library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.3.3
## Warning: package 'ggplot2' was built under R version 4.3.3
## Warning: package 'readr' was built under R version 4.3.3
## Warning: package 'forcats' was built under R version 4.3.3
## Warning: package 'lubridate' was built under R version 4.3.3
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats   1.0.0     ✔ readr     2.1.5
## ✔ ggplot2   3.5.1     ✔ stringr   1.5.1
## ✔ lubridate 1.9.3     ✔ tibble    3.2.1
## ✔ purrr     1.0.2     ✔ tidyr     1.3.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(dplyr)
library(knitr)
## Warning: package 'knitr' was built under R version 4.3.3
library(haven)
## Warning: package 'haven' was built under R version 4.3.3
library(kableExtra)
## Warning: package 'kableExtra' was built under R version 4.3.3
## 
## Attaching package: 'kableExtra'
## 
## The following object is masked from 'package:dplyr':
## 
##     group_rows

AFA denemesi için elimdeki 23 madde 303 kişilik bir veriyi kullanacağım. Veriseti içinde kayıp veri yok. Diğer adımları buradan ilerleteceğim.

veri <- read_sav("data/AFAveri.sav")
afadata <- veri %>% select(starts_with("m"))
head(afadata,10)

Korelasyonları inceleyelim

library(psych)
## Warning: package 'psych' was built under R version 4.3.3
## 
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
polychoric(afadata)$rho %>% kable() %>% kable_styling(full_width = FALSE, bootstrap_options = c("striped", "hover"))
m1_1 m2_1 m3_1 m4_1 m5_1 m6_1 m7_1 m8_1 m9_1 m10_1 m11_1 m12_1 m13_1 m14_1 m15_1 m16_1 m17_1 m18_1 m19_1 m20_1 m21_1 m22_1 m23_1
m1_1 1.0000000 0.5866789 0.1539219 0.0852971 0.1203654 0.2385115 0.0285636 0.0038275 -0.0888320 0.0797458 -0.0612626 -0.0803182 0.0732402 0.1133995 -0.0161694 0.1459090 0.1228250 0.1574978 0.0341145 0.0202259 0.0661953 0.1762901 0.1862396
m2_1 0.5866789 1.0000000 0.2530049 0.1666323 0.1543277 0.2227611 0.2035852 -0.0673656 -0.0901916 0.0151555 -0.0140957 0.0346054 0.1091672 0.1590597 -0.0886169 0.0383842 0.0653000 0.0855347 -0.0156613 0.0497904 0.0948487 0.0194873 0.1970158
m3_1 0.1539219 0.2530049 1.0000000 0.1761982 0.1551650 0.2510047 0.1842553 0.0710665 -0.0034693 0.0127349 0.0657712 -0.0114496 0.1110757 0.1808737 -0.0016871 0.0695622 0.0330670 0.0266628 0.0580680 0.0938846 0.0498746 -0.0232792 0.1271836
m4_1 0.0852971 0.1666323 0.1761982 1.0000000 0.1491921 0.1376151 0.1469049 -0.0096004 0.0318219 -0.0356807 -0.0684506 -0.0611870 -0.0304838 0.1418586 -0.0420508 0.0972066 -0.0483678 0.0444955 0.1365882 -0.0378782 0.0805846 0.0713861 0.0710998
m5_1 0.1203654 0.1543277 0.1551650 0.1491921 1.0000000 0.0905904 0.1880502 0.0725319 0.0145902 0.1465868 -0.0162193 -0.0666723 0.0830135 0.0183900 0.0509165 0.1391643 0.0739143 0.1467514 0.1036952 -0.0862377 0.1118777 0.0120878 0.0667574
m6_1 0.2385115 0.2227611 0.2510047 0.1376151 0.0905904 1.0000000 0.2305296 0.0769750 0.0609532 0.0487604 -0.0677296 -0.0142023 0.0806258 0.2045476 0.0281467 0.1811684 0.1716306 0.0265441 -0.0475941 0.0316225 0.1040741 0.0415324 0.1282524
m7_1 0.0285636 0.2035852 0.1842553 0.1469049 0.1880502 0.2305296 1.0000000 0.1063445 0.2702256 0.0221696 0.0945244 -0.0524823 -0.0927618 0.1584247 -0.0981588 0.0674855 -0.0409051 0.0032611 -0.1017972 -0.0402522 -0.0552635 0.0299839 0.0793924
m8_1 0.0038275 -0.0673656 0.0710665 -0.0096004 0.0725319 0.0769750 0.1063445 1.0000000 0.3958034 0.2080148 0.0599354 0.0788347 -0.0284683 -0.0209994 -0.0967160 -0.0397106 0.0153958 0.0927140 -0.0333900 -0.1129218 0.0206020 0.0174475 -0.0314413
m9_1 -0.0888320 -0.0901916 -0.0034693 0.0318219 0.0145902 0.0609532 0.2702256 0.3958034 1.0000000 0.3275579 0.3435672 0.2284848 -0.0409293 -0.0412879 -0.0191573 -0.0511927 -0.0986139 -0.0560962 -0.0255735 0.0016070 -0.0848623 0.1966889 -0.0846422
m10_1 0.0797458 0.0151555 0.0127349 -0.0356807 0.1465868 0.0487604 0.0221696 0.2080148 0.3275579 1.0000000 0.3174895 0.2456020 0.0704571 0.0294214 0.0691390 0.0648119 0.0993011 -0.0152136 0.0275416 0.0577867 -0.0067847 0.1804264 -0.0591095
m11_1 -0.0612626 -0.0140957 0.0657712 -0.0684506 -0.0162193 -0.0677296 0.0945244 0.0599354 0.3435672 0.3174895 1.0000000 0.2290893 0.0254749 -0.0594333 0.0365641 -0.0860058 -0.1699885 -0.0841701 -0.0163037 0.1115814 -0.0331215 0.1883007 -0.0873763
m12_1 -0.0803182 0.0346054 -0.0114496 -0.0611870 -0.0666723 -0.0142023 -0.0524823 0.0788347 0.2284848 0.2456020 0.2290893 1.0000000 0.1142377 0.1080722 0.1853327 -0.0350983 0.1938269 -0.0604879 0.0704252 0.2125024 -0.0007366 0.3502691 -0.0304627
m13_1 0.0732402 0.1091672 0.1110757 -0.0304838 0.0830135 0.0806258 -0.0927618 -0.0284683 -0.0409293 0.0704571 0.0254749 0.1142377 1.0000000 0.1470972 0.2412543 0.1275395 0.2272843 0.1254302 0.1489531 0.1180626 0.1068019 0.1609882 0.0958767
m14_1 0.1133995 0.1590597 0.1808737 0.1418586 0.0183900 0.2045476 0.1584247 -0.0209994 -0.0412879 0.0294214 -0.0594333 0.1080722 0.1470972 1.0000000 0.1104710 0.1278713 0.2030037 0.2122611 0.1143469 0.0705978 0.1224825 0.0474955 0.1484288
m15_1 -0.0161694 -0.0886169 -0.0016871 -0.0420508 0.0509165 0.0281467 -0.0981588 -0.0967160 -0.0191573 0.0691390 0.0365641 0.1853327 0.2412543 0.1104710 1.0000000 0.1937872 0.1946414 0.1853957 0.3385225 0.2246731 0.1420855 0.2270751 0.0553429
m16_1 0.1459090 0.0383842 0.0695622 0.0972066 0.1391643 0.1811684 0.0674855 -0.0397106 -0.0511927 0.0648119 -0.0860058 -0.0350983 0.1275395 0.1278713 0.1937872 1.0000000 0.2453320 0.2173232 0.1472987 0.0772066 0.2029868 -0.1441935 0.1590037
m17_1 0.1228250 0.0653000 0.0330670 -0.0483678 0.0739143 0.1716306 -0.0409051 0.0153958 -0.0986139 0.0993011 -0.1699885 0.1938269 0.2272843 0.2030037 0.1946414 0.2453320 1.0000000 0.2092030 0.1158169 0.1964967 0.0650119 0.1641378 0.1825351
m18_1 0.1574978 0.0855347 0.0266628 0.0444955 0.1467514 0.0265441 0.0032611 0.0927140 -0.0560962 -0.0152136 -0.0841701 -0.0604879 0.1254302 0.2122611 0.1853957 0.2173232 0.2092030 1.0000000 0.2305348 0.2060302 0.2155499 -0.0145756 0.2005102
m19_1 0.0341145 -0.0156613 0.0580680 0.1365882 0.1036952 -0.0475941 -0.1017972 -0.0333900 -0.0255735 0.0275416 -0.0163037 0.0704252 0.1489531 0.1143469 0.3385225 0.1472987 0.1158169 0.2305348 1.0000000 0.3618779 0.3485327 0.1086655 0.0101837
m20_1 0.0202259 0.0497904 0.0938846 -0.0378782 -0.0862377 0.0316225 -0.0402522 -0.1129218 0.0016070 0.0577867 0.1115814 0.2125024 0.1180626 0.0705978 0.2246731 0.0772066 0.1964967 0.2060302 0.3618779 1.0000000 0.2225619 0.2533892 0.0204981
m21_1 0.0661953 0.0948487 0.0498746 0.0805846 0.1118777 0.1040741 -0.0552635 0.0206020 -0.0848623 -0.0067847 -0.0331215 -0.0007366 0.1068019 0.1224825 0.1420855 0.2029868 0.0650119 0.2155499 0.3485327 0.2225619 1.0000000 -0.0209004 0.0820679
m22_1 0.1762901 0.0194873 -0.0232792 0.0713861 0.0120878 0.0415324 0.0299839 0.0174475 0.1966889 0.1804264 0.1883007 0.3502691 0.1609882 0.0474955 0.2270751 -0.1441935 0.1641378 -0.0145756 0.1086655 0.2533892 -0.0209004 1.0000000 -0.0238364
m23_1 0.1862396 0.1970158 0.1271836 0.0710998 0.0667574 0.1282524 0.0793924 -0.0314413 -0.0846422 -0.0591095 -0.0873763 -0.0304627 0.0958767 0.1484288 0.0553429 0.1590037 0.1825351 0.2005102 0.0101837 0.0204981 0.0820679 -0.0238364 1.0000000

