CAT
T.Tariyel
2023-08-24
setwd("~/Desktop/Bur-2022/Ana_dili")Giriş
Bizim məqsədimiz, 2022-ci il IX siniflərin Azərbaycan dili buraxılış imtahanlarının nəticələrindən istifadə edərək, tapşırıqların bazasını yaratmaq və bu bazadan istifadə edərək, variantlar üzrə iştirakçıların imtahandan sonra (Post-hoc analysis) CAT (kompüterlə adaptiv testləşmə) aparmaqdır. Qeyd edək ki, bu məqsədlə yalnız, imtahanlarda təklif edilən qapalı sualların nətəcələrindən istifadə edəcəyik. (Açıq suallar üzrə nəticələrin bərbadlığı onlardan da istifadə etməyə imkan vermir!). Biz keçən ilin hesabatında burada olan 24 variant imtahanın nəticələrini təhlil etmişik və bu variantlardan yararlı tapşırıqları seçmişik. Burada həmin seçilən tapşırıqlardan də istifadə olunur. 24 variantın hər birində 20 qapalı tipli sual olduğundan cəmi 480 qapalı sual olmalı idi. Lakin, seçimdən sonra bizim məqsədimiz üçün istifadəyə yararli 416 tapşırıq qalmışdır. Həmin tapşırıqların varıantlar üzrə adları aşağıda veriləcəkdir.
İşlək papkanın yüklənilməsi
setwd("~/Desktop/Bur-2022/Ana_dili")Bazada olan tapşırıqların adları.
Baza <- read.csv("Baza.csv")
head(Baza)## X a b g u
## 1 Tap_111.1 3.312 0.046 0.206 1
## 2 Tap_111.2 2.033 0.432 0.186 1
## 3 Tap_111.3 3.925 0.673 0.182 1
## 4 Tap_111.4 1.450 -0.066 0.106 1
## 5 Tap_111.5 1.533 1.192 0.165 1
## 6 Tap_111.6 4.298 0.184 0.161 1Tap_Ad <- Baza$X
Tap_Ad## [1] "Tap_111.1" "Tap_111.2" "Tap_111.3" "Tap_111.4" "Tap_111.5"
## [6] "Tap_111.6" "Tap_111.7" "Tap_111.8" "Tap_111.9" "Tap_111.10"
## [11] "Tap_111.11" "Tap_111.12" "Tap_111.13" "Tap_111.14" "Tap_111.15"
## [16] "Tap_111.16" "Tap_111.17" "Tap_111.18" "Tap_112.1" "Tap_112.2"
## [21] "Tap_112.3" "Tap_112.4" "Tap_112.5" "Tap_112.6" "Tap_112.7"
## [26] "Tap_112.8" "Tap_112.9" "Tap_112.10" "Tap_112.11" "Tap_112.12"
## [31] "Tap_112.13" "Tap_112.14" "Tap_112.15" "Tap_112.16" "Tap_113.1"
## [36] "Tap_113.2" "Tap_113.3" "Tap_113.4" "Tap_113.5" "Tap_113.6"
## [41] "Tap_113.7" "Tap_113.8" "Tap_113.9" "Tap_113.10" "Tap_113.11"
## [46] "Tap_113.12" "Tap_113.13" "Tap_113.14" "Tap_113.15" "Tap_113.16"
## [51] "Tap_113.17" "Tap_113.18" "Tap_113.19" "Tap_113.20" "Tap_114.1"
## [56] "Tap_114.2" "Tap_114.3" "Tap_114.4" "Tap_114.5" "Tap_114.6"
## [61] "Tap_114.7" "Tap_114.8" "Tap_114.9" "Tap_114.10" "Tap_114.11"
## [66] "Tap_114.12" "Tap_114.13" "Tap_114.14" "Tap_114.15" "Tap_114.16"
## [71] "Tap_114.17" "Tap_114.18" "Tap_114.19" "Tap_115.1" "Tap_115.2"
## [76] "Tap_115.3" "Tap_115.4" "Tap_115.5" "Tap_115.6" "Tap_115.7"
## [81] "Tap_115.8" "Tap_115.9" "Tap_115.10" "Tap_115.11" "Tap_115.12"
## [86] "Tap_115.13" "Tap_115.14" "Tap_115.15" "Tap_115.16" "Tap_115.17"
## [91] "Tap_115.18" "Tap_116.1" "Tap_116.2" "Tap_116.3" "Tap_116.4"
## [96] "Tap_116.5" "Tap_116.6" "Tap_116.7" "Tap_116.8" "Tap_116.9"
## [101] "Tap_116.10" "Tap_116.11" "Tap_116.12" "Tap_116.13" "Tap_116.14"
## [106] "Tap_116.15" "Tap_116.16" "Tap_116.17" "Tap_116.18" "Tap_117.1"
## [111] "Tap_117.2" "Tap_117.3" "Tap_117.4" "Tap_117.5" "Tap_117.6"
## [116] "Tap_117.7" "Tap_117.8" "Tap_117.9" "Tap_117.10" "Tap_117.11"
## [121] "Tap_117.12" "Tap_117.13" "Tap_117.14" "Tap_117.15" "Tap_117.16"
## [126] "Tap_117.17" "Tap_118.1" "Tap_118.2" "Tap_118.3" "Tap_118.4"
## [131] "Tap_118.5" "Tap_118.6" "Tap_118.7" "Tap_118.8" "Tap_118.9"
## [136] "Tap_118.10" "Tap_118.11" "Tap_118.12" "Tap_118.13" "Tap_118.14"
## [141] "Tap_118.15" "Tap_118.16" "Tap_118.17" "Tap_118.18" "Tap_211.1"
## [146] "Tap_211.2" "Tap_211.3" "Tap_211.4" "Tap_211.5" "Tap_211.6"
## [151] "Tap_211.7" "Tap_211.8" "Tap_211.9" "Tap_211.10" "Tap_211.11"
## [156] "Tap_211.12" "Tap_211.13" "Tap_211.14" "Tap_211.15" "Tap_211.16"
## [161] "Tap_211.17" "Tap_212.1" "Tap_212.2" "Tap_212.3" "Tap_212.4"
## [166] "Tap_212.5" "Tap_212.6" "Tap_212.7" "Tap_212.8" "Tap_212.9"
## [171] "Tap_212.10" "Tap_212.11" "Tap_212.12" "Tap_212.13" "Tap_212.14"
## [176] "Tap_212.15" "Tap_212.16" "Tap_212.17" "Tap_213.1" "Tap_213.2"
## [181] "Tap_213.3" "Tap_213.4" "Tap_213.5" "Tap_213.6" "Tap_213.7"
## [186] "Tap_213.8" "Tap_213.9" "Tap_213.10" "Tap_213.11" "Tap_213.12"
## [191] "Tap_213.13" "Tap_213.14" "Tap_213.15" "Tap_214.1" "Tap_214.2"
## [196] "Tap_214.3" "Tap_214.4" "Tap_214.5" "Tap_214.6" "Tap_214.7"
## [201] "Tap_214.8" "Tap_214.9" "Tap_214.10" "Tap_214.11" "Tap_214.12"
## [206] "Tap_214.13" "Tap_214.14" "Tap_214.15" "Tap_214.16" "Tap_215.1"
## [211] "Tap_215.2" "Tap_215.3" "Tap_215.4" "Tap_215.5" "Tap_215.6"
