 1 1
## [246,] 1 1 1 0 1 1 1
## [247,] 0 1 1 0 1 0 0
## [248,] 0 0 1 0 1 1 0
## [249,] 0 0 1 0 1 0 1
## [250,] 0 0 0 0 0 0 0
## [251,] 0 0 0 0 1 0 0
## [252,] 0 0 1 0 1 0 0
## [253,] 0 0 1 0 0 0 0
## [254,] 0 0 0 0 0 0 0
## [255,] 1 0 1 0 1 1 0
## [256,] 1 0 1 1 1 0 1
## [257,] 1 1 0 0 0 1 0
## [258,] 0 0 1 0 1 0 0
## [259,] 1 1 1 0 1 1 1
## [260,] 1 0 1 0 0 0 0
## [261,] 0 0 0 0 0 0 0
## [262,] 1 0 0 0 0 0 0
## [263,] 0 1 1 0 1 0 0
## [264,] 0 1 1 0 0 1 0
## [265,] 1 1 0 0 1 0 0
## [266,] 0 0 0 0 1 0 0
## [267,] 0 0 1 0 1 1 1
## [268,] 0 0 0 0 1 0 0
## [269,] 0 0 0 0 0 0 0
## [270,] 1 0 0 0 1 0 0
## [271,] 1 0 1 0 1 0 0
## [272,] 0 0 1 0 0 0 0
## [273,] 0 1 1 0 1 1 0
## [274,] 0 1 1 1 1 0 0
## [275,] 1 1 1 0 1 1 1
## [276,] 0 1 0 1 1 0 0
## [277,] 1 0 1 0 0 1 0
## [278,] 0 0 1 0 1 0 0
## [279,] 0 0 0 0 1 0 0
## [280,] 0 1 1 0 1 1 0
## [281,] 1 0 0 0 1 1 1
## [282,] 0 0 1 0 1 1 0
## [283,] 1 0 1 0 0 0 0
## [284,] 0 0 0 0 1 0 1
## [285,] 1 1 1 0 1 0 1
## [286,] 0 1 1 0 0 0 0
## [287,] 1 1 1 0 1 1 1
## [288,] 1 0 1 1 1 0 0
## [289,] 0 0 0 0 0 0 0
## [290,] 0 1 1 0 0 1 0
## [291,] 0 0 0 0 1 1 1
## [292,] 0 1 1 0 1 0 0
## [293,] 1 1 1 1 0 1 0
## [294,] 0 0 1 0 0 0 1
## [295,] 1 1 1 1 1 1 1
## [296,] 0 0 1 0 0 0 0
## [297,] 1 1 0 0 1 0 0
## [298,] 1 1 1 0 1 0 1
## [299,] 0 1 1 1 1 1 0
## [300,] 0 0 0 1 0 0 0
## [301,] 0 0 1 0 1 1 1
## [302,] 1 0 1 1 1 0 0
## [303,] 0 0 0 0 0 0 0
## [304,] 0 1 0 0 0 0 0
## [305,] 0 0 0 0 1 0 1
## [306,] 0 0 0 0 0 0 0
## [307,] 0 1 1 0 1 1 0
## [308,] 0 0 0 0 0 0 0
## [309,] 0 0 1 0 1 0 0
## [310,] 0 0 0 0 0 1 1
## [311,] 0 0 0 0 0 0 1
## [312,] 0 0 0 0 1 0 1
## [313,] 0 0 0 0 1 0 0
## [314,] 0 0 1 0 1 1 1
## [315,] 1 0 1 0 1 1 0
## [316,] 1 0 1 1 1 0 1
## [317,] 1 0 0 0 1 1 0
## [318,] 1 0 1 0 1 1 0
## [319,] 0 1 1 0 1 0 1
## [320,] 0 0 1 0 1 0 0
## [321,] 0 1 0 0 1 0 0
## [322,] 0 0 1 0 0 0 1
## [323,] 0 0 0 0 0 0 0
## [324,] 0 0 0 0 0 0 1
## [325,] 0 1 1 0 1 0 0
## [326,] 0 0 0 0 0 0 0
## [327,] 1 0 1 0 0 1 0
## [328,] 0 0 1 0 0 0 1
## [329,] 0 1 1 0 1 0 1
## [330,] 0 0 1 0 1 1 0
## [331,] 0 0 1 0 0 0 0
## [332,] 1 1 1 1 0 0 1
## [333,] 0 0 1 0 1 0 0
## [334,] 0 0 0 1 1 0 0
## [335,] 1 1 1 0 1 0 1
## [336,] 1 0 0 0 1 0 0
## [337,] 0 0 0 0 0 0 0
## [338,] 1 0 1 0 1 1 1
## [339,] 0 0 1 1 1 0 0
## [340,] 0 0 1 0 0 0 0
## [341,] 0 0 1 0 1 0 0
## [342,] 0 1 1 0 1 1 0
## [343,] 0 0 1 0 1 0 1
## [344,] 1 0 1 0 0 0 0
## [345,] 1 0 1 0 1 0 0
## [346,] 1 0 1 0 1 0 0
## [347,] 0 0 0 0 1 0 0
## [348,] 1 0 1 0 0 0 0
## [349,] 0 0 1 0 0 1 0
## [350,] 0 0 1 0 0 1 0
## [351,] 1 0 0 0 