Korelasyonlar inanılmaz düşük gözüküyor. Bir bakmak lazım. Deniyoruz sonuçta.

İlişki katsayıları matrisini inceleyelim

matris <- round(polychoric(afadata)$rho,2)
matris[upper.tri(matris)] <- NA
matris
##        m1_1  m2_1  m3_1  m4_1  m5_1  m6_1  m7_1  m8_1  m9_1 m10_1 m11_1 m12_1
## m1_1   1.00    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m2_1   0.59  1.00    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m3_1   0.15  0.25  1.00    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m4_1   0.09  0.17  0.18  1.00    NA    NA    NA    NA    NA    NA    NA    NA
## m5_1   0.12  0.15  0.16  0.15  1.00    NA    NA    NA    NA    NA    NA    NA
## m6_1   0.24  0.22  0.25  0.14  0.09  1.00    NA    NA    NA    NA    NA    NA
## m7_1   0.03  0.20  0.18  0.15  0.19  0.23  1.00    NA    NA    NA    NA    NA
## m8_1   0.00 -0.07  0.07 -0.01  0.07  0.08  0.11  1.00    NA    NA    NA    NA
## m9_1  -0.09 -0.09  0.00  0.03  0.01  0.06  0.27  0.40  1.00    NA    NA    NA
## m10_1  0.08  0.02  0.01 -0.04  0.15  0.05  0.02  0.21  0.33  1.00    NA    NA
## m11_1 -0.06 -0.01  0.07 -0.07 -0.02 -0.07  0.09  0.06  0.34  0.32  1.00    NA
## m12_1 -0.08  0.03 -0.01 -0.06 -0.07 -0.01 -0.05  0.08  0.23  0.25  0.23  1.00
## m13_1  0.07  0.11  0.11 -0.03  0.08  0.08 -0.09 -0.03 -0.04  0.07  0.03  0.11
## m14_1  0.11  0.16  0.18  0.14  0.02  0.20  0.16 -0.02 -0.04  0.03 -0.06  0.11
## m15_1 -0.02 -0.09  0.00 -0.04  0.05  0.03 -0.10 -0.10 -0.02  0.07  0.04  0.19
## m16_1  0.15  0.04  0.07  0.10  0.14  0.18  0.07 -0.04 -0.05  0.06 -0.09 -0.04
## m17_1  0.12  0.07  0.03 -0.05  0.07  0.17 -0.04  0.02 -0.10  0.10 -0.17  0.19
## m18_1  0.16  0.09  0.03  0.04  0.15  0.03  0.00  0.09 -0.06 -0.02 -0.08 -0.06
## m19_1  0.03 -0.02  0.06  0.14  0.10 -0.05 -0.10 -0.03 -0.03  0.03 -0.02  0.07
## m20_1  0.02  0.05  0.09 -0.04 -0.09  0.03 -0.04 -0.11  0.00  0.06  0.11  0.21
## m21_1  0.07  0.09  0.05  0.08  0.11  0.10 -0.06  0.02 -0.08 -0.01 -0.03  0.00
## m22_1  0.18  0.02 -0.02  0.07  0.01  0.04  0.03  0.02  0.20  0.18  0.19  0.35
## m23_1  0.19  0.20  0.13  0.07  0.07  0.13  0.08 -0.03 -0.08 -0.06 -0.09 -0.03
##       m13_1 m14_1 m15_1 m16_1 m17_1 m18_1 m19_1 m20_1 m21_1 m22_1 m23_1
## m1_1     NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m2_1     NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m3_1     NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m4_1     NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m5_1     NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m6_1     NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m7_1     NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m8_1     NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m9_1     NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m10_1    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m11_1    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m12_1    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m13_1  1.00    NA    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m14_1  0.15  1.00    NA    NA    NA    NA    NA    NA    NA    NA    NA
## m15_1  0.24  0.11  1.00    NA    NA    NA    NA    NA    NA    NA    NA
## m16_1  0.13  0.13  0.19  1.00    NA    NA    NA    NA    NA    NA    NA
## m17_1  0.23  0.20  0.19  0.25  1.00    NA    NA    NA    NA    NA    NA
## m18_1  0.13  0.21  0.19  0.22  0.21  1.00    NA    NA    NA    NA    NA
## m19_1  0.15  0.11  0.34  0.15  0.12  0.23  1.00    NA    NA    NA    NA
## m20_1  0.12  0.07  0.22  0.08  0.20  0.21  0.36  1.00    NA    NA    NA
## m21_1  0.11  0.12  0.14  0.20  0.07  0.22  0.35  0.22  1.00    NA    NA
## m22_1  0.16  0.05  0.23 -0.14  0.16 -0.01  0.11  0.25 -0.02  1.00    NA
## m23_1  0.10  0.15  0.06  0.16  0.18  0.20  0.01  0.02  0.08 -0.02     1

