Factor Analysis
updragon
2018년 9월 6일
요인 분석
참고 논문양식 : 이주성(2016). 경영학전공 대학생의 전공만족도와 진로결정 자기효능감이 진로준비행동에 미치는 영향
패키지 불러오기
# echo=TRUE : 코드를 평가하고 실행결과를 포함한다
# eval=TRUE : 실행결과와 함게 코드를 출력한다
# message=FALSE : 메시지를 출력한다
# warning=TRUE : 경고메시지를 출력한다
# error=FALSE : 오류메시지를 출력한다
# tidy=FALSE : 깔끔한 방식으로 코드 형태를 변형한다
# 그림 삽입
# {r echo=FALSE, out.width='50%'}
# knitr::include_graphics('./pic.png')
library(readxl)
library(psych)
library(jmv)데이터 불러오기
# data loading
setwd("C:/Users/user/Desktop/krivet")
edu <- read_excel("data_merge_3_na.xlsx")
str(edu)## Classes 'tbl_df', 'tbl' and 'data.frame': 312 obs. of 22 variables:
## $ satisfaction55: num 4 4 4 5 4 4 4 4 2 3 ...
## $ facilities79_1: num 4 4 4 4 3 1 4 3 1 3 ...
## $ facilities80_2: num 4 4 4 2 3 2 3 4 1 3 ...
## $ facilities81_3: num 4 4 5 3 3 3 3 4 1 3 ...
## $ facilities82_4: num 4 4 5 3 3 2 3 4 1 3 ...
## $ ralation84_1 : num 4 4 4 3 3 1 3 4 1 3 ...
## $ pride85_1 : num 4 4 4 3 4 3 4 4 1 3 ...
## $ pride86_2 : num 4 4 5 3 4 3 4 4 1 3 ...
## $ schoollife87_1: num 4 4 4 3 4 4 2 4 1 3 ...
## $ schoollife88_2: num 4 4 4 3 3 1 4 4 1 3 ...
## $ schoollife89_3: num 3 4 4 3 3 2 4 4 1 3 ...
## $ schoollife90_4: num 4 4 3 3 4 3 4 4 1 3 ...
## $ schoollife91_5: num 4 4 4 3 4 4 4 4 1 3 ...
## $ schoollife92_6: num 4 4 4 3 4 4 4 4 3 4 ...
## $ schoollife93_7: num 4 4 4 1 3 3 3 4 1 3 ...
## $ class94_1 : num 4 4 4 3 4 4 4 4 3 3 ...
## $ class95_2 : num 4 4 4 3 4 4 4 4 2 3 ...
## $ class96_3 : num 4 4 4 3 4 3 4 4 2 3 ...
## $ class97_4 : num 4 4 4 3 4 3 4 4 2 4 ...
## $ class98_5 : num 4 4 4 3 4 5 4 4 3 4 ...
## $ class99_6 : num 4 4 4 3 4 5 3 4 3 4 ...
## $ prof102_1 : num 1 1 2 2 1 1 1 1 1 1 ...summary(edu)## satisfaction55 facilities79_1 facilities80_2 facilities81_3
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000
## Median :4.000 Median :4.000 Median :4.000 Median :4.000
## Mean :3.872 Mean :3.583 Mean :3.506 Mean :3.609
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## facilities82_4 ralation84_1 pride85_1 pride86_2
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000
## Median :4.000 Median :4.000 Median :3.000 Median :4.000
## Mean :3.622 Mean :3.712 Mean :3.465 Mean :3.679
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## schoollife87_1 schoollife88_2 schoollife89_3 schoollife90_4
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000
## Median :3.000 Median :3.000 Median :3.000 Median :4.000
## Mean :3.359 Mean :3.442 Mean :3.279 Mean :3.583
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## schoollife91_5 schoollife92_6 schoollife93_7 class94_1
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:2.000 1st Qu.:3.000
## Median :3.000 Median :4.000 Median :3.000 Median :4.000
## Mean :3.388 Mean :3.619 Mean :2.955 Mean :3.766
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## class95_2 class96_3 class97_4 class98_5