## [216] "Tap_215.7" "Tap_215.8" "Tap_215.9" "Tap_215.10" "Tap_215.11"
## [221] "Tap_215.12" "Tap_215.13" "Tap_215.14" "Tap_215.15" "Tap_215.16"
## [226] "Tap_216.1" "Tap_216.2" "Tap_216.3" "Tap_216.4" "Tap_216.5"
## [231] "Tap_216.6" "Tap_216.7" "Tap_216.8" "Tap_216.9" "Tap_216.10"
## [236] "Tap_216.11" "Tap_216.12" "Tap_216.13" "Tap_216.14" "Tap_216.15"
## [241] "Tap_217.1" "Tap_217.2" "Tap_217.3" "Tap_217.4" "Tap_217.5"
## [246] "Tap_217.6" "Tap_217.7" "Tap_217.8" "Tap_217.9" "Tap_217.10"
## [251] "Tap_217.11" "Tap_217.12" "Tap_217.13" "Tap_217.14" "Tap_217.15"
## [256] "Tap_217.16" "Tap_218.1" "Tap_218.2" "Tap_218.3" "Tap_218.4"
## [261] "Tap_218.5" "Tap_218.6" "Tap_218.7" "Tap_218.8" "Tap_218.9"
## [266] "Tap_218.10" "Tap_218.11" "Tap_218.12" "Tap_218.13" "Tap_218.14"
## [271] "Tap_218.15" "Tap_218.16" "Tap_311.1" "Tap_311.2" "Tap_311.3"
## [276] "Tap_311.4" "Tap_311.5" "Tap_311.6" "Tap_311.7" "Tap_311.8"
## [281] "Tap_311.9" "Tap_311.10" "Tap_311.11" "Tap_311.12" "Tap_311.13"
## [286] "Tap_311.14" "Tap_311.15" "Tap_311.16" "Tap_311.17" "Tap_311.18"
## [291] "Tap_311.1.1" "Tap_311.2.1" "Tap_311.3.1" "Tap_311.4.1" "Tap_311.5.1"
## [296] "Tap_311.6.1" "Tap_311.7.1" "Tap_311.8.1" "Tap_311.9.1" "Tap_311.10.1"
## [301] "Tap_311.11.1" "Tap_311.12.1" "Tap_311.13.1" "Tap_311.14.1" "Tap_311.15.1"
## [306] "Tap_311.16.1" "Tap_311.17.1" "Tap_311.18.1" "Tap_311.1.2" "Tap_311.2.2"
## [311] "Tap_311.3.2" "Tap_311.4.2" "Tap_311.5.2" "Tap_311.6.2" "Tap_311.7.2"
## [316] "Tap_311.8.2" "Tap_311.9.2" "Tap_311.10.2" "Tap_311.11.2" "Tap_311.12.2"
## [321] "Tap_311.13.2" "Tap_311.14.2" "Tap_311.15.2" "Tap_311.16.2" "Tap_311.17.2"
## [326] "Tap_311.18.2" "Tap_311.1.3" "Tap_311.2.3" "Tap_311.3.3" "Tap_311.4.3"
## [331] "Tap_311.5.3" "Tap_311.6.3" "Tap_311.7.3" "Tap_311.8.3" "Tap_311.9.3"
## [336] "Tap_311.10.3" "Tap_311.11.3" "Tap_311.12.3" "Tap_311.13.3" "Tap_311.14.3"
## [341] "Tap_311.15.3" "Tap_311.16.3" "Tap_311.17.3" "Tap_311.18.3" "Tap_311.1.4"
## [346] "Tap_311.2.4" "Tap_311.3.4" "Tap_311.4.4" "Tap_311.5.4" "Tap_311.6.4"
## [351] "Tap_311.7.4" "Tap_311.8.4" "Tap_311.9.4" "Tap_311.10.4" "Tap_311.11.4"
## [356] "Tap_311.12.4" "Tap_311.13.4" "Tap_311.14.4" "Tap_311.15.4" "Tap_311.16.4"
## [361] "Tap_311.17.4" "Tap_311.18.4" "Tap_311.1.5" "Tap_311.2.5" "Tap_311.3.5"
## [366] "Tap_311.4.5" "Tap_311.5.5" "Tap_311.6.5" "Tap_311.7.5" "Tap_311.8.5"
## [371] "Tap_311.9.5" "Tap_311.10.5" "Tap_311.11.5" "Tap_311.12.5" "Tap_311.13.5"
## [376] "Tap_311.14.5" "Tap_311.15.5" "Tap_311.16.5" "Tap_311.17.5" "Tap_311.18.5"
## [381] "Tap_311.1.6" "Tap_311.2.6" "Tap_311.3.6" "Tap_311.4.6" "Tap_311.5.6"
## [386] "Tap_311.6.6" "Tap_311.7.6" "Tap_311.8.6" "Tap_311.9.6" "Tap_311.10.6"
## [391] "Tap_311.11.6" "Tap_311.12.6" "Tap_311.13.6" "Tap_311.14.6" "Tap_311.15.6"
## [396] "Tap_311.16.6" "Tap_311.17.6" "Tap_311.18.6" "Tap_311.1.7" "Tap_311.2.7"
## [401] "Tap_311.3.7" "Tap_311.4.7" "Tap_311.5.7" "Tap_311.6.7" "Tap_311.7.7"
## [406] "Tap_311.8.7" "Tap_311.9.7" "Tap_311.10.7" "Tap_311.11.7" "Tap_311.12.7"
## [411] "Tap_311.13.7" "Tap_311.14.7" "Tap_311.15.7" "Tap_311.16.7" "Tap_311.17.7"
## [416] "Tap_311.18.7" "Tap_311.1.8" "Tap_311.2.8" "Tap_311.3.8" "Tap_311.4.8"
## [421] "Tap_311.5.8" "Tap_311.6.8" "Tap_311.7.8" "Tap_311.8.8" "Tap_311.9.8"
## [426] "Tap_311.10.8" "Tap_311.11.8" "Tap_311.12.8" "Tap_311.13.8" "Tap_311.14.8"
## [431] "Tap_311.15.8" "Tap_311.16.8" "Tap_311.17.8" "Tap_311.18.8"Burada məsələn, “Tap_112.3”- adlı tapşırıq 112-ci variantdan 3-cü tapşırıqdır və sairə.
lazım olacaq paketlər
library(tidyverse)
library(mirt)
library(mirtCAT)
library(readr)
library(irtoys)Birinci variantın (DF_111201_T.csv) yüklənilməsi və baza üçün yararlı qapalı tapşırıqların seçilməsi.
DF_111201_T <- read_csv("~/Desktop/Bur-2022/Ana_dili/DF_111201_T.csv")## Rows: 5209 Columns: 38
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (5): Bölgə, Məktəbin adı, Cins, Bölmə, Fənn
## dbl (33): №, İmtahan verilən xarici dil, Variant, C1, C2, C3, C4, C5, C6, C7...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.str(DF_111201_T)## spc_tbl_ [5,209 × 38] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ № : num [1:5209] 79 87 134 222 269 273 281 294 301 302 ...
## $ Bölgə : chr [1:5209] "Bakı şəhəri" "Gəncə şəhəri" "Bakı şəhəri" "Tərtər rayonu" ...
## $ Məktəbin adı : chr [1:5209] "142 saylı orta məktəb" "17 saylı şəhər orta məktəbi" "148 saylı orta məktəb" "Qazyan kənd orta məktəbi -N.Quliyev adına" ...
