HW2 MVA
Vijola Spasovic
2025-01-27
The dataset used for this homework is Protestant Work Ethic Scale Responses, created by Lucas Greenwell. Retrieved from Kaggle: https://www.kaggle.com/datasets/lucasgreenwell/protestant-work-ethic-scale-responses?resource=download
I will be using the factor analysis method.
mydata <- read.table("~/data1.csv",
header = TRUE,
sep = ";")
head(mydata)## Q1A Q2A Q3A Q4A Q5A Q6A Q7A Q8A Q9A Q10A Q11A Q12A Q13A Q14A Q15A Q16A Q17A
## 1 4 1 5 5 5 2 4 3 5 5 3 4 2 3 5 2 5
## 2 4 4 4 5 4 2 5 2 2 2 4 4 4 2 2 4 4
## 3 3 3 4 2 2 3 3 2 3 3 4 3 3 4 4 3 3
## 4 4 2 4 4 1 4 5 5 5 5 4 4 2 5 5 5 5
## 5 4 1 5 1 1 1 5 5 5 2 1 2 5 5 5 4 2
## 6 1 1 2 1 5 1 5 1 5 3 2 4 4 4 5 4 3
## Q18A Q19A gender age religion
## 1 1 2 1 24 6
## 2 4 5 2 66 6
## 3 2 2 2 17 2
## 4 4 2 2 23 2
## 5 4 2 2 19 1
## 6 1 1 2 40 7All variables are measured on Likert scale (1: Disagree, 2: Slightly disagree, 3: Neutral, 4: Slightly agree, 5: Agree) for the following questions:
Q1A: Most people spend too much time in unprofitable amusements.
Q2A: Our society would have fewer problems if people had less leisure time.
Q3A: Money acquired easily (e.g. through gambling or speculation) is usually spent unwisely.
Q4A: There are few satisfactions equal to the realization that one has done one's best at a job.
Q5A: The most difficult college courses usually turn out to be the most rewarding.
Q6A: Most people who don’t succeed in life are just plain lazy.
Q7A: The self-made person is likely to be more ethical than someone who is born to wealth.
Q8A: I often feel I would be more successful if I sacrificed certain pleasures.
Q9A: People should have more leisure time to spend in relaxation.
Q10A: Anyone who is able and willing to work hard has a good chance of succeeding.
Q11A: People who fail at a job have usually not tried hard enough.
Q12A: Life would have very little meaning if we never had to suffer.
Q13A: Hard work offers little guarantee of success.
Q14A: The credit card is a ticket to careless spending.
Q15A: Life would be more meaningful if we had more leisure time.
Q16A: The person who can approach an unpleasant task with enthusiasm is the one who gets ahead.
Q17A: If one works hard enough they are likely to make a good life for themselves.
Q18A: I feel uneasy when there is little work for me to do.
Q19A: A distaste for hard work usually reflects a weakness of character.
Age.
Gender: 1=Male, 2=Female, 3=Other.
Religion: 1=Agnostic, 2=Atheist, 3=Buddhist, 4=Christian (Catholic), 5=Christian (Mormon), 6=Christian (Protestant), 7=Christian (Other), 8=Hindu, 9=Jewish, 10=Muslim, 11=Sikh, 12=Other.
mydata <- mydata[, -c(20,21,22)]Research Question:
““What are the underlying factors that shape individuals’ attitudes toward work according to the Protestant Work Ethic Scale?”
library(pastecs)
round(stat.desc(mydata, basic = FALSE), 2)## Q1A Q2A Q3A Q4A Q5A Q6A Q7A Q8A Q9A Q10A Q11A Q12A Q13A