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000 1st Qu.:3.000
## Median :4.000 Median :4.000 Median :4.000 Median :4.000
## Mean :3.756 Mean :3.846 Mean :3.798 Mean :3.715
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## class99_6 prof102_1
## Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:1.000
## Median :4.000 Median :2.000
## Mean :3.827 Mean :1.721
## 3rd Qu.:4.000 3rd Qu.:2.000
## Max. :5.000 Max. :5.000# 종속변수 factor 변환
edu$satisfaction55 <- as.factor(edu$satisfaction55)설문문항의 타당도와 신뢰도 검증
탐색적 요인분석 1
# KMO & Bartlett 검정
# 이를 통해 알 수 있는 것은, 우리가 분석하고 하는 요인분석이 타당하다는 것을 말해준다.
# 즉, KMO는 0~1사이의 값으로 추출되는데, 전체의 상관성과 부분의 상관성을 비교하여 나타낸 지표이다.
# 이 값은 0.6이상이 되어야 한다.
edu_kmo <- edu[,-1] # 종속변수 제거
str(edu_kmo) # edu_kmo_cor <- cor(edu_kmo)## Classes 'tbl_df', 'tbl' and 'data.frame': 312 obs. of 21 variables:
## $ facilities79_1: num 4 4 4 4 3 1 4 3 1 3 ...
## $ facilities80_2: num 4 4 4 2 3 2 3 4 1 3 ...
## $ facilities81_3: num 4 4 5 3 3 3 3 4 1 3 ...
## $ facilities82_4: num 4 4 5 3 3 2 3 4 1 3 ...
## $ ralation84_1 : num 4 4 4 3 3 1 3 4 1 3 ...
## $ pride85_1 : num 4 4 4 3 4 3 4 4 1 3 ...
## $ pride86_2 : num 4 4 5 3 4 3 4 4 1 3 ...
## $ schoollife87_1: num 4 4 4 3 4 4 2 4 1 3 ...
## $ schoollife88_2: num 4 4 4 3 3 1 4 4 1 3 ...
## $ schoollife89_3: num 3 4 4 3 3 2 4 4 1 3 ...
## $ schoollife90_4: num 4 4 3 3 4 3 4 4 1 3 ...
## $ schoollife91_5: num 4 4 4 3 4 4 4 4 1 3 ...
## $ schoollife92_6: num 4 4 4 3 4 4 4 4 3 4 ...
## $ schoollife93_7: num 4 4 4 1 3 3 3 4 1 3 ...
## $ class94_1 : num 4 4 4 3 4 4 4 4 3 3 ...
## $ class95_2 : num 4 4 4 3 4 4 4 4 2 3 ...
## $ class96_3 : num 4 4 4 3 4 3 4 4 2 3 ...
## $ class97_4 : num 4 4 4 3 4 3 4 4 2 4 ...
## $ class98_5 : num 4 4 4 3 4 5 4 4 3 4 ...
## $ class99_6 : num 4 4 4 3 4 5 3 4 3 4 ...
## $ prof102_1 : num 1 1 2 2 1 1 1 1 1 1 ...KMO(edu_kmo) ## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = edu_kmo)
## Overall MSA = 0.92
## MSA for each item =
## facilities79_1 facilities80_2 facilities81_3 facilities82_4 ralation84_1
## 0.92 0.87 0.88 0.89 0.93
## pride85_1 pride86_2 schoollife87_1 schoollife88_2 schoollife89_3
## 0.90 0.90 0.92 0.87 0.94
## schoollife90_4 schoollife91_5 schoollife92_6 schoollife93_7 class94_1
## 0.96 0.95 0.93 0.93 0.92
## class95_2 class96_3 class97_4 class98_5 class99_6
## 0.94 0.94 0.94 0.92 0.93
## prof102_1
## 0.85bartlett.test(edu_kmo)##
## Bartlett test of homogeneity of variances
##
## data: edu_kmo
## Bartlett's K-squared = 125.2, df = 20, p-value < 2.2e-16# fa <- fa(edu_kmo,4,fm="pa") # pa 주성분분석 방법
fa <- fa(edu_kmo,5,fm="wls") # wls 잔차제곱합 가중치 방법 , 5개 요인
# 요인분석 결과 요인별 최소 0.6이상끼리 변수 묶어서 하나 요인으로 결ㅈ
fa <- fa(edu_kmo,4,fm="wls") # 본 연구에는 요인 4개로 결정 아래 efa 함수 등 비교해서 결정
str(edu_kmo)## Classes 'tbl_df', 'tbl' and 'data.frame': 312 obs. of 21 variables:
## $ facilities79_1: num 4 4 4 4 3 1 4 3 1 3 ...
## $ facilities80_2: num 4 4 4 2 3 2 3 4 1 3 ...
## $ facilities81_3: num 4 4 5 3 3 3 3 4 1 3 ...
## $ facilities82_4: num 4 4 5 3 3 2 3 4 1 3 ...
## $ ralation84_1 : num 4 4 4 3 3 1 3 4 1 3 ...
## $ pride85_1 : num 4 4 4 3 4 3 4 4 1 3 ...
## $ pride86_2 : num 4 4 5 3 4 3 4 4 1 3 ...
## $ schoollife87_1: num 4 4 4 3 4 4 2 4 1 3 ...
## $ schoollife88_2: num 4 4 4 3 3 1 4 4 1 3 ...
## $ schoollife89_3: num 3 4 4 3 3 2 4 4 1 3 ...
## $ schoollife90_4: num 4 4 3 3 4 3 4 4 1 3 ...
## $ schoollife91_5: num 4 4 4 3 4 4 4 4 1 3 ...
## $ schoollife92_6: num 4 4 4 3 4 4 4 4 3 4 ...
## $ schoollife93_7: num 4 4 4 1 3 3 3 4 1 3 ...
## $ class94_1 : num 4 4 4 3 4 4 4 4 3 3 ...
## $ class95_2 : num 4 4 4 3 4 4 4 4 2 3 ...
## $ class96_3 : num 4 4 4 3 4 3 4 4 2 3 ...
## $ class97_4 : num 4 4 4 3 4 3 4 4 2 4 ...
## $ class98_5 : num 4 4 4 3 4 5 4 4 3 4 ...
## $ class99_6 : num 4 4 4 3 4 5 3 4 3 4 ...
## $ prof102_1 : num 1 1 2 2 1 1 1 1 1 1 ...edu_kmo_1 <- edu_kmo[, c("facilities80_2","facilities81_3","facilities82_4",
"pride85_1","pride86_2","schoollife87_1","schoollife88_2","schoollife89_3",
"class94_1","class95_2","class96_3","class97_4","class98_5","class99_6")]
KMO(edu_kmo_1) # 일반적 0.6 이상## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = edu_kmo_1)
## Overall MSA = 0.9
## MSA for each item =
## facilities80_2 facilities81_3 facilities82_4 pride85_1 pride86_2
## 0.87 0.83 0.88 0.88 0.89
## schoollife87_1 schoollife88_2 schoollife89_3 class94_1 class95_2
## 0.90 0.85 0.92 0.91 0.93
## class96_3 class97_4 class98_5 class99_6
## 0.92 0.92 0.91 0.90bartlett.test(edu_kmo_1) # baartlett 검정 (값+유의확률)##
## Bartlett test of homogeneity of variances
##
## data: edu_kmo_1
## Bartlett's K-squared = 81.441, df = 13, p-value = 5.906e-12#fa <- fa(edu_kmo_1,4,fm="wls") # 본 연구에는 요인 4개로 결정 아래 efa 함수 등 비교해서 결정
fa <- fa(edu_kmo_1,4,fm="pa")
fa # 요인별 고유값, 누적설명비율을 볼수 있다. ## Factor Analysis using method = pa