## $ Cins : chr [1:5209] "Q" "K" "K" "Q" ...
## $ Bölmə : chr [1:5209] "Az" "Az" "Az" "Az" ...
## $ Fənn : chr [1:5209] "Ana dili" "Ana dili" "Ana dili" "Ana dili" ...
## $ İmtahan verilən xarici dil: num [1:5209] 0 0 0 0 0 0 0 0 0 0 ...
## $ Variant : num [1:5209] 111201 111201 111201 111201 111201 ...
## $ C1 : num [1:5209] 1 1 1 0 0 0 1 1 1 1 ...
## $ C2 : num [1:5209] 1 0 1 0 0 1 0 1 1 0 ...
## $ C3 : num [1:5209] 1 0 1 0 1 0 0 1 0 1 ...
## $ C4 : num [1:5209] 1 0 1 0 1 1 1 1 0 0 ...
## $ C5 : num [1:5209] 0 0 0 0 0 0 0 1 0 0 ...
## $ C6 : num [1:5209] 1 0 1 0 0 0 0 1 1 1 ...
## $ C7 : num [1:5209] 1 0 1 0 1 0 0 1 0 1 ...
## $ C8 : num [1:5209] 1 0 0 0 0 0 0 1 0 0 ...
## $ C9 : num [1:5209] 1 0 1 1 0 0 0 1 0 1 ...
## $ C10 : num [1:5209] 1 0 1 1 0 0 0 1 0 1 ...
## $ C11 : num [1:5209] 1 0 0 0 1 0 0 1 0 1 ...
## $ C12 : num [1:5209] 1 0 1 0 1 0 0 1 0 1 ...
## $ C13 : num [1:5209] 1 0 1 0 1 0 0 1 0 1 ...
## $ C14 : num [1:5209] 1 0 1 0 0 0 0 1 0 1 ...
## $ C15 : num [1:5209] 1 0 1 1 1 1 1 1 0 1 ...
## $ C16 : num [1:5209] 1 0 0 0 1 0 1 0 0 1 ...
## $ C17 : num [1:5209] 1 0 1 0 0 0 0 1 0 0 ...
## $ C18 : num [1:5209] 1 0 1 0 0 0 1 1 1 1 ...
## $ C21 : num [1:5209] 0 0 0 0 1 0 0 1 0 1 ...
## $ C22 : num [1:5209] 0 0 1 1 0 0 0 1 0 1 ...
## $ C23 : num [1:5209] 0 1 0 1 0 1 1 0 0 1 ...
## $ C24 : num [1:5209] 1 1 0 1 0 0 0 1 0 1 ...
## $ C25 : num [1:5209] 1 0 1 0 0 0 0 1 1 0 ...
## $ C26 : num [1:5209] 1 0 1 1 1 0 0 1 0 1 ...
## $ C27 : num [1:5209] 0 1 1 0 0 0 1 1 0 1 ...
## $ C28 : num [1:5209] 0 0 0 1 0 0 0 1 0 1 ...
## $ C19 : num [1:5209] 3 NA 3 3 NA NA NA 3 3 3 ...
## $ C20 : num [1:5209] 2 NA 2 NA 2 NA 0 2 NA 2 ...
## $ C29 : num [1:5209] 0 NA 0 0 NA NA NA 2 0 2 ...
## $ C30 : num [1:5209] 2 NA 2 NA NA NA NA 2 NA 2 ...
## - attr(*, "spec")=
## .. cols(
## .. `№` = col_double(),
## .. Bölgə = col_character(),
## .. `Məktəbin adı` = col_character(),
## .. Cins = col_character(),
## .. Bölmə = col_character(),
## .. Fənn = col_character(),
## .. `İmtahan verilən xarici dil` = col_double(),
## .. Variant = col_double(),
## .. C1 = col_double(),
## .. C2 = col_double(),
## .. C3 = col_double(),
## .. C4 = col_double(),
## .. C5 = col_double(),
## .. C6 = col_double(),
## .. C7 = col_double(),
## .. C8 = col_double(),
## .. C9 = col_double(),
## .. C10 = col_double(),
## .. C11 = col_double(),
## .. C12 = col_double(),
## .. C13 = col_double(),
## .. C14 = col_double(),
## .. C15 = col_double(),
## .. C16 = col_double(),
## .. C17 = col_double(),
## .. C18 = col_double(),
## .. C21 = col_double(),
## .. C22 = col_double(),
## .. C23 = col_double(),
## .. C24 = col_double(),
## .. C25 = col_double(),
## .. C26 = col_double(),
## .. C27 = col_double(),
## .. C28 = col_double(),
## .. C19 = col_double(),
## .. C20 = col_double(),
## .. C29 = col_double(),
## .. C30 = col_double()
## .. )
## - attr(*, "problems")=<externalptr>nrow(DF_111201_T)## [1] 5209names(DF_111201_T)## [1] "№" "Bölgə"
## [3] "Məktəbin adı" "Cins"
## [5] "Bölmə" "Fənn"
## [7] "İmtahan verilən xarici dil" "Variant"
## [9] "C1" "C2"
## [11] "C3" "C4"
## [13] "C5" "C6"
## [15] "C7" "C8"
## [17] "C9" "C10"
## [19] "C11" "C12"
## [21] "C13" "C14"
## [23] "C15" "C16"
## [25] "C17" "C18"
## [27] "C21" "C22"
## [29] "C23" "C24"
## [31] "C25" "C26"
## [33] "C27" "C28"
## [35] "C19" "C20"
## [37] "C29" "C30"DF_111201_T <- as.data.frame(DF_111201_T)
DF_111201_T_D <- DF_111201_T[, c(9:23, 27:31)]
names(DF_111201_T_D)## [1] "C1" "C2" "C3" "C4" "C5" "C6" "C7" "C8" "C9" "C10" "C11" "C12"
## [13] "C13" "C14" "C15" "C21" "C22" "C23" "C24" "C25"## [1] "C12" "C13"
DF_111201_T_D_C <- DF_111201_T_D[, -c(12,13)]
names(DF_111201_T_D_C)## [1] "C1" "C2" "C3" "C4" "C5" "C6" "C7" "C8" "C9" "C10" "C11" "C14"
## [13] "C15" "C21" "C22" "C23" "C24" "C25"write_csv(DF_111201_T_D_C, file = "DF_111201_T_D_C.csv")Bu kod çəngəsində əvvəlcə C1-dən C15-ə qədər və C21-dən C25-ə qədər qapalı tapşırıqlar seçilib sonra isə onların içərisindən C12 və C13 nömrəli tapşırıqlar çıxarılıb. Qalan tapşırıqların adları işlək papkada yazılıb.