Bir de KMO denemesi, Faktör yok gibi geliyor ama denemek lazım

KMO(afadata)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = afadata)
## Overall MSA =  0.68
## MSA for each item = 
##  m1_1  m2_1  m3_1  m4_1  m5_1  m6_1  m7_1  m8_1  m9_1 m10_1 m11_1 m12_1 m13_1 
##  0.57  0.59  0.71  0.63  0.64  0.75  0.61  0.57  0.64  0.70  0.66  0.68  0.79 
## m14_1 m15_1 m16_1 m17_1 m18_1 m19_1 m20_1 m21_1 m22_1 m23_1 
##  0.75  0.77  0.71  0.73  0.72  0.72  0.70  0.74  0.63  0.82

Yani şaşırtıcı olsa da yola devam etmeye bir iki madde dışında engel yok gibi (MSA>0.6). Sanırım o maddeleri görmezden geleceğim.

Bartlett Testine de bakalım

cortest.bartlett(afadata)
## R was not square, finding R from data
## $chisq
## [1] 929.0887
## 
## $p.value
## [1] 5.951553e-78
## 
## $df
## [1] 253

Çok şaşırtıcı. Durmak yok.

Faktör Sayısı Belirleme

Yani adet olmuş K1’e bakacağım ama buradan desteklediğim anlamı çıkmasın.

fa(veri)$e.values
##  [1] 3.3354370 2.4684482 2.1085581 1.5742683 1.4072110 1.1862457 1.1154548
##  [8] 1.0170884 0.9873431 0.9543550 0.9112528 0.8544246 0.8160868 0.7859924
## [15] 0.7540383 0.7078609 0.6824253 0.6485610 0.6028691 0.5591987 0.5523819
## [22] 0.4814849 0.4615243 0.4223779 0.3436202 0.2614914

:)

sum(fa(veri)$e.values>=1)
## [1] 8

:):)

Yani K1 kuralına göre 8 boyutlu bir yapı bulunmaktadır.

Maksat deneme olduğu için 8 boyutlu bir deneme biz de yapalım. 8 boyut çıktığına göre zeka falan ölçüyoruz sanırım. Principal Axis Factoring kullanacağım. Normalde bu aşamada dönürme yapmasam da olur ama bir de promax döndürelim.

faktor8 <- fa(afadata, nfactors = 8, fm="pa", rotate="promax",max.iter = 1000)
## Loading required namespace: GPArotation
faktor8
## Factor Analysis using method =  pa
## Call: fa(r = afadata, nfactors = 8, rotate = "promax", max.iter = 1000, 
##     fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##         PA5   PA1   PA3   PA2   PA6   PA4   PA7   PA8   h2   u2 com
## m1_1   0.00 -0.03  0.91  0.01 -0.13  0.20  0.05  0.13 0.70 0.30 1.2
## m2_1   0.02 -0.08  0.65  0.09  0.16 -0.02 -0.05 -0.09 0.50 0.50 1.2
## m3_1   0.05 -0.02  0.07  0.07  0.33 -0.06 -0.06  0.00 0.15 0.85 1.4
## m4_1   0.10 -0.09 -0.02 -0.13  0.40  0.13 -0.01  0.07 0.15 0.85 1.8
## m5_1   0.04  0.00  0.04  0.05  0.12  0.05  0.03  0.33 0.15 0.85 1.4
## m6_1  -0.11  0.17  0.11  0.00  0.31  0.05  0.02  0.09 0.20 0.80 2.4
## m7_1  -0.18 -0.07 -0.13  0.08  0.63  0.00  0.06  0.13 0.41 0.59 1.5
## m8_1   0.08  0.03  0.01  0.06 -0.05 -0.01  0.67  0.01 0.43 0.57 1.1
## m9_1  -0.02 -0.11 -0.13  0.46  0.21  0.06  0.39  0.05 0.55 0.45 2.8
## m10_1 -0.06  0.09  0.09  0.54 -0.13 -0.02  0.14  0.15 0.34 0.66 1.6
## m11_1  0.06 -0.26  0.03  0.64  0.03 -0.06 -0.10  0.03 0.37 0.63 1.4
## m12_1  0.00  0.26 -0.02  0.32 -0.01  0.12  0.07 -0.24 0.33 0.67 3.3
## m13_1  0.03  0.32  0.02  0.07 -0.04  0.07 -0.10  0.06 0.15 0.85 1.6
## m14_1  0.05  0.32 -0.06 -0.02  0.30 -0.07 -0.01 -0.14 0.25 0.75 2.6
## m15_1  0.22  0.29 -0.14  0.07 -0.06  0.17 -0.13  0.13 0.31 0.69 4.3
## m16_1  0.10  0.30 -0.07  0.07  0.05 -0.17 -0.10  0.34 0.32 0.68 3.2
## m17_1 -0.13  0.80 -0.05 -0.14 -0.09  0.09  0.10 -0.02 0.46 0.54 1.2
## m18_1  0.33  0.22  0.03 -0.13 -0.03 -0.07  0.20  0.05 0.25 0.75 3.0
## m19_1  0.76 -0.15 -0.04 -0.03  0.00  0.08  0.04  0.06 0.48 0.52 1.1
## m20_1  0.47  0.05  0.02  0.10  0.02  0.08 -0.04 -0.19 0.33 0.67 1.5
## m21_1  0.51 -0.07  0.05  0.02  0.01 -0.11  0.04  0.08 0.25 0.75 1.2
## m22_1  0.00  0.13  0.15 -0.05  0.13  0.88 -0.01  0.03 0.71 0.29 1.2
## m23_1 -0.04  0.28  0.08 -0.10  0.11 -0.06  0.00  0.02 0.14 0.86 1.9
## 
##                        PA5  PA1  PA3  PA2  PA6  PA4  PA7  PA8
## SS loadings           1.26 1.26 1.25 1.11 0.97 0.86 0.75 0.48
## Proportion Var        0.05 0.05 0.05 0.05 0.04 0.04 0.03 0.02
## Cumulative Var        0.05 0.11 0.16 0.21 0.25 0.29 0.32 0.35
## Proportion Explained  0.16 0.16 0.16 0.14 0.12 0.11 0.09 0.06
## Cumulative Proportion 0.16 0.32 0.47 0.61 0.74 0.84 0.94 1.00
## 
##  With factor correlations of 
##       PA5   PA1   PA3   PA2   PA6   PA4   PA7   PA8
## PA5  1.00  0.57  0.13  0.07  0.14  0.10 -0.29  0.12
## PA1  0.57  1.00  0.34  0.16  0.31  0.03 -0.13  0.13
## PA3  0.13  0.34  1.00 -0.12  0.45 -0.29 -0.06  0.20
## PA2  0.07  0.16 -0.12  1.00  0.10  0.45  0.16 -0.14
## PA6  0.14  0.31  0.45  0.10  1.00 -0.21  0.16  0.18
## PA4  0.10  0.03 -0.29  0.45 -0.21  1.00 -0.06 -0.33
## PA7 -0.29 -0.13 -0.06  0.16  0.16 -0.06  1.00  0.20
## PA8  0.12  0.13  0.20 -0.14  0.18 -0.33  0.20  1.00
## 
## Mean item complexity =  1.9
## Test of the hypothesis that 8 factors are sufficient.
## 
## df null model =  253  with the objective function =  3.17 with Chi Square =  929.09
## df of  the model are 97  and the objective function was  0.26 
## 
## The root mean square of the residuals (RMSR) is  0.02 
## The df corrected root mean square of the residuals is  0.03 
## 
## The harmonic n.obs is  303 with the empirical chi square  71.54  with prob <  0.98 
## The total n.obs was  303  with Likelihood Chi Square =  75.87  with prob <  0.94 
## 
## Tucker Lewis Index of factoring reliability =  1.084
## RMSEA index =  0  and the 90 % confidence intervals are  0 0.005
## BIC =  -478.36
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy             
##                                                    PA5  PA1  PA3  PA2  PA6  PA4
## Correlation of (regression) scores with factors   0.84 0.84 0.88 0.82 0.79 0.85
## Multiple R square of scores with factors          0.71 0.70 0.78 0.67 0.62 0.73
## Minimum correlation of possible factor scores     0.41 0.40 0.56 0.34 0.25 0.46
##                                                    PA7   PA8
## Correlation of (regression) scores with factors   0.77  0.67
## Multiple R square of scores with factors          0.60  0.45
## Minimum correlation of possible factor scores     0.19 -0.10