1 0 0
## [352,] 0 0 1 0 0 1 0
## [353,] 1 0 1 0 0 0 1
## [354,] 1 1 0 0 1 1 1
## [355,] 1 0 0 0 1 0 1
## [356,] 0 0 1 1 1 0 0
## [357,] 0 0 1 0 0 1 0
## [358,] 0 0 1 0 1 0 0
## [359,] 0 1 1 0 1 0 1
## [360,] 0 0 1 0 0 0 1
## [361,] 1 1 1 1 1 1 1
## [362,] 0 0 0 0 1 0 0
## [363,] 0 0 0 0 0 1 1
## [364,] 1 1 1 0 1 1 1
## [365,] 0 0 1 1 1 1 1
## [366,] 1 1 0 1 1 1 0
## [367,] 1 1 1 1 0 0 0
## [368,] 0 1 1 0 1 0 1
## [369,] 1 0 1 1 1 0 0
## [370,] 0 0 0 0 0 1 0
## [371,] 0 0 1 0 0 0 0
## [372,] 1 0 1 0 1 0 0
## [373,] 0 0 1 0 0 0 0
## [374,] 1 0 0 0 0 0 0
## [375,] 0 0 0 0 1 1 0
## [376,] 0 0 1 0 1 1 0
## [377,] 0 0 1 0 0 0 0
## [378,] 0 1 1 0 1 0 1
## [379,] 0 0 1 0 1 0 1
## [380,] 0 1 1 0 1 0 0
## [381,] 1 1 1 1 1 1 1
## [382,] 0 0 0 0 0 0 0
## [383,] 0 1 1 1 1 1 0
## [384,] 1 0 1 0 1 1 0
## [385,] 1 1 1 0 1 1 1
## [386,] 0 0 0 0 0 0 0
## [387,] 1 1 1 0 1 0 1
## [388,] 1 1 1 0 1 0 0
## [389,] 0 1 1 0 1 0 1
## [390,] 1 0 0 0 0 0 0
## [391,] 0 0 0 0 1 0 0
## [392,] 1 0 0 1 1 0 0
## [393,] 1 1 1 1 0 0 1
## [394,] 1 1 1 0 0 0 0
## [395,] 0 0 0 0 0 0 0
## [396,] 1 0 1 0 0 1 0
## [397,] 1 0 1 0 1 0 0
## [398,] 0 0 0 0 1 0 0
## [399,] 0 1 0 0 1 1 1
## [400,] 1 1 1 0 1 0 1## [1] 0.653 1.258 0.907 1.180 0.921 1.030 1.026 1.201## b1 b2 b3 b4
## [1,] -2.50 -1.25 0.00 1.25
## [2,] -2.25 -1.00 0.25 1.50
## [3,] -2.00 -0.75 0.50 1.75
## [4,] -1.75 -0.50 0.75 2.00
## [5,] -1.50 -0.25 1.00 2.25
## [6,] -1.25 0.00 1.25 2.50
## [7,] -1.00 0.25 1.50 2.75
## [8,] -0.75 0.50 1.75 3.00## [1] 8## [1] 400aa <- rep(a, each=n)
bb1 <- rep(b1, each=n)
bb2 <- rep(b2, each=n)
bb3 <- rep(b3, each=n)
bb4 <- rep(b4, each=n)
p1 <- 1/(1+exp(-((aa)*(theta-bb1))))
p2 <- 1/(1+exp(-((aa)*(theta-bb2))))
p3 <- 1/(1+exp(-((aa)*(theta-bb3))))
p4 <- 1/(1+exp(-((aa)*(theta-bb4))))
par <- cbind(p1,p2,p3,p4)
head(par)## p1 p2 p3 p4
## [1,] 0.7399113 0.5570647 0.3573252 0.1973021
## [2,] 0.8545847 0.7220738 0.5345751 0.3367685
## [3,] 0.7607382 0.5843073 0.3832516 0.2155112
## [4,] 0.9197751 0.8352146 0.6914261 0.4976362
## [5,] 0.9165028 0.8291341 0.6820595 0.4867537
## [6,] 0.7731207 0.6010321 0.3997558 0.2274559## p1 p2 p3 p4
## [1,] 0.7399113 0.5570647 0.3573252 0.1973021
## [2,] 0.8545847 0.7220738 0.5345751 0.3367685
## [3,] 0.7607382 0.5843073 0.3832516 0.2155112
## [4,] 0.9197751 0.8352146 0.6914261 0.4976362
## [5,] 0.9165028 0.8291341 0.6820595 0.4867537
## [6,] 0.7731207 0.6010321 0.3997558 0.2274559## [1] 0.3757090 0.4476721 0.7699587 0.7494361 0.9873121 0.9012236## cevaplama olasılığının daha düşük olduğu kategori değerini alıyoruz.
