library(psych)
library(moments)
library(lavaan)
library(reshape2)
library(tidyverse)
library(GPArotation)
匯入資料並命名為dta
data("bfi")
dta <- bfi
檢視資料結構
str(bfi)
## 'data.frame': 2800 obs. of 28 variables:
## $ A1 : int 2 2 5 4 2 6 2 4 4 2 ...
## $ A2 : int 4 4 4 4 3 6 5 3 3 5 ...
## $ A3 : int 3 5 5 6 3 5 5 1 6 6 ...
## $ A4 : int 4 2 4 5 4 6 3 5 3 6 ...
## $ A5 : int 4 5 4 5 5 5 5 1 3 5 ...
## $ C1 : int 2 5 4 4 4 6 5 3 6 6 ...
## $ C2 : int 3 4 5 4 4 6 4 2 6 5 ...
## $ C3 : int 3 4 4 3 5 6 4 4 3 6 ...
## $ C4 : int 4 3 2 5 3 1 2 2 4 2 ...
## $ C5 : int 4 4 5 5 2 3 3 4 5 1 ...
## $ E1 : int 3 1 2 5 2 2 4 3 5 2 ...
## $ E2 : int 3 1 4 3 2 1 3 6 3 2 ...
## $ E3 : int 3 6 4 4 5 6 4 4 NA 4 ...
## $ E4 : int 4 4 4 4 4 5 5 2 4 5 ...
## $ E5 : int 4 3 5 4 5 6 5 1 3 5 ...
## $ N1 : int 3 3 4 2 2 3 1 6 5 5 ...
## $ N2 : int 4 3 5 5 3 5 2 3 5 5 ...
## $ N3 : int 2 3 4 2 4 2 2 2 2 5 ...
## $ N4 : int 2 5 2 4 4 2 1 6 3 2 ...
## $ N5 : int 3 5 3 1 3 3 1 4 3 4 ...
## $ O1 : int 3 4 4 3 3 4 5 3 6 5 ...
## $ O2 : int 6 2 2 3 3 3 2 2 6 1 ...
## $ O3 : int 3 4 5 4 4 5 5 4 6 5 ...
## $ O4 : int 4 3 5 3 3 6 6 5 6 5 ...
## $ O5 : int 3 3 2 5 3 1 1 3 1 2 ...
## $ gender : int 1 2 2 2 1 2 1 1 1 2 ...
## $ education: int NA NA NA NA NA 3 NA 2 1 NA ...
## $ age : int 16 18 17 17 17 21 18 19 19 17 ...
擷取資料的第1 ~ 25個變項(題目1 ~ 25)
dta <- dta[, -c(26:28)]
轉換反向題
dta[, c("A1", "C4", "C5", "E1", "E2", "O2", "O5")] <- 7 - dta[, c("A1", "C4", "C5", "E1", "E2", "O2", "O5")]
Drop掉遺漏的資料
dta <- na.omit(dta)
平行分析 25 個題目背後的因素數目
需挑出特徵值大於1，因為表示此 factor
只能解釋非常少部分的變異量這對減少變數量並沒有什麼幫助
fa.parallel(dta[, 1:25], fa = "pc", show.legend = FALSE)
## Parallel analysis suggests that the number of factors = NA and the number of components = 5
得出此量表應該要有五個因素
因素負載量-因素對構念的影響
因素負載量越高代表此題越能反映子構念，意即越重要越好
print.psych(fa(dta[, 1:25], nfactor = 5, fm = "pa", rotate = "promax"), cut = .3)
## Factor Analysis using method = pa
## Call: fa(r = dta[, 1:25], nfactors = 5, rotate = "promax", fm = "pa")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PA2 PA1 PA3 PA5 PA4 h2 u2 com
## A1 0.46 0.20 0.80 1.4
## A2 0.61 0.46 0.54 1.1
## A3 0.62 0.54 0.46 1.3
## A4 0.41 0.30 0.70 2.0
## A5 0.33 0.49 0.47 0.53 1.8
## C1 0.57 0.35 0.65 1.2
## C2 0.70 0.45 0.55 1.2
## C3 0.60 0.32 0.68 1.1
## C4 0.65 0.48 0.52 1.2
## C5 0.56 0.44 0.56 1.4
## E1 0.64 0.35 0.65 1.1
## E2 0.71 0.55 0.45 1.1
## E3 0.55 0.44 0.56 1.6
## E4 0.66 0.54 0.46 1.3
## E5 0.50 0.41 0.59 1.8
## N1 0.84 0.68 0.32 1.3
## N2 0.79 0.61 0.39 1.2
## N3 0.74 0.54 0.46 1.0
## N4 0.53 -0.31 0.51 0.49 1.8
## N5 0.53 0.35 0.65 1.5
## O1 0.49 0.32 0.68 1.3
## O2 0.48 0.27 0.73 1.5
## O3 0.58 0.47 0.53 1.5
## O4 0.37 0.25 0.75 2.7
## O5 0.54 0.30 0.70 1.1
##
## PA2 PA1 PA3 PA5 PA4
## SS loadings 2.69 2.59 2.02 1.79 1.50
## Proportion Var 0.11 0.10 0.08 0.07 0.06
## Cumulative Var 0.11 0.21 0.29 0.36 0.42
## Proportion Explained 0.25 0.24 0.19 0.17 0.14
## Cumulative Proportion 0.25 0.50 0.69 0.86 1.00
##
## With factor correlations of
## PA2 PA1 PA3 PA5 PA4
## PA2 1.00 -0.26 -0.22 -0.01 0.04
## PA1 -0.26 1.00 0.40 0.35 0.14
## PA3 -0.22 0.40 1.00 0.24 0.19
## PA5 -0.01 0.35 0.24 1.00 0.16
## PA4 0.04 0.14 0.19 0.16 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 5 factors are sufficient.
##
## The degrees of freedom for the null model are 300 and the objective function was 7.48 with Chi Square of 18146.07
## The degrees of freedom for the model are 185 and the objective function was 0.64
##
## 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 number of observations is 2436 with the empirical chi square 1131.91 with prob < 1.1e-135
## The total number of observations was 2436 with Likelihood Chi Square = 1538.69 with prob < 8e-212
##
## Tucker Lewis Index of factoring reliability = 0.877
## RMSEA index = 0.055 and the 90 % confidence intervals are 0.052 0.057
## BIC = 96.03
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## PA2 PA1 PA3 PA5 PA4
## Correlation of (regression) scores with factors 0.93 0.91 0.89 0.87 0.84
## Multiple R square of scores with factors 0.86 0.83 0.79 0.75 0.70
## Minimum correlation of possible factor scores 0.72 0.66 0.58 0.51 0.40
cut = .3 不顯示.3以下的因素負載量
由圖可知
PA1外向性 (Extroversion)中因素負載量E2=0.71, E4=0.66,
E1=0.64為最高的三題，因此最能代表此向度。
PA2神經質 (Neuroticism)中因素負載量N1=0.84, N2=0.79,
N3=0.74為最高的三題，因此最能代表此向度。
PA3嚴謹性 (Conscientiousness)中因素負載量C2=0.70, C4=0.65,
C3=0.60為最高的三題，因此最能代表此向度。
PA4開放性 (Openness)中因素負載量O3=0.58, O5=0.54,
O1=0.49為最高的三題，因此最能代表此向度。
PA5親和性 (Agreeableness)中因素負載量A3=0.62, A2=0.61,
A5=0.49為最高的三題，因此最能代表此向度。