Sonra bu yolla qalan 23 variantın da yararlı tapşırıqları seçilir və işlək papkada yazılılr
Hər bir varıantda seçilmiş tapşırıqların 3 parametrli Birnbaum modeli ilə parametrlərinin hesablanması
DF_111 <- read_csv("DF_111201_T_D_C.csv")## Rows: 5209 Columns: 18
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (18): C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C14, C15, C21, C22, ...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.nitems = ncol(DF_111)
colnames(DF_111) <- paste0("Tap_111-", 1:nitems)
DF_111_fit3pl <- mirt(DF_111, model = 1, itemtype = "3PL", SE = TRUE,
verbose = FALSE)## Warning: data contains response patterns with only NAs## EM cycles terminated after 500 iterations.Coef_DF_111 <- coef(DF_111_fit3pl, IRTpars = TRUE, simplify = TRUE)$items
Coef_DF_111 <- round(Coef_DF_111, 3)
Coef_DF_111## a b g u
## Tap_111-1 3.312 0.046 0.206 1
## Tap_111-2 2.033 0.432 0.186 1
## Tap_111-3 3.925 0.673 0.182 1
## Tap_111-4 1.450 -0.066 0.106 1
## Tap_111-5 1.533 1.192 0.165 1
## Tap_111-6 4.298 0.184 0.161 1
## Tap_111-7 2.964 0.441 0.215 1
## Tap_111-8 3.031 1.343 0.091 1
## Tap_111-9 2.316 1.103 0.167 1
## Tap_111-10 1.930 0.463 0.118 1
## Tap_111-11 2.217 0.846 0.129 1
## Tap_111-12 1.470 -0.293 0.004 1
## Tap_111-13 1.408 -0.783 0.014 1
## Tap_111-14 1.846 2.128 0.106 1
## Tap_111-15 1.130 0.280 0.071 1
## Tap_111-16 1.389 1.295 0.222 1
## Tap_111-17 1.599 -0.380 0.007 1
## Tap_111-18 1.466 1.487 0.085 1fs_DF_111_3PL_mirt_SE <- fscores(DF_111_fit3pl, full.scores = TRUE,
full.scores.SE = TRUE)
fs_DF_111_3PL_mirt_SE <- as.data.frame(fs_DF_111_3PL_mirt_SE)
head(fs_DF_111_3PL_mirt_SE)## F1 SE_F1
## 1 1.3976214 0.3475159
## 2 -0.9095560 0.5350780
## 3 0.8858661 0.2986966
## 4 -0.4222942 0.3846932
## 5 -0.6936435 0.5205692
## 6 -0.7511050 0.4755225Baza <- read.csv("Baza.csv")
names(Baza) <- c("Tapsh_adi", "alpha", "delta", "chi")
head(Baza)## Tapsh_adi alpha delta chi NA
## 1 Tap_111.1 3.312 0.046 0.206 1
## 2 Tap_111.2 2.033 0.432 0.186 1
## 3 Tap_111.3 3.925 0.673 0.182 1
## 4 Tap_111.4 1.450 -0.066 0.106 1
## 5 Tap_111.5 1.533 1.192 0.165 1
## 6 Tap_111.6 4.298 0.184 0.161 1dim(Baza)## [1] 434 5Alt bazanın seçilməsi
## Alt tapşırıqların seçilməsi
set.seed(123)
items_1 <- sample(nrow(Baza), nrow(Baza)*0.25) # 70% for training
Baza_1 <- Baza[items_1, ]
head(Baza_1)## Tapsh_adi alpha delta chi NA
## 415 Tap_311.17.7 0.753 0.099 0.002 1
## 179 Tap_213.1 1.716 0.219 0.104 1
## 14 Tap_111.14 1.846 2.128 0.106 1
## 195 Tap_214.2 2.165 1.363 0.090 1
## 426 Tap_311.10.8 0.929 -0.121 0.003 1
## 306 Tap_311.16.1 1.610 0.278 0.160 1dim(Baza_1)## [1] 108 5Seçilən bazaya görə
set.seed(123)
true_theta_111 <- rnorm(nrow(DF_111201_T))
length(true_theta_111)## [1] 5209head(Baza_1)## Tapsh_adi alpha delta chi NA
## 415 Tap_311.17.7 0.753 0.099 0.002 1
## 179 Tap_213.1 1.716 0.219 0.104 1
## 14 Tap_111.14 1.846 2.128 0.106 1
## 195 Tap_214.2 2.165 1.363 0.090 1
## 426 Tap_311.10.8 0.929 -0.121 0.003 1
## 306 Tap_311.16.1 1.610 0.278 0.160 1Baza_1_S <- as.matrix(Baza_1[, c(2, 3, 4)])
head(Baza_1_S)## alpha delta chi
## 415 0.753 0.099 0.002
## 179 1.716 0.219 0.104
## 14 1.846 2.128 0.106
## 195 2.165 1.363 0.090
## 426 0.929 -0.121 0.003
## 306 1.610 0.278 0.160set.seed(123)
T1 <- irtoys::sim(ip = Baza_1_S, x = true_theta_111)
colnames(T1) <- rownames(Baza_1)
head(T1)## 415 179 14 195 426 306 118 299 229 244 432 374 153 90 91 256 197 420 348
## [1,] 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0
## [3,] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
## [4,] 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1
## [5,] 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1
## [6,] 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1
## 137 355 328 26 7 434 254 211 78 81 43 359 373 332 143 32 109 263 393 330
## [1,] 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0 1
## [2,] 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
## [3,] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4,] 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0
## [5,] 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1
## [6,] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 23 309 135 394 224 166 217 290 69 72 76 63 141 210 353 347 422 294 277 41
## [1,] 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 0
## [2,] 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0
## [3,] 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1
## [4,] 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0
## [5,] 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0
## [6,] 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1
## 421 316 223 16 116 94 262 235 86 342 39 159 240 209 429 34 4 13 387 243
## [1,] 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0
## [2,] 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1
## [3,] 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4,] 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0
## [5,] 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1
## [6,] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 308 278 89 25 291 286 364 121 110 158 64 199 67 151 335 85 165 136 51 74
## [1,] 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1
## [2,] 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0
## [3,] 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1
## [4,] 0 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0
## [5,] 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0
## [6,] 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1
## 178 236 98 396 214 127 212 174 273
## [1,] 0 1 0 0 0 0 0 0 0
## [2,] 1 1 0 1 0 0 0 1 0
## [3,] 1 1 1 1 1 1 1 1 1
## [4,] 0 1 1 0 1 0 0 0 0
## [5,] 1 1 0 0 0 0 1 1 0
## [6,] 1 1 1 1 1 1 1 1 1Baza_1_S <- as.data.frame(Baza_1_S)fitDF_111_3PL <- mirt(T1, model = 1, itemtype = "3PL", SE = TRUE, verbose = FALSE)## EM cycles terminated after 500 iterations.coef(fitDF_111_3PL, IRTpars = TRUE, simplify = TRUE)$items## a b g u
## 415 0.8801931 0.301744093 0.073888916 1
## 179 1.6719963 0.169973983 0.089181839 1
## 14 1.5127673 2.203442319 0.098805704 1
## 195 2.2088387 1.314956205 0.087043420 1
## 426 0.9742511 0.109650605 0.079553059 1
## 306 1.6004258 0.296523264 0.174787156 