düzgün biçimli bir faktörleşme olmuyor haliyle.

Diğer faktör sayısı belirleme metotlarına bakalım

scree(polychoric(afadata)$rho, factors=F)

K1 bakış açısıyla bakmazsak ben olsam 3 boyutlu çözümü bir denerdim. En yüksek kırılma orada gözüküyor. Biraz arada bırakan bir sonuç var.

artik8 <- round(faktor8$residual,2)
artik8
##        m1_1  m2_1  m3_1  m4_1  m5_1  m6_1  m7_1  m8_1  m9_1 m10_1 m11_1 m12_1
## m1_1   0.30  0.01 -0.01 -0.01 -0.03  0.03  0.00  0.00  0.01  0.00  0.00 -0.02
## m2_1   0.01  0.50 -0.01  0.01  0.04 -0.03  0.02 -0.02  0.00  0.00 -0.02  0.04
## m3_1  -0.01 -0.01  0.85  0.02  0.05  0.04 -0.02  0.05 -0.05 -0.01  0.03 -0.02
## m4_1  -0.01  0.01  0.02  0.85 -0.01  0.01 -0.04 -0.01  0.01  0.02 -0.02  0.01
## m5_1  -0.03  0.04  0.05 -0.01  0.85 -0.04  0.03  0.00 -0.04  0.04 -0.01  0.01
## m6_1   0.03 -0.03  0.04  0.01 -0.04  0.80  0.00  0.02  0.00  0.00 -0.02 -0.01
## m7_1   0.00  0.02 -0.02 -0.04  0.03  0.00  0.59 -0.01  0.03 -0.03  0.00 -0.02
## m8_1   0.00 -0.02  0.05 -0.01  0.00  0.02 -0.01  0.57 -0.01  0.01 -0.01  0.01
## m9_1   0.01  0.00 -0.05  0.01 -0.04  0.00  0.03 -0.01  0.45  0.00  0.01  0.01
## m10_1  0.00  0.00 -0.01  0.02  0.04  0.00 -0.03  0.01  0.00  0.66  0.01  0.00
## m11_1  0.00 -0.02  0.03 -0.02 -0.01 -0.02  0.00 -0.01  0.01  0.01  0.63 -0.02
## m12_1 -0.02  0.04 -0.02  0.01  0.01 -0.01 -0.02  0.01  0.01  0.00 -0.02  0.67
## m13_1 -0.03  0.02  0.07 -0.03  0.02  0.00 -0.03  0.02 -0.01 -0.02  0.01 -0.01
## m14_1  0.01 -0.02  0.01  0.02 -0.04  0.00  0.01 -0.02 -0.02  0.03  0.01  0.01
## m15_1  0.01 -0.01 -0.01 -0.04 -0.01  0.02  0.02 -0.01  0.01 -0.02 -0.01  0.02
## m16_1  0.02 -0.03 -0.03  0.03 -0.03  0.03  0.01 -0.02  0.02  0.00  0.00  0.01
## m17_1 -0.01  0.00 -0.01  0.00  0.02  0.01  0.00 -0.01 -0.01  0.02 -0.02  0.01
## m18_1  0.01  0.01 -0.04 -0.02  0.03 -0.07  0.01  0.01  0.02 -0.03  0.04 -0.06
## m19_1  0.01  0.00  0.00  0.04  0.02 -0.03 -0.01  0.00  0.01  0.01 -0.02  0.01
## m20_1  0.00 -0.01  0.03 -0.04 -0.04  0.02  0.03 -0.02  0.00  0.00  0.01 -0.01
## m21_1 -0.02  0.01 -0.01  0.00  0.01  0.04 -0.03  0.03 -0.02 -0.01  0.00  0.02
## m22_1  0.00 -0.01 -0.01  0.02  0.01  0.00  0.00  0.00 -0.01 -0.01  0.02  0.00
## m23_1  0.00  0.01  0.01  0.00 -0.02 -0.04  0.00 -0.01  0.01 -0.02  0.02 -0.01
##       m13_1 m14_1 m15_1 m16_1 m17_1 m18_1 m19_1 m20_1 m21_1 m22_1 m23_1
## m1_1  -0.03  0.01  0.01  0.02 -0.01  0.01  0.01  0.00 -0.02  0.00  0.00
## m2_1   0.02 -0.02 -0.01 -0.03  0.00  0.01  0.00 -0.01  0.01 -0.01  0.01
## m3_1   0.07  0.01 -0.01 -0.03 -0.01 -0.04  0.00  0.03 -0.01 -0.01  0.01
## m4_1  -0.03  0.02 -0.04  0.03  0.00 -0.02  0.04 -0.04  0.00  0.02  0.00
## m5_1   0.02 -0.04 -0.01 -0.03  0.02  0.03  0.02 -0.04  0.01  0.01 -0.02
## m6_1   0.00  0.00  0.02  0.03  0.01 -0.07 -0.03  0.02  0.04  0.00 -0.04
## m7_1  -0.03  0.01  0.02  0.01  0.00  0.01 -0.01  0.03 -0.03  0.00  0.00
## m8_1   0.02 -0.02 -0.01 -0.02 -0.01  0.01  0.00 -0.02  0.03  0.00 -0.01
## m9_1  -0.01 -0.02  0.01  0.02 -0.01  0.02  0.01  0.00 -0.02 -0.01  0.01
## m10_1 -0.02  0.03 -0.02  0.00  0.02 -0.03  0.01  0.00 -0.01 -0.01 -0.02
## m11_1  0.01  0.01 -0.01  0.00 -0.02  0.04 -0.02  0.01  0.00  0.02  0.02
## m12_1 -0.01  0.01  0.02  0.01  0.01 -0.06  0.01 -0.01  0.02  0.00 -0.01
## m13_1  0.85  0.00  0.04 -0.02  0.00  0.00 -0.01 -0.03  0.00  0.01  0.00
## m14_1  0.00  0.75  0.01 -0.03 -0.01  0.05  0.01 -0.05  0.00  0.00  0.00
## m15_1  0.04  0.01  0.69  0.00 -0.04  0.02  0.03 -0.02 -0.02  0.00  0.00
## m16_1 -0.02 -0.03  0.00  0.68  0.01  0.00 -0.01  0.01  0.04 -0.01  0.02
## m17_1  0.00 -0.01 -0.04  0.01  0.54 -0.01  0.01  0.03 -0.02  0.00 -0.01
## m18_1  0.00  0.05  0.02  0.00 -0.01  0.75 -0.03  0.04 -0.02  0.01  0.06
## m19_1 -0.01  0.01  0.03 -0.01  0.01 -0.03  0.52  0.01 -0.01 -0.02 -0.02
## m20_1 -0.03 -0.05 -0.02  0.01  0.03  0.04  0.01  0.67  0.01  0.01 -0.02
## m21_1  0.00  0.00 -0.02  0.04 -0.02 -0.02 -0.01  0.01  0.75  0.01 -0.01
## m22_1  0.01  0.00  0.00 -0.01  0.00  0.01 -0.02  0.01  0.01  0.29  0.02
## m23_1  0.00  0.00  0.00  0.02 -0.01  0.06 -0.02 -0.02 -0.01  0.02  0.86
sum(abs(artik8[lower.tri(artik8)])>0.05)
## [1] 4