## median 3.00 2.00 4.00 4.00 4.00 2.00 4.00 4.00 4.00 4.00 3.00 4.00 2.00
## mean 3.15 2.10 3.71 3.76 3.48 2.31 3.65 3.57 3.85 3.75 2.75 3.44 2.81
## SE.mean 0.04 0.04 0.03 0.04 0.04 0.04 0.04 0.04 0.03 0.04 0.04 0.04 0.04
## CI.mean.0.95 0.08 0.07 0.07 0.07 0.07 0.08 0.07 0.08 0.06 0.07 0.07 0.08 0.08
## var 2.07 1.70 1.65 1.73 1.91 2.00 1.88 1.98 1.42 1.91 1.97 2.14 2.02
## std.dev 1.44 1.31 1.28 1.31 1.38 1.41 1.37 1.41 1.19 1.38 1.40 1.46 1.42
## coef.var 0.46 0.62 0.35 0.35 0.40 0.61 0.38 0.39 0.31 0.37 0.51 0.43 0.50
## Q14A Q15A Q16A Q17A Q18A Q19A
## median 4.00 4.00 4.00 4.00 4.00 4.00
## mean 3.30 3.63 3.97 3.72 3.28 3.24
## SE.mean 0.04 0.04 0.03 0.04 0.04 0.04
## CI.mean.0.95 0.08 0.07 0.06 0.07 0.08 0.08
## var 2.14 1.75 1.33 1.77 2.23 2.20
## std.dev 1.46 1.32 1.15 1.33 1.49 1.48
## coef.var 0.44 0.36 0.29 0.36 0.46 0.46Q18A has the strongest variability.
sapply(mydata[-c(20, 21, 22)], FUN = min)## Q1A Q2A Q3A Q4A Q5A Q6A Q7A Q8A Q9A Q10A Q11A Q12A Q13A Q14A Q15A Q16A
## 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
## Q17A Q18A Q19A
## 0 0 0sapply(mydata[-c(20, 21, 22)], FUN = max)## Q1A Q2A Q3A Q4A Q5A Q6A Q7A Q8A Q9A Q10A Q11A Q12A Q13A Q14A Q15A Q16A
## 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
## Q17A Q18A Q19A
## 5 5 5mydata[mydata == 0] <- NA #Since I got minimum values 0s, which shouldn't be here since the Likert scale is 1-5, I replaced the 0s with NAs and omitted them.
mydata <- na.omit(mydata)
sapply(mydata[1:19], min)## Q1A Q2A Q3A Q4A Q5A Q6A Q7A Q8A Q9A Q10A Q11A Q12A Q13A Q14A Q15A Q16A
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## Q17A Q18A Q19A
## 1 1 1R <- cor(mydata[-c(20, 21, 22)])
library(psych)
corPlot(R)
det(R)## [1] 0.00266095Checking the determinant of correlation matrix. If it weren’t bigger than 0.0001, I’d have to remove variables with the highest correlation.
library(psych)
cortest.bartlett(R, n = nrow(mydata)) #Bartlett's test of sphericity## $chisq
## [1] 7949.897
##
## $p.value
## [1] 0
##
## $df
## [1] 171H₀: P = I
H₁: P ≠ I
df: (px(p-1))/2 = (19x18)/2 = 171
We reject H0 at p < 0.001.
library(psych)
KMO(R)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = R)
## Overall MSA = 0.92
## MSA for each item =
## Q1A Q2A Q3A Q4A Q5A Q6A Q7A Q8A Q9A Q10A Q11A Q12A Q13A Q14A Q15A Q16A
## 0.95 0.93 0.95 0.92 0.94 0.92 0.89 0.91 0.88 0.89 0.93 0.96 0.94 0.82 0.88 0.94
## Q17A Q18A Q19A
## 0.90 0.90 0.94library(psych)
fa.parallel(mydata,
sim = FALSE,
fa = "fa")
## Parallel analysis suggests that the number of factors = 5 and the number of components = NABased on the parallel analysis, it makes sense to extract 5 factors from the indicators.
library(psych)
library(GPArotation)##
## Attaching package: 'GPArotation'## The following objects are masked from 'package:psych':
##
## equamax, variminfactors <- fa(mydata,
covar = FALSE,
nfactors = 5,
fm = "minres",
rotate = "oblimin",
impute = "mean")print.psych(factors,
cut = 0.3,
sort = TRUE)## Factor Analysis using method = minres
## Call: fa(r = mydata, nfactors = 5, rotate = "oblimin", covar = FALSE,
## impute = "mean", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item MR1 MR2 MR5 MR4 MR3 h2 u2 com
## Q10A 10 0.86 0.72 0.28 1.0
## Q17A 17 0.76 0.72 0.28 1.0
## Q13A 13 -0.54 0.36 0.64 1.1
## Q16A 16 0.38 0.33 0.67 2.4
## Q9A 9 0.79 0.67 0.33 1.0
## Q15A 15 0.76 0.60 0.40 1.0
## Q2A 2 -0.43 0.32 0.46 0.54 2.1
## Q6A 6 0.76 0.67 0.33 1.0
## Q11A 11 0.59 0.52 0.48 1.2
## Q18A 18 0.62 0.37 0.63 1.1
## Q4A 4 0.57 0.43 0.57 1.1
## Q19A 19 0.40 0.50 0.50 2.0
## Q5A 5 0.17 0.83 2.0
## Q8A 8 0.51 0.29 0.71 1.2
## Q3A 3 0.37 0.29 0.71 1.5
## Q1A 1 0.37 0.45 0.55 2.3
## Q7A 7 0.33 0.15 0.85 1.4
## Q14A 14 