## Call: fa(r = edu_kmo_1, nfactors = 4, fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA1 PA2 PA3 PA4 h2 u2 com
## facilities80_2 0.01 0.78 0.03 -0.05 0.61 0.39 1.0
## facilities81_3 -0.01 0.84 -0.08 0.09 0.71 0.29 1.0
## facilities82_4 0.04 0.70 0.08 -0.03 0.55 0.45 1.0
## pride85_1 -0.03 0.04 0.06 0.87 0.82 0.18 1.0
## pride86_2 0.22 0.00 0.07 0.61 0.62 0.38 1.3
## schoollife87_1 0.03 0.05 0.67 0.13 0.61 0.39 1.1
## schoollife88_2 0.01 -0.03 0.93 0.01 0.87 0.13 1.0
## schoollife89_3 0.05 0.12 0.61 0.08 0.54 0.46 1.1
## class94_1 0.92 -0.05 -0.15 0.10 0.78 0.22 1.1
## class95_2 0.77 0.02 0.02 0.04 0.66 0.34 1.0
## class96_3 0.79 0.01 0.11 -0.05 0.69 0.31 1.0
## class97_4 0.74 0.08 0.17 -0.12 0.66 0.34 1.2
## class98_5 0.72 0.11 -0.01 0.01 0.59 0.41 1.0
## class99_6 0.73 0.00 0.09 0.04 0.64 0.36 1.0
##
## PA1 PA2 PA3 PA4
## SS loadings 3.96 1.98 2.03 1.40
## Proportion Var 0.28 0.14 0.15 0.10
## Cumulative Var 0.28 0.42 0.57 0.67
## Proportion Explained 0.42 0.21 0.22 0.15
## Cumulative Proportion 0.42 0.63 0.85 1.00
##
## With factor correlations of
## PA1 PA2 PA3 PA4
## PA1 1.00 0.44 0.53 0.55
## PA2 0.44 1.00 0.39 0.37
## PA3 0.53 0.39 1.00 0.49
## PA4 0.55 0.37 0.49 1.00
##
## Mean item complexity = 1.1
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 91 and the objective function was 8.93 with Chi Square of 2729.58
## The degrees of freedom for the model are 41 and the objective function was 0.47
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.04
##
## The harmonic number of observations is 312 with the empirical chi square 35.35 with prob < 0.72
## The total number of observations was 312 with Likelihood Chi Square = 142.29 with prob < 4.2e-13
##
## Tucker Lewis Index of factoring reliability = 0.914
## RMSEA index = 0.091 and the 90 % confidence intervals are 0.073 0.105
## BIC = -93.18
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## PA1 PA2 PA3 PA4
## Correlation of (regression) scores with factors 0.96 0.92 0.95 0.93
## Multiple R square of scores with factors 0.93 0.85 0.90 0.86
## Minimum correlation of possible factor scores 0.86 0.69 0.81 0.71plot(fa)
fa.diagram(fa) 