4 tane .5 üstü artık var. Farklı döndürmelerle farklı çözümler bulunabilirdi belki. Bir paralel analize de bakmak gerekiyorm.

Paralel Analiz

fa.parallel(afadata, fa = "fa")

## Parallel analysis suggests that the number of factors =  5  and the number of components =  NA

Paralel analiz 5 faktörlü yapıyı öneriyor. Örnekleme hatası 3 farklı boyut gözükmesine neden olmuş. Ben paralel analizi temel alacağım.

Pattern Coeffs

out8 <- fa(afadata,5,fm="pa",rotate="none")
out8$loadings[,1:5]
##               PA1         PA2         PA3          PA4         PA5
## m1_1  0.399259617 -0.03297469  0.40724287 -0.287996799  0.05024999
## m2_1  0.397513529  0.00147396  0.52999836 -0.352771914  0.15498500
## m3_1  0.244698882  0.06743903  0.22228012  0.026700114  0.08564910
## m4_1  0.186669512  0.03819245  0.16744435  0.090555666  0.09856839
## m5_1  0.201454560  0.08555331  0.15365022  0.167360676  0.04454646
## m6_1  0.307368376  0.11884804  0.27697917  0.033919909 -0.07137152
## m7_1  0.084608720  0.33092123  0.35777095  0.187898334  0.01351317
## m8_1  0.002183037  0.35380945  0.07975228  0.225428147 -0.08887687
## m9_1  0.002986012  0.76994999 -0.02573947  0.186225513  0.03005985
## m10_1 0.147120476  0.44786682 -0.07927802 -0.014750053 -0.02375331
## m11_1 0.005738494  0.42949554 -0.13670224 -0.102223573  0.20306288
## m12_1 0.217568686  0.34462883 -0.30071384 -0.226679374 -0.09616934
## m13_1 0.335097512 -0.02289354 -0.12580506 -0.063186850 -0.08969855
## m14_1 0.388030201  0.01562976  0.07053289  0.053741807 -0.08955213
## m15_1 0.395778413 -0.04612496 -0.37390479  0.010101754 -0.01144027
## m16_1 0.393342071 -0.09486294  0.06561313  0.269318848 -0.04796831
## m17_1 0.489921093 -0.07066061 -0.13064684  0.002640702 -0.48209353
## m18_1 0.390928716 -0.13558550 -0.01027756  0.221978830 -0.02823991
## m19_1 0.427357954 -0.16654696 -0.32759560  0.169550515  0.33322804
## m20_1 0.394920947 -0.03716696 -0.32064858 -0.091102236  0.16135860
## m21_1 0.365440901 -0.14988091 -0.05980224  0.192576037  0.23000845
## m22_1 0.302840536  0.24101172 -0.28248464 -0.318557372 -0.01146261
## m23_1 0.287199892 -0.09327097  0.17936355  0.051182592 -0.12930746

Ortak Varyans Kats.