puan <- 0
for (j in 1:(k*n)){
if((rr[j]>p1[j]))puan[j] <- 0
else if((rr[j]<p1[j]&rr[j]>p2[j]))puan[j] <- 1
else if((rr[j]<p2[j]&rr[j]>p3[j]))puan[j] <- 2
else if((rr[j]<p3[j]&rr[j]>p4[j]))puan[j] <- 3
else puan[j] <- 4
}
puan <- matrix(puan, ncol=k)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## [1,] 2 1 3 0 0 2 0 0
## [2,] 3 4 3 3 2 2 1 4## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 1 2 1 3 0 0 2 0 0
## [2,] 2 3 4 3 3 2 2 1 4
## [3,] 3 0 2 2 1 1 2 1 1
## [4,] 4 2 3 2 4 3 3 1 2
## [5,] 5 0 4 1 2 0 0 1 2
## [6,] 6 0 2 1 1 2 2 1 2
## [7,] 7 1 2 2 2 4 3 0 1
## [8,] 8 4 3 2 3 2 1 2 0
## [9,] 9 4 4 2 3 3 4 4 3
## [10,] 10 3 3 1 1 3 1 2 0
## [11,] 11 3 3 2 4 1 2 0 3
## [12,] 12 3 4 2 4 3 3 4 3
## [13,] 13 3 4 3 0 0 0 0 0
## [14,] 14 0 3 4 4 0 3 3 2
## [15,] 15 3 2 1 2 2 1 1 0
## [16,] 16 3 1 2 1 3 1 1 0
## [17,] 17 4 3 2 2 0 2 3 2
## [18,] 18 1 3 3 2 1 0 2 3
## [19,] 19 1 3 4 1 1 3 0 1
## [20,] 20 4 0 3 3 0 2 1 2
## [21,] 21 2 3 2 2 2 1 2 1
## [22,] 22 1 1 0 0 0 1 0 1
## [23,] 23 3 2 0 3 4 3 4 3
## [24,] 24 4 3 3 2 1 3 3 0
## [25,] 25 1 2 3 4 4 3 2 0
## [26,] 26 0 0 2 3 2 1 2 0
## [27,] 27 1 2 0 1 0 1 1 1
## [28,] 28 2 2 0 2 1 1 1 1
## [29,] 29 2 1 2 1 0 0 0 0
## [30,] 30 4 2 2 1 0 1 2 0
## [31,] 31 3 2 3 0 2 0 2 0
## [32,] 32 3 2 1 4 3 2 1 1
## [33,] 33 0 2 2 1 1 2 4 0
## [34,] 34 3 2 0 1 2 2 3 1
## [35,] 35 3 3 4 4 1 3 2 2
## [36,] 36 1 2 0 2 0 0 0 0
## [37,] 37 4 4 4 3 4 4 2 1
## [38,] 38 1 0 2 2 0 4 3 2
## [39,] 39 4 3 1 2 1 0 2 0
## [40,] 40 4 4 2 4 3 4 1 4
## [41,] 41 2 2 3 3 3 4 1 2
## [42,] 42 0 3 3 3 4 2 3 2
## [43,] 43 0 2 2 1 0 1 0 0
## [44,] 44 4 3 2 2 0 1 2 2
## [45,] 45 2 3 1 4 1 4 3 0
## [46,] 46 0 1 0 4 4 1 1 0
## [47,] 47 4 3 4 2 2 2 1 0
## [48,] 48 0 0 1 0 0 0 0 0
## [49,] 49 0 3 2 1 1 1 2 1
## [50,] 50 0 4 0 1 1 0 3 1
## [51,] 51 4 3 4 3 0 2 3 0
## [52,] 52 2 2 2 3 1 1 0 4
## [53,] 53 4 3 3 3 2 2 3 0
## [54,] 54 4 2 3 1 2 4 1 0
## [55,] 55 3 1 3 2 2 2 2 1
## [56,] 56 1 0 4 0 0 2 2 2
## [57,] 57 2 4 4 2 3 2 2 3
## [58,] 58 3 3 3 2 0 3 4 0
## [59,] 59 0 3 3 3 0 2 0 1
## [60,] 60 1 0 1 0 1 0 3 0
## [61,] 61 2 2 0 0 1 