factanal(edu_kmo_1, factors = 4,rotation = "varimax" , scores = "regression")##
## Call:
## factanal(x = edu_kmo_1, factors = 4, scores = "regression", rotation = "varimax")
##
## Uniquenesses:
## facilities80_2 facilities81_3 facilities82_4 pride85_1 pride86_2
## 0.398 0.289 0.443 0.107 0.407
## schoollife87_1 schoollife88_2 schoollife89_3 class94_1 class95_2
## 0.389 0.121 0.473 0.207 0.316
## class96_3 class97_4 class98_5 class99_6
## 0.297 0.349 0.423 0.384
##
## Loadings:
## Factor1 Factor2 Factor3 Factor4
## facilities80_2 0.169 0.144 0.741
## facilities81_3 0.177 0.803 0.161
## facilities82_4 0.194 0.208 0.686
## pride85_1 0.258 0.288 0.180 0.843
## pride86_2 0.405 0.273 0.155 0.575
## schoollife87_1 0.263 0.676 0.189 0.222
## schoollife88_2 0.260 0.879 0.123 0.155
## schoollife89_3 0.252 0.610 0.236 0.188
## class94_1 0.846 0.110 0.238
## class95_2 0.758 0.209 0.171 0.190
## class96_3 0.764 0.271 0.167 0.132
## class97_4 0.705 0.314 0.228
## class98_5 0.682 0.158 0.243 0.169
## class99_6 0.696 0.274 0.160 0.174
##
## Factor1 Factor2 Factor3 Factor4
## SS loadings 3.849 2.154 2.033 1.360
## Proportion Var 0.275 0.154 0.145 0.097
## Cumulative Var 0.275 0.429 0.574 0.671
##
## Test of the hypothesis that 4 factors are sufficient.
## The chi square statistic is 139.72 on 41 degrees of freedom.
## The p-value is 1.07e-12탐색적 요인분석 2
# library(jmv)
efa(edu, vars = c("facilities79_1","facilities80_2","facilities81_3","facilities82_4",
"ralation84_1","pride85_1","pride86_2","schoollife87_1","schoollife88_2","schoollife89_3",
"schoollife90_4","schoollife91_5","schoollife92_6","schoollife93_7","class94_1","class95_2",
"class96_3","class97_4","class98_5","class99_6","prof102_1"))##
## EXPLORATORY FACTOR ANALYSIS
##
## Factor Loadings
## ─────────────────────────────────────────────────────────────────────────────
## 1 2 3 4 5 Uniqueness
## ─────────────────────────────────────────────────────────────────────────────
## facilities79_1 0.566 0.488
## facilities80_2 0.857 0.296
## facilities81_3 0.804 0.352
## facilities82_4 0.709 0.470
## ralation84_1 0.614
## pride85_1 0.888 0.217
## pride86_2 0.692 0.338
## schoollife87_1 0.669 0.385
## schoollife88_2 0.806 0.249
## schoollife89_3 0.693 0.378
## schoollife90_4 0.464 0.444
## schoollife91_5 0.518
## schoollife92_6 0.710 0.377
## schoollife93_7 0.361 0.350 0.744
## class94_1 0.653 0.235
## class95_2 0.581 0.340
## class96_3 0.837 0.212
## class97_4 0.645 0.329
## class98_5 0.645 0.281
## class99_6 0.336 0.452 0.343
## prof102_1 0.909
## ─────────────────────────────────────────────────────────────────────────────
## Note. 'oblimin' rotation was used# 제외 "facilities79_1", "schoollife93_7", "schoollife90_4" , "ralation84_1","prof102_1" "schoollife91_5","schoollife92_6",
efa(edu, vars = c("facilities80_2","facilities81_3","facilities82_4",
"pride85_1","pride86_2","schoollife87_1","schoollife88_2","schoollife89_3",
"class94_1","class95_2","class96_3","class97_4","class98_5","class99_6"))##
## EXPLORATORY FACTOR ANALYSIS
##
## Factor Loadings
## ────────────────────────────────────────────────────────────────────
## 1 2 3 4 Uniqueness
## ────────────────────────────────────────────────────────────────────
## facilities80_2 0.780 0.393
## facilities81_3 0.842 0.289
## facilities82_4 0.705 0.446
## pride85_1 0.906 0.124
## pride86_2 0.573 0.399
## schoollife87_1 0.671 0.386
## schoollife88_2 0.932 0.132
## schoollife89_3 0.608 0.461
## class94_1 0.926 0.216
## class95_2 0.767 0.340
## class96_3 0.788 0.311
## class97_4 0.731 0.344
## class98_5 0.717 0.409
## class99_6 0.729 0.360
## ────────────────────────────────────────────────────────────────────
## Note. 'oblimin' rotation was used# 신뢰도분석_알파
# library(jmv)
# vars 에 묶여진 문항의 전체 신뢰도계수 계산
a <- reliability(edu_kmo, vars = c("pride85_1","pride86_2"),omegaScale = TRUE)
a##
## RELIABILITY ANALYSIS
##
## Scale Reliability Statistics
## ─────────────────────────────────────────
## Cronbach's α McDonald's ω
## ─────────────────────────────────────────
## scale 0.821 0.822
## ─────────────────────────────────────────결과 도표