0.11 0.89 3.0
## Q12A 12 0.26 0.74 2.5
##
## MR1 MR2 MR5 MR4 MR3
## SS loadings 2.10 1.76 1.51 1.44 1.27
## Proportion Var 0.11 0.09 0.08 0.08 0.07
## Cumulative Var 0.11 0.20 0.28 0.36 0.42
## Proportion Explained 0.26 0.22 0.19 0.18 0.16
## Cumulative Proportion 0.26 0.48 0.66 0.84 1.00
##
## With factor correlations of
## MR1 MR2 MR5 MR4 MR3
## MR1 1.00 -0.50 0.63 0.51 0.42
## MR2 -0.50 1.00 -0.54 -0.40 -0.36
## MR5 0.63 -0.54 1.00 0.42 0.49
## MR4 0.51 -0.40 0.42 1.00 0.47
## MR3 0.42 -0.36 0.49 0.47 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 171 with the objective function = 5.93 with Chi Square = 7949.9
## df of the model are 86 and the objective function was 0.14
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 1349 with the empirical chi square 131.91 with prob < 0.0011
## The total n.obs was 1349 with Likelihood Chi Square = 183.26 with prob < 5.3e-09
##
## Tucker Lewis Index of factoring reliability = 0.975
## RMSEA index = 0.029 and the 90 % confidence intervals are 0.023 0.035
## BIC = -436.55
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR5 MR4 MR3
## Correlation of (regression) scores with factors 0.93 0.90 0.89 0.84 0.80
## Multiple R square of scores with factors 0.87 0.82 0.79 0.70 0.64
## Minimum correlation of possible factor scores 0.73 0.63 0.59 0.40 0.29library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:pastecs':
##
## first, last## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionmydata1 <- mydata %>%
select(-c("Q1A", "Q19A", "Q5A", "Q16A", "Q12A"))library(psych)
fa.parallel(mydata1,
sim = FALSE,
fa = "fa")
## Parallel analysis suggests that the number of factors = 5 and the number of components = NAlibrary(psych)
library(GPArotation)
factors1 <- fa(mydata1,
covar = FALSE,
nfactors = 5,
fm = "minres",
rotate = "oblimin",
impute = "mean")
print.psych(factors,
cut = 0.3,
sort = TRUE)## Factor Analysis using method = minres
## Call: fa(r = mydata, nfactors = 5, rotate = "oblimin", covar = FALSE,
## impute = "mean", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item MR1 MR2 MR5 MR4 MR3 h2 u2 com
## Q10A 10 0.86 0.72 0.28 1.0
## Q17A 17 0.76 0.72 0.28 1.0
## Q13A 13 -0.54 0.36 0.64 1.1
## Q16A 16 0.38 0.33 0.67 2.4
## Q9A 9 0.79 0.67 0.33 1.0
## Q15A 15 0.76 0.60 0.40 1.0
## Q2A 2 -0.43 0.32 0.46 0.54 2.1
## Q6A 6 0.76 0.67 0.33 1.0
## Q11A 11 0.59 0.52 0.48 1.2
## Q18A 18 0.62 0.37 0.63 1.1
## Q4A 4 0.57 0.43 0.57 1.1
## Q19A 19 0.40 0.50 0.50 2.0
## Q5A 5 0.17 0.83 2.0
## Q8A 8 0.51 0.29 0.71 1.2
## Q3A 3 0.37 0.29 0.71 1.5
## Q1A 1 0.37 0.45 0.55 2.3
## Q7A 7 0.33 0.15 0.85 1.4
## Q14A 14 0.11 0.89 3.0
## Q12A 12 0.26 0.74 2.5
##
## MR1 MR2 MR5 MR4 MR3
## SS loadings 2.10 1.76 1.51 1.44 1.27
## Proportion Var 0.11 0.09 0.08 0.08 0.07
## Cumulative Var 0.11 0.20 0.28 0.36 0.42
## Proportion Explained 0.26 0.22 0.19 0.18 0.16
## Cumulative Proportion 0.26 0.48 0.66 0.84 1.00
##
## With factor correlations of
## MR1 MR2 MR5 MR4 MR3
## MR1 1.00 -0.50 0.63 0.51 0.42
## MR2 -0.50 1.00 -0.54 -0.40 -0.36
## MR5 0.63 -0.54 1.00 0.42 0.49
## MR4 0.51 -0.40 0.42 1.00 0.47
## MR3 0.42 -0.36 0.49 0.47 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 171 with the objective function = 5.93 with Chi Square = 7949.9
## df of the model are 86 and the objective function was 0.14
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 1349 with the empirical chi square 131.91 with prob < 0.0011
## The total n.obs was 1349 with Likelihood Chi Square = 183.26 with prob < 5.3e-09
##
## Tucker Lewis Index of factoring reliability = 0.975
## RMSEA index = 0.029 and the 90 % confidence intervals are 0.023 0.035
## BIC = -436.55
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR5 MR4 MR3