4 1 1
## [62,] 62 4 1 4 4 4 3 1 3
## [63,] 63 3 4 4 2 4 3 0 3
## [64,] 64 1 1 2 0 4 3 0 0
## [65,] 65 2 2 2 0 2 2 2 1
## [66,] 66 4 3 2 4 2 0 4 2
## [67,] 67 2 3 4 1 2 3 4 1
## [68,] 68 2 3 3 1 2 3 1 1
## [69,] 69 4 2 2 1 0 1 2 3
## [70,] 70 1 2 1 1 0 3 0 2
## [71,] 71 4 3 0 1 4 0 2 1
## [72,] 72 4 3 2 3 0 4 0 0
## [73,] 73 4 2 1 1 3 2 2 0
## [74,] 74 1 3 0 0 0 2 0 2
## [75,] 75 4 0 0 2 1 1 1 0
## [76,] 76 0 2 0 0 4 0 1 0
## [77,] 77 2 3 4 1 0 2 2 1
## [78,] 78 4 1 0 1 0 0 0 1
## [79,] 79 3 3 4 1 0 1 2 0
## [80,] 80 1 3 2 0 2 2 1 0
## [81,] 81 3 4 2 2 2 1 1 2
## [82,] 82 2 4 4 3 2 3 3 0
## [83,] 83 0 2 4 2 4 0 1 0
## [84,] 84 0 1 0 2 4 1 1 1
## [85,] 85 4 3 3 3 0 1 4 2
## [86,] 86 1 0 0 0 1 0 0 0
## [87,] 87 1 2 3 1 0 1 3 1
## [88,] 88 2 0 4 3 0 1 2 2
## [89,] 89 3 4 1 3 3 1 1 1
## [90,] 90 2 3 4 2 3 2 2 3
## [91,] 91 2 0 1 1 3 0 0 0
## [92,] 92 4 3 2 2 2 1 0 1
## [93,] 93 2 3 0 2 0 0 3 2
## [94,] 94 4 3 1 1 2 0 3 1
## [95,] 95 0 0 4 2 3 1 3 2
## [96,] 96 1 4 4 3 1 3 2 0
## [97,] 97 2 4 4 3 4 3 4 1
## [98,] 98 1 3 4 2 2 0 0 0
## [99,] 99 0 4 0 0 0 0 0 0
## [100,] 100 2 3 4 2 0 4 1 2
## [101,] 101 0 0 1 0 0 0 0 0
## [102,] 102 4 4 4 4 4 3 3 4
## [103,] 103 1 1 3 1 0 2 2 1
## [104,] 104 4 4 4 3 4 4 0 1
## [105,] 105 4 4 4 4 4 4 4 4
## [106,] 106 2 2 4 3 0 0 3 2
## [107,] 107 3 1 3 2 3 2 1 2
## [108,] 108 0 3 2 1 4 1 1 2
## [109,] 109 3 2 3 4 3 3 2 1
## [110,] 110 4 4 2 2 1 2 0 2
## [111,] 111 3 4 2 3 4 4 2 1
## [112,] 112 4 4 4 3 1 3 2 4
## [113,] 113 3 4 4 3 0 2 1 2
## [114,] 114 3 2 2 1 0 3 1 0
## [115,] 115 0 2 4 4 3 3 4 0
## [116,] 116 0 1 3 2 4 2 0 2
## [117,] 117 1 2 0 1 3 2 0 1
## [118,] 118 4 2 0 2 2 3 0 3
## [119,] 119 3 2 1 0 0 1 0 2
## [120,] 120 2 1 2 0 0 0 0 0
## [121,] 121 4 2 4 2 2 1 1 2
## [122,] 122 3 3 4 2 0 2 1 2
## [123,] 123 0 0 3 0 0 0 0 0
## [124,] 124 3 3 3 3 1 1 2 2
## [125,] 125 0 4 0 2 4 1 3 0
## [126,] 126 0 3 4 2 3 1 0 2
## [127,] 127 1 1 0 0 1 0 0 0
## [128,] 128 1 1 3 1 0 3 1 0
## [129,] 129 4 3 1 2 2 4 1 0
## [130,] 130 4 2 0 2 2 2 2 3
## [131,] 131 0 3 0 1 2 0 1 1
## [132,] 132 2 4 3 4 2 3 4 2
## [133,] 133 0 1 2 