out8
## Factor Analysis using method =  pa
## Call: fa(r = afadata, nfactors = 5, rotate = "none", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
##        PA1   PA2   PA3   PA4   PA5    h2   u2 com
## m1_1  0.40 -0.03  0.41 -0.29  0.05 0.412 0.59 2.8
## m2_1  0.40  0.00  0.53 -0.35  0.15 0.587 0.41 2.9
## m3_1  0.24  0.07  0.22  0.03  0.09 0.122 0.88 2.4
## m4_1  0.19  0.04  0.17  0.09  0.10 0.082 0.92 3.1
## m5_1  0.20  0.09  0.15  0.17  0.04 0.102 0.90 3.4
## m6_1  0.31  0.12  0.28  0.03 -0.07 0.192 0.81 2.4
## m7_1  0.08  0.33  0.36  0.19  0.01 0.280 0.72 2.6
## m8_1  0.00  0.35  0.08  0.23 -0.09 0.190 0.81 2.0
## m9_1  0.00  0.77 -0.03  0.19  0.03 0.629 0.37 1.1
## m10_1 0.15  0.45 -0.08 -0.01 -0.02 0.229 0.77 1.3
## m11_1 0.01  0.43 -0.14 -0.10  0.20 0.255 0.75 1.8
## m12_1 0.22  0.34 -0.30 -0.23 -0.10 0.317 0.68 3.7
## m13_1 0.34 -0.02 -0.13 -0.06 -0.09 0.141 0.86 1.5
## m14_1 0.39  0.02  0.07  0.05 -0.09 0.167 0.83 1.2
## m15_1 0.40 -0.05 -0.37  0.01 -0.01 0.299 0.70 2.0
## m16_1 0.39 -0.09  0.07  0.27 -0.05 0.243 0.76 2.0
## m17_1 0.49 -0.07 -0.13  0.00 -0.48 0.495 0.51 2.2
## m18_1 0.39 -0.14 -0.01  0.22 -0.03 0.221 0.78 1.9
## m19_1 0.43 -0.17 -0.33  0.17  0.33 0.457 0.54 3.6
## m20_1 0.39 -0.04 -0.32 -0.09  0.16 0.294 0.71 2.4
## m21_1 0.37 -0.15 -0.06  0.19  0.23 0.250 0.75 2.8
## m22_1 0.30  0.24 -0.28 -0.32 -0.01 0.331 0.67 3.9
## m23_1 0.29 -0.09  0.18  0.05 -0.13 0.143 0.86 2.5
## 
##                        PA1  PA2  PA3  PA4  PA5
## SS loadings           2.24 1.51 1.38 0.74 0.57
## Proportion Var        0.10 0.07 0.06 0.03 0.02
## Cumulative Var        0.10 0.16 0.22 0.26 0.28
## Proportion Explained  0.35 0.24 0.21 0.11 0.09
## Cumulative Proportion 0.35 0.58 0.80 0.91 1.00
## 
## Mean item complexity =  2.4
## Test of the hypothesis that 5 factors are sufficient.
## 
## df null model =  253  with the objective function =  3.17 with Chi Square =  929.09
## df of  the model are 148  and the objective function was  0.52 
## 
## The root mean square of the residuals (RMSR) is  0.03 
## The df corrected root mean square of the residuals is  0.04 
## 
## The harmonic n.obs is  303 with the empirical chi square  164.38  with prob <  0.17 
## The total n.obs was  303  with Likelihood Chi Square =  151.94  with prob <  0.4 
## 
## Tucker Lewis Index of factoring reliability =  0.99
## RMSEA index =  0.009  and the 90 % confidence intervals are  0 0.029
## BIC =  -693.7
## Fit based upon off diagonal values = 0.93
## Measures of factor score adequacy             
##                                                    PA1  PA2  PA3  PA4   PA5
## Correlation of (regression) scores with factors   0.88 0.86 0.83 0.74  0.71
## Multiple R square of scores with factors          0.77 0.74 0.69 0.54  0.50
## Minimum correlation of possible factor scores     0.54 0.48 0.38 0.08 -0.01

Tüm değerler kötü ama deneme yapıyoruz sonuçta. O yüzden bir de açıklanan varyansa bakalım

sum(out8$loadings[,1]^2)/23*100
## [1] 9.72521

İlk boyut neredeyse varyansın onda birini açıklıyor. Diğerlerine de bakalım.

sum(out8$loadings[,2]^2)/23*100
## [1] 6.580498
sum(out8$loadings[,3]^2)/23*100
## [1] 6.011768
sum(out8$loadings[,4]^2)/23*100
## [1] 3.197156
sum(out8$loadings[,5]^2)/23*100
## [1] 2.475

Üretilen ve artık korelasyon matrislerine bakalım.