1
## 118 2.0073950 -1.428526011 0.010249044 1
## 299 6.2488706 0.725778573 0.224699743 1
## 229 3.1592694 0.634868956 0.152112435 1
## 244 3.1344899 0.063571515 0.106344309 1
## 432 1.4387951 0.188743138 0.112162722 1
## 374 1.9675306 0.360450236 0.091383449 1
## 153 2.4010738 0.690552389 0.157543916 1
## 90 1.5007277 -0.273238421 0.026788226 1
## 91 2.0593542 -0.216244271 0.130319251 1
## 256 1.4958749 -0.377114485 0.006580086 1
## 197 3.3670366 0.734002249 0.197955045 1
## 420 1.6100267 0.690401183 0.202309864 1
## 348 1.7747216 0.722673352 0.222389214 1
## 137 1.4517521 -0.434115951 0.002338064 1
## 355 1.9848221 -0.331696289 0.098354447 1
## 328 3.1480716 0.676135923 0.207894822 1
## 26 3.1992967 0.553284764 0.243703029 1
## 7 3.0648195 0.448141837 0.216286448 1
## 434 1.7643992 1.128562601 0.205664830 1
## 254 1.5447334 -0.424639779 0.005434368 1
## 211 2.8613576 -0.065798578 0.259066546 1
## 78 4.5393575 0.941859358 0.165857056 1
## 81 3.9914416 0.741192047 0.225138365 1
## 43 1.8748621 0.978997480 0.157063138 1
## 359 1.4891182 -0.057402602 0.001210649 1
## 373 1.8515852 -0.398587787 0.019392111 1
## 332 3.9378574 1.096134542 0.245758855 1
## 143 1.6962881 0.497032223 0.098648671 1
## 32 1.4532983 0.838117072 0.196106033 1
## 109 1.6920768 0.555481549 0.131809035 1
## 263 2.1309857 0.975722382 0.166795226 1
## 393 2.0367291 -0.123023064 0.007027221 1
## 330 2.0006107 0.743706450 0.241937735 1
## 23 3.3508304 0.037758474 0.145484577 1
## 309 2.2904470 1.005055155 0.222295985 1
## 135 3.7766884 0.918072732 0.163089763 1
## 394 1.1604367 1.053146433 0.082565003 1
## 224 0.5184060 0.121579876 0.067373236 1
## 166 1.1769646 0.235969015 0.009922128 1
## 217 2.3065678 0.267269179 0.229955558 1
## 290 1.5802225 1.168531736 0.196990438 1
## 69 1.3982676 2.069361006 0.064937630 1
## 72 1.0521843 0.302360429 0.002291166 1
## 76 2.5923998 1.183344350 0.113574725 1
## 63 3.3293443 1.093897714 0.222990260 1
## 141 1.6541460 -0.275761848 0.126444405 1
## 210 5.3382979 1.577918939 0.213596186 1
## 353 6.6869921 0.710047399 0.221127878 1
## 347 3.2477244 0.756116943 0.206828815 1
## 422 4.1946156 1.081165144 0.247958328 1
## 294 1.6260331 0.577135289 0.202414718 1
## 277 1.7295295 1.449790208 0.240503663 1
## 41 4.0022958 0.688798564 0.103841899 1
## 421 1.6691724 1.501545775 0.217619638 1
## 316 2.7432031 0.712572421 0.164670387 1
## 223 1.4294959 -0.343194494 0.003105680 1
## 16 1.4047185 1.292332774 0.231833930 1
## 116 3.4982672 0.923427147 0.172474875 1
## 94 2.2659129 0.372876001 0.182563493 1
## 262 2.9080575 0.607232516 0.125851603 1
## 235 1.5819318 0.146039675 0.159964504 1
## 86 2.0209078 -0.394842865 0.195370023 1
## 342 1.5768505 0.262444364 0.146938822 1
## 39 3.1880522 0.390719938 0.231375078 1
## 159 0.8086348 0.579279540 0.053391597 1
## 240 2.2928500 -0.539093811 0.007037543 1
## 209 1.6655989 1.268520774 0.099006571 1
## 429 2.0850278 -0.107809502 0.013258575 1
## 34 1.6216359 -0.517398544 0.054847048 1
## 4 1.3907058 0.001062523 0.113840519 1
## 13 1.4412897 -0.770772242 0.010551593 1
## 387 3.2027402 1.040153301 0.192583458 1
## 243 2.9848495 0.496022460 0.242856221 1
## 308 1.6103758 1.164373146 0.199641469 1
## 278 4.4070667 1.072555505 0.257167733 1
## 89 1.5548615 0.518221028 0.151048993 1
## 25 1.9276404 0.131793959 0.275351904 1
## 291 2.2161178 0.859529906 0.195226901 1
## 286 1.2447051 1.145608370 0.121937991 1
## 364 3.2542928 0.613872698 0.186232740 1
## 121 2.1357853 -1.552854181 0.010270570 1
## 110 2.0527192 0.591282204 0.110837199 1
## 158 1.2253602 1.328790779 0.240780563 1
## 64 3.0075618 1.435043371 0.099897719 1
## 199 2.4975608 -0.279031206 0.069980676 1
## 67 1.2388809 -0.860087877 0.015452226 1
## 151 1.4708517 0.214554174 0.180504581 1
## 335 6.7858136 0.728205496 0.214980519 1
## 85 1.4656996 -0.474830380 0.013644651 1
## 165 2.7202152 0.703394859 0.187411648 1
## 136 0.7519891 1.699651387 0.049419768 1
## 51 1.1108091 1.137663718 0.133379740 1
## 74 2.5433900 0.310516020 0.340119164 1
## 178 1.0796232 1.348935991 0.284891483 1
## 236 0.5424318 0.005648825 0.006544832 1
## 98 3.4613797 0.712549866 0.219538099 1
## 396 1.5788250 0.252440529 0.138222702 1
## 214 2.7333880 0.080602393 0.119449562 1
## 127 2.7290545 1.157104444 0.116799808 1
## 212 1.8032235 -0.159644624 0.098080367 1
## 174 0.8933907 0.934679294 0.176051874 1
## 273 2.6816761 0.960592372 0.231811263 1Birinci variant üzrə iştirakçıların balları
fs_DF_111_3PL_mirt_SE <- fscores(fitDF_111_3PL, full.scores = TRUE,
full.scores.SE = TRUE)
fs_DF_111_3PL_mirt_SE <- as.data.frame(fs_DF_111_3PL_mirt_SE)
head(fs_DF_111_3PL_mirt_SE)## F1 SE_F1
## 1 -0.419531193 0.1897251
## 2 -0.180054098 0.1720061
## 3 1.634583423 0.1586784
## 4 0.028805875 0.1643247
## 5 -0.006075106 0.1499870
## 6 1.690861336 0.1713347Birinci baza tapşırıqlar üzrə birinci iştirakçının CAT balı
posthocSim1_Baza_1 <- mirtCAT(mo = fitDF_111_3PL, local_pattern = T1[1, ],
start_item = "MI", method = "MAP",
criteria = "MI",design = list(min_SEM = .3))
print(posthocSim1_Baza_1)## n.items.answered Theta_1 SE.Theta_1
## 3 0.6142941 0.2798501summary(posthocSim1_Baza_1)## $final_estimates
## Theta_1
## Estimates 0.6142941
## SEs 0.2798501
##
## $raw_responses
## [1] "2" "2" "1"
##
## $scored_responses
## [1] 1 1 0
##
## $items_answered
## [1] 40 54 94
##
## $thetas_history
## Theta_1
## [1,] 0.0000000
## [2,] 0.4942439
## [3,] 0.9521151
## [4,] 0.6142941
##
## $thetas_SE_history
## Theta_1
## [1,] 1.0000000
## [2,] 0.6578938
## [3,] 0.4161058
## [4,] 0.2798501plot(posthocSim1_Baza_1)
Birinci baza tapşırıqlar üzrə ikinci iştirakçının CAT balı
posthocSim2_Baza_1 <- mirtCAT(mo = fitDF_111_3PL, local_pattern = T1[2, ],
start_item = "MI", method = "MAP",
criteria = "MI",design = list(min_SEM = .3))
print(posthocSim2_Baza_1)## n.items.answered Theta_1 SE.Theta_1