2 2 1 0 1
## [134,] 134 3 0 2 3 0 1 4 2
## [135,] 135 2 3 3 2 4 4 2 2
## [136,] 136 3 3 2 3 2 0 1 1
## [137,] 137 0 0 3 0 2 0 3 0
## [138,] 138 2 4 4 3 4 4 2 1
## [139,] 139 3 1 0 2 0 1 1 0
## [140,] 140 2 3 4 4 1 0 3 1
## [141,] 141 4 4 3 1 0 2 1 1
## [142,] 142 1 2 2 1 0 3 0 0
## [143,] 143 2 3 1 2 2 3 3 1
## [144,] 144 1 3 3 2 2 0 0 2
## [145,] 145 0 1 1 1 1 1 3 0
## [146,] 146 3 3 4 1 0 0 1 0
## [147,] 147 3 2 4 2 4 3 3 2
## [148,] 148 4 1 1 3 0 2 4 0
## [149,] 149 4 4 3 2 2 2 2 2
## [150,] 150 4 3 4 4 1 2 2 2
## [151,] 151 3 4 3 1 4 2 2 2
## [152,] 152 2 3 2 1 2 0 1 2
## [153,] 153 3 2 1 1 4 2 2 2
## [154,] 154 4 2 0 3 3 2 1 2
## [155,] 155 2 3 3 2 0 2 1 1
## [156,] 156 3 2 2 2 0 0 1 3
## [157,] 157 1 3 1 1 3 0 1 1
## [158,] 158 3 4 1 1 1 2 1 0
## [159,] 159 4 3 4 2 2 4 1 3
## [160,] 160 0 2 3 0 0 0 0 0
## [161,] 161 3 4 3 2 1 3 3 1
## [162,] 162 2 4 2 3 4 3 1 2
## [163,] 163 4 2 3 2 4 0 2 2
## [164,] 164 4 2 3 3 3 2 0 1
## [165,] 165 4 3 4 3 4 2 2 2
## [166,] 166 4 0 0 0 1 2 2 0
## [167,] 167 4 3 2 3 1 0 3 1
## [168,] 168 4 4 3 3 0 0 0 2
## [169,] 169 0 0 0 1 0 1 1 0
## [170,] 170 4 4 3 3 0 2 3 1
## [171,] 171 4 4 1 4 4 4 4 3
## [172,] 172 0 0 0 1 0 0 0 0
## [173,] 173 3 2 3 0 2 0 3 0
## [174,] 174 4 4 4 3 2 4 4 3
## [175,] 175 1 1 1 2 2 3 2 2
## [176,] 176 0 3 0 1 0 3 0 1
## [177,] 177 4 3 2 2 0 1 2 1
## [178,] 178 4 2 0 2 2 1 1 0
## [179,] 179 1 0 1 0 0 0 0 0
## [180,] 180 0 1 3 1 4 0 0 1
## [181,] 181 4 2 3 1 3 1 1 0
## [182,] 182 0 1 2 1 1 0 1 0
## [183,] 183 1 0 0 0 0 4 1 0
## [184,] 184 3 4 2 2 0 2 2 1
## [185,] 185 3 0 4 0 1 0 1 2
## [186,] 186 4 3 1 4 3 2 2 1
## [187,] 187 3 3 4 1 1 1 0 0
## [188,] 188 0 3 0 3 2 3 0 1
## [189,] 189 4 3 2 2 2 2 4 1
## [190,] 190 3 3 0 2 0 0 0 1
## [191,] 191 2 2 4 1 1 4 2 2
## [192,] 192 3 4 4 4 3 4 1 4
## [193,] 193 4 4 0 3 4 3 4 4
## [194,] 194 3 2 4 2 1 0 0 2
## [195,] 195 1 3 2 1 2 1 1 0
## [196,] 196 4 2 2 2 0 1 1 0
## [197,] 197 2 2 4 1 4 4 1 0
## [198,] 198 1 3 0 0 1 3 2 1
## [199,] 199 4 4 3 2 1 2 3 3
## [200,] 200 0 2 0 3 3 1 2 0
## [201,] 201 2 2 4 1 0 2 1 0
## [202,] 202 4 1 1 3 0 1 1 0