factor.model(out8$loadings)
##               m1_1         m2_1         m3_1         m4_1         m5_1
## m1_1   0.411809544  0.483885724  0.182610914  0.120334051  0.094223654
## m2_1   0.483885724  0.587385810  0.219033893  0.146336309  0.109505267
## m3_1   0.182610914  0.219033893  0.121882682  0.096333175  0.097502641
## m4_1   0.120334051  0.146336309  0.096333175  0.082257838  0.086147108
## m5_1   0.094223654  0.109505267  0.097502641  0.086147108  0.101505682
## m6_1   0.218243353  0.246129266  0.139587417  0.104330666  0.117144026
## m7_1   0.115133406  0.159547975  0.128720332  0.106686518  0.132376561
## m8_1  -0.047705260 -0.049641437  0.040528830  0.038927772  0.076731964
## m9_1  -0.086800730 -0.072356324  0.054480820  0.045480475  0.095024328
## m10_1  0.014739952  0.018647298  0.046153714  0.027616358  0.052246791
## m11_1 -0.027898377 -0.002004467  0.014645546  0.005343330  0.008834008
## m12_1  0.013489218 -0.007322066 -0.004651646 -0.026583533 -0.015111625
## m13_1  0.097002859  0.074884193  0.043120409  0.026049413  0.031647582
## m14_1  0.163155957  0.158814770  0.105447524  0.080880297  0.095350060
## m15_1  0.003785088 -0.046246323  0.009914180  0.009297014  0.019515682
## m16_1  0.106920789  0.088551329  0.107519797  0.100448661  0.124142753
## m17_1  0.119745017  0.049754669  0.044857294  0.019598502  0.051544062
## m18_1  0.091019227  0.067067855  0.087739705  0.083393088  0.101467973
## m19_1  0.010622335 -0.012157358  0.053591960  0.066759340  0.064729647
## m20_1  0.062665129  0.044134891  0.034244186  0.026264443  0.019052168
## m21_1  0.082590675  0.081064137  0.090864128  0.092589221  0.094084019
## m22_1  0.089092362  0.081623619  0.018080336 -0.011541560 -0.015600466
## m23_1  0.169549307  0.170994255  0.094147854  0.071971876  0.080243100
##               m6_1          m7_1         m8_1        m9_1        m10_1
## m1_1   0.218243353  0.1151334055 -0.047705260 -0.08680073  0.014739952
## m2_1   0.246129266  0.1595479748 -0.049641437 -0.07235632  0.018647298
## m3_1   0.139587417  0.1287203323  0.040528830  0.05448082  0.046153714
## m4_1   0.104330666  0.1066865180  0.038927772  0.04548047  0.027616358
## m5_1   0.117144026  0.1323765611  0.076731964  0.09502433  0.052246791
## m6_1   0.191562092  0.1698395277  0.078800057  0.08946689  0.077684908
## m7_1   0.169839528  0.2801559424  0.186957377  0.28123428  0.129200454
## m8_1   0.078800057  0.1869573774  0.190263266  0.30967816  0.151244124
## m9_1   0.089466894  0.2812342765  0.309678164  0.62907795  0.343854076
## m10_1  0.077684908  0.1292004541  0.151244124  0.34385408  0.229295915
## m11_1 -0.003015458  0.0772430130  0.099978126  0.32129326  0.200722922
## m12_1  0.023715532 -0.0190257004  0.055872602  0.22863252  0.215824499
## m13_1  0.069690775 -0.0373179954 -0.023673626 -0.02785145  0.052082672
## m14_1  0.148876309  0.0721254405  0.032076230  0.01869349  0.059829997
## m15_1  0.013763228 -0.1138061865 -0.041981210 -0.02317069  0.067334443
## m16_1  0.140358952  0.0753188399  0.037503394 -0.02484192  0.007347968
## m17_1  0.140499240 -0.0346915703  0.009091996 -0.06357934  0.062200670
## m18_1  0.110743408  0.0258586847  0.004612472 -0.06247296 -0.004999253
## m19_1  0.002793528 -0.0997986806 -0.075514253 -0.07693318  0.003837230
## m20_1  0.013549425 -0.1085418177 -0.072738404 -0.03129928  0.064386457
## m21_1  0.068064057 -0.0007819356 -0.034031251 -0.06999373 -0.016925815
## m22_1  0.033497681 -0.0556972475 -0.007388495  0.13407418  0.179861031
## m23_1  0.137836039  0.0654751090  0.004961908 -0.06992858 -0.011423043
##              m11_1        m12_1        m13_1       m14_1        m15_1
## m1_1  -0.027898377  0.013489218  0.097002859  0.16315596  0.003785088
## m2_1  -0.002004467 -0.007322066  0.074884193  0.15881477 -0.046246323
## m3_1   0.014645546 -0.004651646  0.043120409  0.10544752  0.009914180
## m4_1   0.005343330 -0.026583533  0.026049413  0.08088030  0.009297014
## m5_1   0.008834008 -0.015111625  0.031647582  0.09535006  0.019515682
## m6_1  -0.003015458  0.023715532  0.069690775  0.14887631  0.013763228
## m7_1   0.077243013 -0.019025700 -0.037317995  0.07212544 -0.113806186
## m8_1   0.099978126  0.055872602 -0.023673626  0.03207623 -0.041981210
## m9_1   0.321293263  0.228632522 -0.027851446  0.01869349 -0.023170689
## m10_1  0.200722922  0.215824499  0.052082672  0.05983000  0.067334443
## m11_1  0.254871041  0.194016870 -0.002467144 -0.02438077  0.030218599
## m12_1  0.194016870  0.317166061  0.125797681  0.06502948  0.181461690
## m13_1 -0.002467144  0.125797681  0.140679777  0.12543366  0.181107316
## m14_1 -0.024380775  0.065029482  0.125433661  0.16669438  0.128047858
## m15_1  0.030218599  0.181461690  0.181107316  0.12804786  0.298805781
## m16_1 -0.084726798 -0.023280312  0.113010511  0.17454315  0.138788148
## m17_1 -0.107842534  0.167291141  0.225301277  0.22309929  0.251550848
## m18_1 -0.083011005 -0.006184429  0.123903177  0.16330656  0.167383301
## m19_1  0.026038456  0.063615434  0.147629183  0.11938911  0.297211126
## m20_1  0.072215327  0.174670341  0.164809953  0.11069807  0.275141269
## m21_1 -0.027080633 -0.019934202  0.100613366  0.12499312  0.173221211
## m22_1  0.174104028  0.307207982  0.152658312  0.08526043  0.211276598
## m23_1 -0.094420385 -0.022761893  0.084175055  0.13696586  0.052901092
##              m16_1        m17_1        m18_1        m19_1       m20_1
## m1_1   0.106920789  0.119745017  0.091019227  0.010622335  0.06266513
## m2_1   0.088551329  0.049754669  0.067067855 -0.012157358  0.04413489
## m3_1   0.107519797  0.044857294  0.087739705  0.053591960  0.03424419
## m4_1   0.100448661  0.019598502  0.083393088  0.066759340  0.02626444
## m5_1   0.124142753  0.051544062  0.101467973  0.064729647  0.01905217
## m6_1   0.140358952  0.140499240  0.110743408  0.002793528  0.01354943
## m7_1   0.075318840 -0.034691570  0.025858685 -0.099798681 -0.10854182
## m8_1   0.037503394  0.009091996  0.004612472 -0.075514253 -0.07273840
## m9_1  -0.024841923 -0.063579340 -0.062472964 -0.076933178 -0.03129928
## m10_1  0.007347968  0.062200670 -0.004999253  0.003837230  0.06438646
## m11_1 -0.084726798 -0.107842534 -0.083011005  0.026038456  0.07221533
## m12_1 -0.023280312  0.167291141 -0.006184429  0.063615434  0.17467034
## m13_1  0.113010511  0.225301277  0.123903177  0.147629183  0.16480995
## m14_1  0.174543147  0.223099292  0.163306560  0.119389109  0.11069807
## m15_1  0.138788148  0.251550848  0.167383301  0.297211126  0.27514127
## m16_1  0.242855646  0.214673903  0.227094110  0.192081187  0.10555038
## m17_1  0.214673903  0.494505337  0.216647965  0.103739968  0.15996756
## m18_1  0.227094110  0.216647965  0.221386411  0.221241031  0.13794121
## m19_1  0.192081187  0.103739968  0.221241031  0.457479892  0.31832849
## m20_1  0.105550384  0.159967556  0.137941206  0.318328493  0.29449566
## m21_1  0.194868853  0.087063806  0.200050029  0.310023870  0.18863612
## m22_1 -0.007521521  0.172928495  0.018225332  0.123991037  0.22839039
## m23_1  0.153571461  0.186336036  0.138090539  0.045101606  0.03384746
##               m21_1         m22_1         m23_1
## m1_1   0.0825906752  0.0890923623  0.1695493075
## m2_1   0.0810641375  0.0816236190  0.1709942550
## m3_1   0.0908641280  0.0180803358  0.0941478536
## m4_1   0.0925892213 -0.0115415600  0.0719718759
## m5_1   0.0940840186 -0.0156004658  0.0802430999
## m6_1   0.0680640570  0.0334976811  0.1378360390
## m7_1  -0.0007819356 -0.0556972475  0.0654751090
## m8_1  -0.0340312505 -0.0073884951  0.0049619080
## m9_1  -0.0699937267  0.1340741831 -0.0699285849
## m10_1 -0.0169258149  0.1798610307 -0.0114230430
## m11_1 -0.0270806333  0.1741040283 -0.0944203854
## m12_1 -0.0199342019  0.3072079824 -0.0227618928
## m13_1  0.1006133665  0.1526583121  0.0841750548
## m14_1  0.1249931155  0.0852604258  0.1369658620
## m15_1  0.1732212108  0.2112765977  0.0529010920
## m16_1  0.1948688531 -0.0075215208  0.1535714606
## m17_1  0.0870638056  0.1729284948  0.1863360360
## m18_1  0.2000500292  0.0182253321  0.1380905387
## m19_1  0.3100238696  0.1239910369  0.0451016058
## m20_1  0.1886361216  0.2283903932  0.0338474635
## m21_1  0.2495770676  0.0274574615  0.0883225145
## m22_1  0.0274574615  0.3312067980 -0.0009934671
## m23_1  0.0883225145 -0.0009934671  0.1426946148