## 12 -0.3685604 0.2825292summary(posthocSim2_Baza_1)## $final_estimates
## Theta_1
## Estimates -0.3685604
## SEs 0.2825292
##
## $raw_responses
## [1] "1" "2" "2" "1" "2" "1" "1" "1" "1" "1" "2" "2"
##
## $scored_responses
## [1] 0 1 1 0 1 0 0 0 0 0 1 1
##
## $items_answered
## [1] 40 72 10 104 91 27 74 38 32 21 15 68
##
## $thetas_history
## Theta_1
## [1,] 0.00000000
## [2,] -0.48930991
## [3,] -0.22820949
## [4,] 0.04924730
## [5,] -0.11833420
## [6,] -0.01813923
## [7,] -0.15981922
## [8,] -0.25043493
## [9,] -0.33233672
## [10,] -0.42680681
## [11,] -0.51727338
## [12,] -0.42628946
## [13,] -0.36856045
##
## $thetas_SE_history
## Theta_1
## [1,] 1.0000000
## [2,] 0.6454302
## [3,] 0.4735853
## [4,] 0.4007529
## [5,] 0.3687392
## [6,] 0.3313128
## [7,] 0.3119904
## [8,] 0.3106651
## [9,] 0.3122720
## [10,] 0.3214387
## [11,] 0.3292684
## [12,] 0.3003625
## [13,] 0.2825292plot(posthocSim2_Baza_1)
Birinci baza tapşırıqlar üzrə üçüncü iştirakçının CAT balı
posthocSim3_Baza_1 <- mirtCAT(mo = fitDF_111_3PL, local_pattern = T1[3, ],
start_item = "MI", method = "MAP",
criteria = "MI",design = list(min_SEM = .3))
print(posthocSim3_Baza_1)## n.items.answered Theta_1 SE.Theta_1
## 6 1.244201 0.2950543summary(posthocSim3_Baza_1)## $final_estimates
## Theta_1
## Estimates 1.2442015
## SEs 0.2950543
##
## $raw_responses
## [1] "2" "2" "2" "2" "2" "1"
##
## $scored_responses
## [1] 1 1 1 1 1 0
##
## $items_answered
## [1] 40 54 94 28 81 53
##
## $thetas_history
## Theta_1
## [1,] 0.0000000
## [2,] 0.4942439
## [3,] 0.9521151
## [4,] 1.0562570
## [5,] 1.2163553
## [6,] 1.3541188
## [7,] 1.2442015
##
## $thetas_SE_history
## Theta_1
## [1,] 1.0000000
## [2,] 0.6578938
## [3,] 0.4161058
## [4,] 0.3768503
## [5,] 0.4033462
## [6,] 0.4057396
## [7,] 0.2950543plot(posthocSim3_Baza_1)
Birinci baza tapşırıqlar üzrə dördüncü iştirakçının CAT balı
posthocSim4_Baza_1 <- mirtCAT(mo = fitDF_111_3PL, local_pattern = T1[4, ],
start_item = "MI", method = "MAP",
criteria = "MI",design = list(min_SEM = .3))
print(posthocSim4_Baza_1)## n.items.answered Theta_1 SE.Theta_1
## 3 0.6142941 0.2798501summary(posthocSim4_Baza_1)## $final_estimates
## Theta_1
## Estimates 0.6142941
## SEs 0.2798501
##
## $raw_responses
## [1] "2" "2" "1"
##
## $scored_responses
## [1] 1 1 0
##
## $items_answered
## [1] 40 54 94
##
## $thetas_history
## Theta_1
## [1,] 0.0000000
## [2,] 0.4942439
## [3,] 0.9521151
## [4,] 0.6142941
##
## $thetas_SE_history
## Theta_1
## [1,] 1.0000000
## [2,] 0.6578938
## [3,] 0.4161058
## [4,] 0.2798501plot(posthocSim4_Baza_1)
Birinci baza tapşırıqlar üzrə beşinci iştirakçının CAT balı
posthocSim5_Baza_1 <- mirtCAT(mo = fitDF_111_3PL, local_pattern = T1[5, ],
start_item = "MI", method = "MAP",
criteria = "MI",design = list(min_SEM = .3))
print(posthocSim5_Baza_1)## n.items.answered Theta_1 SE.Theta_1
## 5 0.4163058 0.2782172summary(posthocSim5_Baza_1)## $final_estimates
## Theta_1
## Estimates 0.4163058
## SEs 0.2782172
##
## $raw_responses
## [1] "2" "1" "2" "1" "2"
##
## $scored_responses
## [1] 1 0 1 0 1
##
## $items_answered
## [1] 40 54 10 59 70
##
## $thetas_history
## Theta_1
## [1,] 0.0000000
## [2,] 0.4942439
## [3,] 0.3162633
## [4,] 0.4205751
## [5,] 0.3263464
## [6,] 0.4163058
##
## $thetas_SE_history
## Theta_1
## [1,] 1.0000000
## [2,] 0.6578938
## [3,] 0.4264859
## [4,] 0.3347345
## [5,] 0.3198082
## [6,] 0.2782172plot(posthocSim5_Baza_1)
İkinci dəst tapşırıqlar bazasının yaradılması (Baza_2) və bazanın əsasında süni T2 datasının törədilməsi. T2 datasında birinci variantda olan qədər iştirakçı vardır və onların cavabları süni törədilmişdir.
Baza_Qalan <- Baza[-items_1, ]
dim(Baza_Qalan)## [1] 326 5set.seed(123)
Baza_Qalan <- as.data.frame(Baza_Qalan)
Baza_2 <- Baza_Qalan[sample(nrow(Baza_Qalan), 104), ]
head(Baza_2)## Tapsh_adi alpha delta chi NA
## 246 Tap_217.6 2.830 -0.078 0.202 1
## 19 Tap_112.1 5.135 1.300 0.136 1
## 266 Tap_218.10 0.772 -0.212 0.001 1
## 406 Tap_311.8.7 2.743 0.702 0.166 1
## 163 Tap_212.2 3.398 0.592 0.141 1
## 399 Tap_311.1.7 2.491 0.938 0.223 1dim(Baza_2)## [1] 104 5set.seed(123)
true_theta_111 <- rnorm(nrow(DF_111201_T))
length(true_theta_111)## [1] 5209head(Baza_2)## Tapsh_adi alpha delta chi NA
## 246 Tap_217.6 2.830 -0.078 0.202 1
## 19 Tap_112.1 5.135 1.300 0.136 1
## 266 Tap_218.10 0.772 -0.212 0.001 1
## 406 Tap_311.8.7 2.743 0.702 0.166 1
## 163 Tap_212.2 3.398 0.592 0.141 1
## 399 Tap_311.1.7 2.491 0.938 0.223 1Baza_2_S <- as.matrix(Baza_2[, c(2, 3, 4)])
head(Baza_2_S)## alpha delta chi
## 246 2.830 -0.078 0.202
## 19 5.135 1.300 0.136
## 266 0.772 -0.212 0.001
## 406 2.743 0.702 0.166
## 163 3.398 0.592 0.141
## 399 2.491 0.938 0.223set.seed(123)
T2 <- irtoys::sim(ip = Baza_2_S, x = true_theta_111)
colnames(T2) <- rownames(Baza_2)
head(T2)## 246 19 266 406 163 399 311 327 431 206 125 126 344 268 416 187 36 9 411
## [1,] 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0
## [2,] 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0
## [3,] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1
## [4,] 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1
## [5,] 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0 0 1
## [6,] 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1
## 341 285 108 113 57 193 45 150 354 31 185 303 227 295 386 99 102 106 88 191
## [1,] 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1
## [2,] 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0
## [3,] 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
## [4,] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1
## [5,] 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1
## [6,] 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
## 284 418 371 55 417 302 21 161 130 352 318 120 53 218 323 283 47 5 18 389
## [1,] 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1
## [2,] 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1
## [3,] 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1
## [4,] 1 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0
## [5,] 1 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 0
## [6,] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1
## 326 124 35 368 168 152 216 92 270 96 204 331 169 111 119 226 186 68 104
## [1,] 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0
## [2,] 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1
## [3,] 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1
## [4,] 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1
## [5,] 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1
## [6,] 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 245 147 319 134 336 289 175 276 287 238 22 259 60 73 222 314 372 375 407
## [1,] 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0
## [2,] 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0
## [3,] 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1
## [4,] 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0
## [5,] 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 0
## [6,] 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1
## 33 156 292 148 397 300 281
## [1,] 1 1 0 0 0 0 0
## [2,] 1 0 1 1 0 1 0
## [3,] 1 1 1 1 1 1 1
## [4,] 1 0 0 1 1 0 0
## [5,] 1 0 1 0 0 0 0
## [6,] 1 0 1 1 1 1 1Baza_2_S <- as.data.frame(Baza_2_S)T2 datasının əsasında tapşırıqların parametrlərinin yenidən hesablanması
fitDF_111_3PL <- mirt(T2, model = 1, itemtype = "3PL", SE = TRUE, verbose = FALSE)## EM cycles terminated after 500 iterations.coef(fitDF_111_3PL, IRTpars = TRUE, simplify = TRUE)$items## a b g u