## [203,] 203 4 1 1 0 0 0 0 0
## [204,] 204 3 0 3 1 1 4 3 1
## [205,] 205 4 1 1 2 2 0 2 0
## [206,] 206 3 2 2 2 0 1 3 1
## [207,] 207 2 2 0 2 3 2 4 2
## [208,] 208 4 1 4 1 2 1 1 1
## [209,] 209 3 2 4 2 0 2 1 2
## [210,] 210 3 3 2 1 3 0 2 1
## [211,] 211 3 1 2 2 1 0 4 1
## [212,] 212 4 0 1 4 0 2 1 0
## [213,] 213 4 4 1 1 3 4 4 0
## [214,] 214 4 2 2 3 0 2 2 0
## [215,] 215 4 3 3 4 0 3 3 1
## [216,] 216 0 3 1 1 1 1 1 0
## [217,] 217 3 2 2 0 1 1 2 3
## [218,] 218 3 2 4 2 1 0 0 3
## [219,] 219 0 2 1 3 3 2 0 3
## [220,] 220 3 1 1 1 2 3 2 0
## [221,] 221 2 2 3 2 4 1 0 3
## [222,] 222 4 1 0 3 3 0 0 0
## [223,] 223 1 2 1 0 2 0 0 1
## [224,] 224 3 3 1 2 0 3 3 3
## [225,] 225 3 2 4 0 1 1 2 2
## [226,] 226 3 3 4 3 3 2 1 2
## [227,] 227 4 3 2 3 1 3 3 2
## [228,] 228 4 3 2 3 4 2 3 4
## [229,] 229 0 1 1 0 0 0 0 0
## [230,] 230 1 3 1 1 2 2 1 2
## [231,] 231 1 1 4 4 1 2 1 0
## [232,] 232 3 2 1 1 3 0 1 1
## [233,] 233 1 4 4 3 4 4 3 3
## [234,] 234 2 4 2 0 0 0 1 0
## [235,] 235 2 3 4 2 4 1 2 1
## [236,] 236 2 3 1 0 3 1 0 2
## [237,] 237 4 3 1 2 3 3 1 1
## [238,] 238 4 3 2 0 1 3 2 2
## [239,] 239 0 1 0 2 0 0 2 1
## [240,] 240 1 3 1 0 1 2 0 0
## [241,] 241 0 2 3 1 1 0 3 0
## [242,] 242 2 4 1 1 0 0 1 1
## [243,] 243 3 4 4 3 2 4 4 3
## [244,] 244 1 4 4 3 2 3 4 3
## [245,] 245 2 3 3 2 1 4 2 2
## [246,] 246 1 2 0 1 1 2 0 0
## [247,] 247 0 3 4 0 1 3 2 0
## [248,] 248 4 4 2 3 1 0 1 1
## [249,] 249 3 1 1 1 0 0 2 0
## [250,] 250 1 2 0 0 4 3 2 0
## [251,] 251 4 2 1 2 1 1 2 4
## [252,] 252 2 1 0 0 4 0 1 0
## [253,] 253 0 1 1 1 1 0 1 0
## [254,] 254 0 3 2 4 3 4 4 4
## [255,] 255 2 1 0 1 2 1 1 0
## [256,] 256 1 3 2 3 1 3 3 4
## [257,] 257 3 0 3 1 1 2 1 1
## [258,] 258 4 1 3 1 1 3 3 2
## [259,] 259 1 1 2 2 2 1 1 1
## [260,] 260 2 4 2 4 3 0 3 4
## [261,] 261 2 0 3 1 2 1 2 4
## [262,] 262 4 3 3 3 2 2 1 1
## [263,] 263 4 4 4 3 2 4 4 1
## [264,] 264 0 1 0 0 2 0 0 0
## [265,] 265 2 3 4 4 1 2 1 2
## [266,] 266 4 3 4 4 1 2 2 3
## [267,] 267 1 0 1 0 1 0 3 0
## [268,] 268 1 2 2 1 3 0 1 2
## [269,] 269 2 4 2 0 2 3 1 2
## [270,] 270 4 2 3 4 4 2 1 2
## [271,] 271 4 2 4 0 2 1 0 2
## [272,] 