çıkarılan ortak varyanslara da bakalım

rep_matrix <- factor.model(out8$loadings)
diag(rep_matrix)
##       m1_1       m2_1       m3_1       m4_1       m5_1       m6_1       m7_1 
## 0.41180954 0.58738581 0.12188268 0.08225784 0.10150568 0.19156209 0.28015594 
##       m8_1       m9_1      m10_1      m11_1      m12_1      m13_1      m14_1 
## 0.19026327 0.62907795 0.22929591 0.25487104 0.31716606 0.14067978 0.16669438 
##      m15_1      m16_1      m17_1      m18_1      m19_1      m20_1      m21_1 
## 0.29880578 0.24285565 0.49450534 0.22138641 0.45747989 0.29449566 0.24957707 
##      m22_1      m23_1 
## 0.33120680 0.14269461

Faktörlerin Yorumlanması

out8$loadings
## 
## Loadings:
##       PA1    PA2    PA3    PA4    PA5   
## m1_1   0.399         0.407 -0.288       
## m2_1   0.398         0.530 -0.353  0.155
## m3_1   0.245         0.222              
## m4_1   0.187         0.167              
## m5_1   0.201         0.154  0.167       
## m6_1   0.307  0.119  0.277              
## m7_1          0.331  0.358  0.188       
## m8_1          0.354         0.225       
## m9_1          0.770         0.186       
## m10_1  0.147  0.448                     
## m11_1         0.429 -0.137 -0.102  0.203
## m12_1  0.218  0.345 -0.301 -0.227       
## m13_1  0.335        -0.126              
## m14_1  0.388                            
## m15_1  0.396        -0.374              
## m16_1  0.393                0.269       
## m17_1  0.490        -0.131        -0.482
## m18_1  0.391 -0.136         0.222       
## m19_1  0.427 -0.167 -0.328  0.170  0.333
## m20_1  0.395        -0.321         0.161
## m21_1  0.365 -0.150         0.193  0.230
## m22_1  0.303  0.241 -0.282 -0.319       
## m23_1  0.287         0.179        -0.129
## 
##                  PA1   PA2   PA3   PA4   PA5
## SS loadings    2.237 1.514 1.383 0.735 0.569
## Proportion Var 0.097 0.066 0.060 0.032 0.025
## Cumulative Var 0.097 0.163 0.223 0.255 0.280

Ciddi dercede fazlaca sorun var. Ortak yük veren maddeler, çok düşük yük verenler vs. Hangi birini çözeceğimi, analiz dışı bırakacağımı bilmediğimden devam ediyorum.

Dik Döndürme deneyeceğim bir de

outvari <- fa(afadata, 5, fm="pa", rotate="varimax")
print(outvari$loadings[,1:5], digits = 3, cut = 0.30)
##            PA3      PA4      PA2     PA5      PA1
## m1_1   0.61649  0.09088 -0.10694 -0.0122  0.10912
## m2_1   0.75552  0.07519 -0.09879 -0.0339  0.00277
## m3_1   0.30988 -0.01097  0.10966  0.1053  0.05120
## m4_1   0.21940 -0.05595  0.10867  0.1349  0.03144
## m5_1   0.18219 -0.06434  0.18978  0.1418  0.08964
## m6_1   0.34792  0.00924  0.17329  0.0253  0.19940
## m7_1   0.27668 -0.11620  0.43223 -0.0569  0.00596
## m8_1  -0.01131 -0.00784  0.42990 -0.0539  0.04851
## m9_1  -0.02837  0.26039  0.73216 -0.0655 -0.14189
## m10_1  0.03920  0.31642  0.35695 -0.0149 -0.00180
## m11_1  0.00201  0.32724  0.27136  0.0168 -0.27177
## m12_1 -0.04760  0.54182  0.12929 -0.0145  0.06635
## m13_1  0.07523  0.22735 -0.05621  0.1551  0.23686
## m14_1  0.21654  0.09198  0.07053  0.1629  0.28256
## m15_1 -0.08844  0.32665 -0.07519  0.3556  0.22840
## m16_1  0.15053 -0.08314  0.09256  0.3151  0.32468
## m17_1  0.03707  0.24294 -0.03917  0.0648  0.65451
## m18_1  0.10905 -0.03518  0.02088  0.3382  0.30567
## m19_1 -0.01463  0.15233 -0.09529  0.6511  0.03264
## m20_1  0.02421  0.35571 -0.12117  0.3852  0.06562
## m21_1  0.12658 -0.01696 -0.02600  0.4750  0.08358
## m22_1  0.05335  0.56855 -0.00341  0.0559  0.04442
## m23_1  0.23294 -0.05285 -0.00631  0.0717  0.28365

EGA

library(EGAnet); library(psychTools)
## Warning: package 'EGAnet' was built under R version 4.3.3
## 
## EGAnet (version 2.2.0) 
## 
## For help getting started, see <https://r-ega.net> 
## 
## For bugs and errors, submit an issue to <https://github.com/hfgolino/EGAnet/issues>
## Warning: package 'psychTools' was built under R version 4.3.3
## 
## Attaching package: 'psychTools'
## The following object is masked from 'package:dplyr':
## 
##     recode
bfi_uva <- UVA(
  data = afadata
)
# Print results
bfi_uva$keep_remove
## $keep
## [1] "m1_1" "m8_1"
## 
## $remove
## [1] "m2_1" "m9_1"
EGA(afadata)

## Model: GLASSO (EBIC with gamma = 0)
## Correlations: auto
## Lambda: 0.112521046460677 (n = 100, ratio = 0.1)
## 
## Number of nodes: 23
## Number of edges: 81
## Edge density: 0.320
## 
## Non-zero edge weights: 
##      M    SD    Min   Max
##  0.068 0.071 -0.066 0.458
## 
## ----
## 
## Algorithm:  Walktrap
## 
## Number of communities:  4
## 
##  m1_1  m2_1  m3_1  m4_1  m5_1  m6_1  m7_1  m8_1  m9_1 m10_1 m11_1 m12_1 m13_1 
##     1     1     1     1     1     1     1     2     2     2     2     3     4 
## m14_1 m15_1 m16_1 m17_1 m18_1 m19_1 m20_1 m21_1 m22_1 m23_1 
##     1     4     4     4     4     4     4     4     3     1 
## 
## ----
## 
## Unidimensional Method: Louvain
## Unidimensional: No
## 
## ----
## 
## TEFI: -18.227

Açımlayıcı Grafik Analizi de incelendiğinde 4 boyutlu bir yapı görülmekte. Her metot ve her döndürme yöntemi kafamı ayrı ayrı karıştırdığından bu işlemleri bu noktada bitiriyorum. Bu denemeler ders materyalleri kullanılarak kodlarda akıcılık kazanmak için yapılmıştır. Bana derste öğretilen bundan çok daha fazlası ve doğru bilgilerdir :)