## 246 2.8644121 -0.04493890 0.2154423203 1
## 19 5.8318546 1.31302354 0.1313728836 1
## 266 0.8079375 -0.21892672 0.0033199517 1
## 406 2.7153335 0.68051006 0.1663395302 1
## 163 3.4497857 0.60659032 0.1465074622 1
## 399 2.6294761 0.94689589 0.2377255850 1
## 311 3.4323416 0.79455507 0.2385994342 1
## 327 2.3992534 0.94338073 0.2169974035 1
## 431 1.4832842 -0.06900834 0.0012956819 1
## 206 0.7225557 0.81706157 0.0654663523 1
## 125 1.5007430 -0.23774546 0.0074217530 1
## 126 1.1317132 0.49937858 0.1385880925 1
## 344 1.6014534 1.08789586 0.1859144073 1
## 268 1.5990562 -0.31493130 0.0145829958 1
## 416 1.7720998 1.13143480 0.2047562106 1
## 187 0.9791198 -0.06077318 0.0059719863 1
## 36 3.5331288 0.12532547 0.1810976638 1
## 9 2.3605271 1.13308364 0.1667907357 1
## 411 2.0074899 -0.13356050 0.0005146356 1
## 341 1.5817663 -0.05291242 0.0023420188 1
## 285 2.0180407 -0.11479639 0.0108747761 1
## 108 1.3693669 -0.24911487 0.0921361130 1
## 113 4.3064673 0.94643846 0.1499477166 1
## 57 3.4902738 0.52332117 0.2729594184 1
## 193 0.9752987 0.66382246 0.1130837385 1
## 45 2.0213912 0.51646313 0.1107021122 1
## 150 4.4786060 1.80562391 0.1707441494 1
## 354 0.9440083 -0.12904526 0.0051303503 1
## 31 1.2144734 -0.50850089 0.0020786971 1
## 185 2.1161696 0.14067841 0.2032591399 1
## 303 1.9895428 -0.12966978 0.0005198245 1
## 227 1.8928583 0.96537299 0.1504896088 1
## 295 1.7465708 1.40410148 0.2276263615 1
## 386 4.4537320 1.07285234 0.2292041767 1
## 99 5.0564577 0.92265542 0.1931649955 1
## 102 1.5406714 -0.42207544 0.0017199494 1
## 106 1.6886641 0.16355262 0.1195859433 1
## 88 1.1939328 0.36570346 0.0478996274 1
## 191 1.9098149 -0.12168156 0.0031729703 1
## 284 1.8393873 0.39731515 0.0837452653 1
## 418 2.8768810 0.62710211 0.1938472232 1
## 371 6.7316193 0.73296961 0.2145998708 1
## 55 4.0554328 0.67414559 0.1278099085 1
## 417 2.7646592 0.94943968 0.2245613644 1
## 302 1.9371238 0.37850236 0.0782377772 1
## 21 1.6766346 2.25224668 0.1280659635 1
## 161 1.8153474 -0.02368478 0.0238271033 1
## 130 4.4136780 0.94338268 0.2133000611 1
## 352 2.8064678 0.77291860 0.1781081640 1
## 318 0.8959236 -0.16273044 0.0047648061 1
## 120 1.3019927 -0.46029486 0.0932679301 1
## 53 1.2447259 0.12827536 0.0299417504 1
## 218 1.1805577 0.15972474 0.0049226119 1
## 323 1.5575383 -0.07886633 0.0040894710 1
## 283 2.0602496 -0.35781037 0.0603649102 1
## 47 1.3532109 -0.45889813 0.0273198745 1
## 5 1.4752981 1.15938553 0.1553273955 1
## 18 1.5495902 1.47665711 0.0948416036 1
## 389 5.8954748 0.75995438 0.2199008616 1
## 326 1.7104343 1.15905389 0.1992033209 1
## 124 1.7156381 -0.24180696 0.1293641232 1
## 35 3.1347936 1.10463426 0.1974063189 1
## 368 3.6992607 1.08693131 0.2461300199 1
## 168 1.6262545 1.07684181 0.1362538858 1
## 152 3.9541112 1.36068810 0.1969520876 1
## 216 2.5863169 1.04214081 0.1951079723 1
## 92 2.2281045 0.03931555 0.0908656458 1
## 270 1.4857777 -0.38899052 0.0987223378 1
## 96 2.6871084 1.15407823 0.0893239308 1
## 204 1.1722638 -0.49275643 0.0036868653 1
## 331 1.7159157 1.43614516 0.2197660952 1
## 169 1.7737324 0.08488815 0.1267277810 1
## 111 3.3373379 0.70578581 0.2463174043 1
## 119 1.2052723 1.75474726 0.1638817599 1
## 226 2.8408522 -0.02352614 0.3181254249 1
## 186 2.5708041 1.23889639 0.1029233834 1
## 68 1.1881020 -0.20195855 0.0041024135 1
## 104 1.6824904 -0.33876397 0.0027581412 1
## 245 2.1439027 0.98209058 0.1681169250 1
## 147 1.7370106 1.15868689 0.1416702360 1
## 319 2.0866092 -0.31449984 0.0957533360 1
## 134 3.0248829 0.92840684 0.2725546769 1
## 336 0.9936260 -0.09167900 0.0017179349 1
## 289 0.8276147 0.09919520 0.0054629750 1
## 175 0.9419403 0.91667884 0.1071823473 1
## 276 1.7651795 0.64390786 0.1965304927 1
## 287 1.6181930 0.04941805 0.0610642177 1
## 238 1.4067988 -0.38636277 0.0955254178 1
## 22 4.5106291 0.39532059 0.2636480699 1
## 259 2.7465359 -0.05354178 0.2272618179 1
## 60 1.7523143 0.46043227 0.1438623825 1
## 73 0.5874754 0.43353849 0.0051510037 1
## 222 1.7222746 -0.40563415 0.0040740063 1
## 314 3.9328833 1.05936421 0.2316198390 1
## 372 1.0763478 0.01888816 0.0767365864 1
## 375 2.1101773 -0.13475044 0.0005409595 1
## 407 6.5122759 0.72068062 0.2228178820 1
## 33 1.8708972 -0.89248619 0.0084375454 1
## 156 1.4575428 1.05693606 0.1400046001 1
## 292 3.1325883 0.62897664 0.2103640527 1
## 148 3.0742349 0.68401903 0.2192147931 1
## 397 0.8208288 0.35310419 0.0727737601 1
## 300 0.8746484 -0.08738571 0.0020293109 1
## 281 6.6399002 0.76071342 0.2414738924 1Birinci variant üzrə iştirakçıların balları
fs_DF_111_3PL_mirt_SE <- fscores(fitDF_111_3PL, full.scores = TRUE,
full.scores.SE = TRUE)
fs_DF_111_3PL_mirt_SE <- as.data.frame(fs_DF_111_3PL_mirt_SE)
head(fs_DF_111_3PL_mirt_SE)## F1 SE_F1
## 1 -0.46790775 0.1978293
## 2 -0.22494310 0.1956633
## 3 1.63080012 0.1575982
## 4 -0.01934629 0.1643630
## 5 -0.03734718 0.1514400
## 6 1.77185724 0.1777099İkinca baza tapşırıqlar üzrə birinci iştirakçının CAT balı
posthocSim1_Baza_2 <- mirtCAT(mo = fitDF_111_3PL, local_pattern = T2[1, ],
start_item = "MI", method = "MAP",
criteria = "MI",design = list(min_SEM = .3))
print(posthocSim1_Baza_2)## n.items.answered Theta_1 SE.Theta_1