272 0 3 1 2 2 0 2 2
## [273,] 273 4 4 2 1 3 0 2 0
## [274,] 274 0 1 0 0 1 0 1 0
## [275,] 275 2 3 2 2 4 0 0 3
## [276,] 276 2 2 0 2 0 1 1 2
## [277,] 277 0 0 3 0 1 0 1 0
## [278,] 278 2 2 0 1 0 0 2 0
## [279,] 279 0 4 0 1 3 0 2 1
## [280,] 280 2 2 0 3 0 2 1 2
## [281,] 281 4 1 4 2 2 0 0 1
## [282,] 282 3 4 4 1 4 2 2 1
## [283,] 283 4 1 3 3 4 2 2 2
## [284,] 284 4 3 4 3 4 0 2 1
## [285,] 285 1 2 0 1 0 1 0 0
## [286,] 286 4 2 2 2 4 0 1 1
## [287,] 287 3 1 3 3 0 2 0 1
## [288,] 288 4 3 1 3 1 3 3 1
## [289,] 289 2 4 2 3 4 0 2 1
## [290,] 290 2 1 3 0 4 2 2 3
## [291,] 291 3 3 0 1 0 0 0 2
## [292,] 292 2 3 3 2 2 3 1 0
## [293,] 293 4 2 2 3 3 3 3 1
## [294,] 294 4 4 1 2 3 1 1 2
## [295,] 295 3 2 2 2 4 3 1 0
## [296,] 296 2 1 1 1 2 1 1 1
## [297,] 297 0 0 1 0 0 0 0 0
## [298,] 298 2 4 4 3 3 3 2 1
## [299,] 299 4 1 0 2 0 0 1 1
## [300,] 300 4 2 1 2 0 0 1 0
## [301,] 301 4 4 1 2 4 1 1 2
## [302,] 302 0 3 1 1 1 0 0 0
## [303,] 303 4 3 4 2 3 4 4 4
## [304,] 304 4 3 2 2 0 0 0 0
## [305,] 305 3 3 4 4 0 3 3 2
## [306,] 306 2 2 4 3 3 2 2 2
## [307,] 307 3 2 2 0 1 0 1 0
## [308,] 308 4 3 1 4 4 1 2 2
## [309,] 309 0 0 3 3 1 0 1 1
## [310,] 310 3 2 1 4 4 4 3 2
## [311,] 311 2 3 4 4 4 1 4 4
## [312,] 312 1 2 2 1 1 2 0 0
## [313,] 313 4 4 4 3 3 4 4 4
## [314,] 314 0 0 0 0 0 1 0 0
## [315,] 315 4 4 1 4 2 2 1 1
## [316,] 316 1 4 1 2 2 2 0 0
## [317,] 317 2 1 2 2 0 0 3 2
## [318,] 318 4 3 1 2 3 2 1 1
## [319,] 319 4 3 3 0 4 2 1 2
## [320,] 320 3 3 2 4 3 2 0 1
## [321,] 321 2 0 1 2 0 1 1 0
## [322,] 322 1 2 3 0 1 1 1 1
## [323,] 323 3 3 4 2 4 0 2 2
## [324,] 324 4 3 1 4 2 1 3 4
## [325,] 325 0 1 0 0 4 0 0 0
## [326,] 326 3 2 2 1 2 1 0 0
## [327,] 327 4 4 2 3 2 4 3 1
## [328,] 328 0 4 3 2 3 2 4 1
## [329,] 329 4 4 2 2 4 1 1 1
## [330,] 330 2 2 0 4 0 1 1 0
## [331,] 331 3 1 3 2 0 2 1 1
## [332,] 332 4 0 3 3 1 2 3 1
## [333,] 333 3 2 3 4 2 2 2 2
## [334,] 334 0 2 2 4 1 2 0 3
## [335,] 335 1 3 1 0 0 1 0 1
## [336,] 336 0 2 2 3 1 1 0 1
## [337,] 337 1 3 3 4 2 2 1 1
## [338,] 338 3 1 2 2 4 1 4 0
## [339,] 339 1 2 1 3 3 3 2 2
## [340,] 340 4 3 1 2 2 3 2 2
## [341,] 341 4 1 2 