## 11 -0.1426159 0.2853612summary(posthocSim1_Baza_2)## $final_estimates
## Theta_1
## Estimates -0.1426159
## SEs 0.2853612
##
## $raw_responses
## [1] "1" "1" "2" "1" "1" "2" "2" "2" "2" "1" "2"
##
## $scored_responses
## [1] 0 0 1 0 0 1 1 1 1 0 1
##
## $items_answered
## [1] 17 96 98 55 19 31 21 1 90 67 81
##
## $thetas_history
## Theta_1
## [1,] 0.0000000
## [2,] -0.4323238
## [3,] -0.6887031
## [4,] -0.4787506
## [5,] -0.6753313
## [6,] -0.7807411
## [7,] -0.5160026
## [8,] -0.3431132
## [9,] -0.2226568
## [10,] -0.1267878
## [11,] -0.2078079
## [12,] -0.1426159
##
## $thetas_SE_history
## Theta_1
## [1,] 1.0000000
## [2,] 0.6535941
## [3,] 0.6407041
## [4,] 0.5062079
## [5,] 0.4850234
## [6,] 0.4664972
## [7,] 0.3912406
## [8,] 0.3475638
## [9,] 0.3299034
## [10,] 0.3097202
## [11,] 0.3040932
## [12,] 0.2853612plot(posthocSim1_Baza_2)
İkinca baza tapşırıqları üzrə ikinci iştirakçının CAT balı
posthocSim2_Baza_2 <- mirtCAT(mo = fitDF_111_3PL, local_pattern = T2[2, ],
start_item = "MI", method = "MAP",
criteria = "MI",design = list(min_SEM = .3))
print(posthocSim2_Baza_2)## n.items.answered Theta_1 SE.Theta_1
## 8 -0.1879645 0.2937641summary(posthocSim2_Baza_2)## $final_estimates
## Theta_1
## Estimates -0.1879645
## SEs 0.2937641
##
## $raw_responses
## [1] "1" "2" "1" "1" "2" "2" "2" "1"
##
## $scored_responses
## [1] 0 1 0 0 1 1 1 0
##
## $items_answered
## [1] 17 96 1 19 55 31 90 75
##
## $thetas_history
## Theta_1
## [1,] 0.00000000
## [2,] -0.43232379
## [3,] -0.09644003
## [4,] -0.30676001
## [5,] -0.44062822
## [6,] -0.30160814
## [7,] -0.17182057
## [8,] -0.07938494
## [9,] -0.18796447
##
## $thetas_SE_history
## Theta_1
## [1,] 1.0000000
## [2,] 0.6535941
## [3,] 0.4566084
## [4,] 0.4191210
## [5,] 0.4173520
## [6,] 0.3637634
## [7,] 0.3271181
## [8,] 0.3096834
## [9,] 0.2937641plot(posthocSim2_Baza_2)
İkinca baza tapşırıqları üzrə üçüncü iştirakçının CAT balı
posthocSim3_Baza_2 <- mirtCAT(mo = fitDF_111_3PL, local_pattern = T2[3, ],
start_item = "MI", method = "MAP",
criteria = "MI",design = list(min_SEM = .3))
print(posthocSim3_Baza_2)## n.items.answered Theta_1 SE.Theta_1
## 7 1.511772 0.2789421summary(posthocSim3_Baza_2)## $final_estimates
## Theta_1
## Estimates 1.5117719
## SEs 0.2789421
##
## $raw_responses
## [1] "2" "2" "2" "2" "2" "2" "1"
##
## $scored_responses
## [1] 1 1 1 1 1 1 0
##
## $items_answered
## [1] 17 97 104 35 2 65 27
##
## $thetas_history
## Theta_1
## [1,] 0.0000000
## [2,] 0.5322814
## [3,] 0.9640597
## [4,] 1.0764146
## [5,] 1.2143988
## [6,] 1.5023460
## [7,] 1.6246116
## [8,] 1.5117719
##
## $thetas_SE_history
## Theta_1
## [1,] 1.0000000
## [2,] 0.6399265
## [3,] 0.4195153
## [4,] 0.3790362
## [5,] 0.3863006
## [6,] 0.3655525
## [7,] 0.3712383
## [8,] 0.2789421plot(posthocSim3_Baza_2)
İkinca baza tapşırıqları üzrə dördüncü iştirakçının CAT balı
posthocSim4_Baza_2 <- mirtCAT(mo = fitDF_111_3PL, local_pattern = T2[4, ],
start_item = "MI", method = "MAP",
criteria = "MI",design = list(min_SEM = .3))
print(posthocSim4_Baza_2)## n.items.answered Theta_1 SE.Theta_1
## 7 0.1486785 0.2881041summary(posthocSim4_Baza_2)## $final_estimates
## Theta_1
## Estimates 0.1486785
## SEs 0.2881041
##
## $raw_responses
## [1] "2" "1" "1" "1" "2" "2" "2"
##
## $scored_responses
## [1] 1 0 0 0 1 1 1
##
## $items_answered
## [1] 17 97 89 1 96 90 75
##
## $thetas_history
## Theta_1
## [1,] 0.000000000
## [2,] 0.532281393
## [3,] 0.341212891
## [4,] 0.116198508
## [5,] -0.156061649
## [6,] 0.005950212
## [7,] 0.091489935
## [8,] 0.148678538
##
## $thetas_SE_history
## Theta_1
## [1,] 1.0000000
## [2,] 0.6399265
## [3,] 0.4131306
## [4,] 0.3844626
## [5,] 0.4827978
## [6,] 0.3546725
## [7,] 0.3116772
## [8,] 0.2881041plot(posthocSim4_Baza_2)
İkinca baza tapşırıqları üzrə beşinci iştirakçının CAT balı
posthocSim5_Baza_2 <- mirtCAT(mo = fitDF_111_3PL, local_pattern = T2[5, ],
start_item = "MI", method = "MAP",
criteria = "MI",design = list(min_SEM = .3))
print(posthocSim5_Baza_2)## n.items.answered Theta_1 SE.Theta_1
## 7 -0.07286121 0.2914878summary(posthocSim5_Baza_2)## $final_estimates
## Theta_1
## Estimates -0.07286121
## SEs 0.29148777
##
## $raw_responses
## [1] "1" "2" "1" "2" "1" "2" "2"
##
## $scored_responses
## [1] 0 1 0 1 0 1 1
##
## $items_answered
## [1] 17 96 1 19 90 31 21
##
## $thetas_history
## Theta_1
## [1,] 0.00000000
## [2,] -0.43232379
## [3,] -0.09644003
## [4,] -0.30676001
## [5,] -0.14310492
## [6,] -0.27594365
## [7,] -0.16210665
## [8,] -0.07286121
##
## $thetas_SE_history
## Theta_1
## [1,] 1.0000000
## [2,] 0.6535941
## [3,] 0.4566084
## [4,] 0.4191210
## [5,] 0.3617906
## [6,] 0.3411367
## [7,] 0.3104321
## [8,] 0.2914878plot(posthocSim5_Baza_2)
Aşağıda bu iki tamamilə fərqli tapşırıqlar toplusu (Baza_1 və Baza_2) üzrə birinci variantdan birinci beş iştirakçının aldıqları və onların aldıaları CAT ballar verilmişdir. Bu zaman onların səviyyələrinin 0.3-logit dəqiqliklə ölçülməsi üçün müvafiq bazadan neçə sual lazım gəldiyi də verilir.
print(posthocSim1_Baza_1)## n.items.answered Theta_1 SE.Theta_1
## 3 0.6142941 0.2798501print(posthocSim1_Baza_2)## n.items.answered Theta_1 SE.Theta_1
## 11 -0.1426159 0.2853612print(posthocSim2_Baza_1)## n.items.answered Theta_1 SE.Theta_1
## 12 -0.3685604 0.2825292print(posthocSim2_Baza_2)## n.items.answered Theta_1 SE.Theta_1
## 8 -0.1879645 0.2937641print(posthocSim3_Baza_1)## n.items.answered Theta_1 SE.Theta_1
## 6 1.244201 0.2950543print(posthocSim3_Baza_2)## n.items.answered Theta_1 SE.Theta_1
## 7 1.511772 0.2789421print(posthocSim4_Baza_1)## n.items.answered Theta_1 SE.Theta_1
## 3 0.6142941 0.2798501print(posthocSim4_Baza_2)## n.items.answered Theta_1 SE.Theta_1
## 7 0.1486785 0.2881041print(posthocSim5_Baza_1)## n.items.answered Theta_1 SE.Theta_1
## 5 0.4163058 0.2782172print(posthocSim5_Baza_2)## n.items.answered Theta_1 SE.Theta_1
## 7 -0.07286121 0.2914878Buradan məlum olur ki, məsələn 4-cü iştirakçının səviyyəsini birinci baza tapşırıqlar üzrə .3-logit dəqiqliklə ölçmək üçün cəmi 4 tapşırıq kifayət edir. (22, 36, 74 və 57 nömrəli tapşırıqlar). Ən çox tapşırıq birinci baza üzrə birinci iştirakçını ölçməyə lazım gəlib (32 tapşırıq). Lakin, 10 ölçmənin yarısında 10-dan az, 4-də 20-dən az tapşırıq istifadə olunubdur. Beləliklə, CAT ölçmənin nə qədər səmərəli və dəqiq ölçmə olduğunu buradan görmək olur.