1 1 1 0 0
## [342,] 342 1 4 0 2 3 2 1 1
## [343,] 343 3 3 3 1 2 0 2 0
## [344,] 344 3 1 3 0 3 2 1 2
## [345,] 345 0 4 3 4 2 1 4 2
## [346,] 346 4 1 3 1 2 1 1 1
## [347,] 347 3 2 4 1 0 2 0 1
## [348,] 348 1 3 1 0 0 0 0 1
## [349,] 349 0 1 0 0 0 0 0 0
## [350,] 350 2 2 1 1 0 4 0 3
## [351,] 351 3 3 0 3 1 3 2 3
## [352,] 352 3 4 4 3 3 4 3 3
## [353,] 353 4 3 0 0 0 4 1 1
## [354,] 354 4 3 1 1 2 0 4 0
## [355,] 355 4 4 2 3 1 2 4 3
## [356,] 356 0 1 3 2 3 2 2 2
## [357,] 357 0 2 2 2 0 1 4 1
## [358,] 358 4 2 2 2 1 2 1 2
## [359,] 359 4 1 4 0 3 3 1 0
## [360,] 360 0 2 1 2 1 3 2 0
## [361,] 361 1 1 3 2 3 1 0 1
## [362,] 362 3 0 0 1 1 3 0 1
## [363,] 363 0 1 1 1 1 1 3 0
## [364,] 364 2 0 0 0 0 2 3 0
## [365,] 365 4 4 3 2 2 1 0 0
## [366,] 366 0 0 0 0 2 0 2 0
## [367,] 367 0 4 0 4 3 0 1 2
## [368,] 368 1 2 4 3 0 0 0 0
## [369,] 369 4 4 3 4 0 3 2 2
## [370,] 370 1 2 1 1 1 0 0 0
## [371,] 371 4 1 3 0 1 1 2 1
## [372,] 372 4 0 0 0 3 1 0 1
## [373,] 373 0 1 2 3 2 2 1 0
## [374,] 374 0 1 2 1 4 0 0 0
## [375,] 375 3 3 0 1 1 0 0 0
## [376,] 376 3 4 4 4 4 4 0 3
## [377,] 377 1 2 1 2 4 1 0 1
## [378,] 378 4 2 4 2 0 4 4 0
## [379,] 379 1 2 0 0 0 0 0 0
## [380,] 380 0 1 1 1 0 0 0 0
## [381,] 381 1 3 0 0 0 0 1 1
## [382,] 382 2 4 0 2 3 2 2 1
## [383,] 383 1 2 0 0 1 0 1 1
## [384,] 384 4 3 4 3 2 3 4 1
## [385,] 385 0 2 3 2 2 2 3 3
## [386,] 386 0 4 3 3 4 3 1 1
## [387,] 387 4 4 4 3 2 1 4 1
## [388,] 388 0 3 2 1 0 1 2 2
## [389,] 389 4 2 2 2 3 2 2 1
## [390,] 390 4 4 1 2 0 3 3 2
## [391,] 391 4 1 1 0 2 1 1 1
## [392,] 392 4 2 3 1 2 1 3 3
## [393,] 393 2 4 4 3 0 1 2 0
## [394,] 394 4 4 4 2 3 3 2 3
## [395,] 395 2 2 3 1 4 1 1 2
## [396,] 396 2 1 0 1 2 1 1 1
## [397,] 397 4 1 3 1 2 3 1 1
## [398,] 398 3 1 3 2 3 4 1 1
## [399,] 399 1 2 3 3 0 0 0 1
## [400,] 400 1 3 2 2 2 2 2 1## a b1 b2 b3 b4
## [1,] 0.653 -2.50 -1.25 0.00 1.25
## [2,] 1.258 -2.25 -1.00 0.25 1.50
## [3,] 0.907 -2.00 -0.75 0.50 1.75
## [4,] 1.180 -1.75 -0.50 0.75 2.00
## [5,] 0.921 -1.50 -0.25 1.00 2.25
## [6,] 1.030 -1.25 0.00 1.25 2.50
## [7,] 1.026 -1.00 0.25 1.50 2.75
## [8,] 1.201 -0.75 0.50 1.75 3.00