## Correlation of (regression) scores with factors 0.93 0.90 0.89 0.84 0.80
## Multiple R square of scores with factors 0.87 0.82 0.79 0.70 0.64
## Minimum correlation of possible factor scores 0.73 0.63 0.59 0.40 0.29library(dplyr)
mydata2 <- mydata %>%
select(-c("Q4A", "Q18A"))library(psych)
fa.parallel(mydata2,
sim = FALSE,
fa = "fa")
## Parallel analysis suggests that the number of factors = 4 and the number of components = NAlibrary(psych)
library(GPArotation)
factors2 <- fa(mydata2,
covar = FALSE,
nfactors = 4,
fm = "minres",
rotate = "oblimin",
impute = "mean")
print.psych(factors,
cut = 0.3,
sort = TRUE)## Factor Analysis using method = minres
## Call: fa(r = mydata, nfactors = 5, rotate = "oblimin", covar = FALSE,
## impute = "mean", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## item MR1 MR2 MR5 MR4 MR3 h2 u2 com
## Q10A 10 0.86 0.72 0.28 1.0
## Q17A 17 0.76 0.72 0.28 1.0
## Q13A 13 -0.54 0.36 0.64 1.1
## Q16A 16 0.38 0.33 0.67 2.4
## Q9A 9 0.79 0.67 0.33 1.0
## Q15A 15 0.76 0.60 0.40 1.0
## Q2A 2 -0.43 0.32 0.46 0.54 2.1
## Q6A 6 0.76 0.67 0.33 1.0
## Q11A 11 0.59 0.52 0.48 1.2
## Q18A 18 0.62 0.37 0.63 1.1
## Q4A 4 0.57 0.43 0.57 1.1
## Q19A 19 0.40 0.50 0.50 2.0
## Q5A 5 0.17 0.83 2.0
## Q8A 8 0.51 0.29 0.71 1.2
## Q3A 3 0.37 0.29 0.71 1.5
## Q1A 1 0.37 0.45 0.55 2.3
## Q7A 7 0.33 0.15 0.85 1.4
## Q14A 14 0.11 0.89 3.0
## Q12A 12 0.26 0.74 2.5
##
## MR1 MR2 MR5 MR4 MR3
## SS loadings 2.10 1.76 1.51 1.44 1.27
## Proportion Var 0.11 0.09 0.08 0.08 0.07
## Cumulative Var 0.11 0.20 0.28 0.36 0.42
## Proportion Explained 0.26 0.22 0.19 0.18 0.16
## Cumulative Proportion 0.26 0.48 0.66 0.84 1.00
##
## With factor correlations of
## MR1 MR2 MR5 MR4 MR3
## MR1 1.00 -0.50 0.63 0.51 0.42
## MR2 -0.50 1.00 -0.54 -0.40 -0.36
## MR5 0.63 -0.54 1.00 0.42 0.49
## MR4 0.51 -0.40 0.42 1.00 0.47
## MR3 0.42 -0.36 0.49 0.47 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 5 factors are sufficient.
##
## df null model = 171 with the objective function = 5.93 with Chi Square = 7949.9
## df of the model are 86 and the objective function was 0.14
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.02
##
## The harmonic n.obs is 1349 with the empirical chi square 131.91 with prob < 0.0011
## The total n.obs was 1349 with Likelihood Chi Square = 183.26 with prob < 5.3e-09
##
## Tucker Lewis Index of factoring reliability = 0.975
## RMSEA index = 0.029 and the 90 % confidence intervals are 0.023 0.035
## BIC = -436.55
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR5 MR4 MR3
## Correlation of (regression) scores with factors 0.93 0.90 0.89 0.84 0.80
## Multiple R square of scores with factors 0.87 0.82 0.79 0.70 0.64
## Minimum correlation of possible factor scores 0.73 0.63 0.59 0.40 0.29Q10A: Anyone who is able and willing to work hard has a good chance of succeeding.
Q17A: If one works hard enough they are likely to make a good life for themselves.
Q13A: Hard work offers little guarantee of success.
Q9A: People should have more leisure time to spend in relaxation.
Q15A: Life would be more meaningful if we had more leisure time.
Q2A: Our society would have fewer problems if people had less leisure time.
Q6A: Most people who don’t succeed in life are just plain lazy.
Q11A: People who fail at a job have usually not tried hard enough.
Q3A: Money acquired easily (e.g. through gambling or speculation) is usually spent unwisely.
Q14A: The credit card is a ticket to careless spending.
Q7A: The self-made person is likely to be more ethical than someone who is born to wealth.
Q8A: I often feel I would be more successful if I sacrificed certain pleasures.
F1 -> Meritocracy (Q10A - Q13A)
F2 -> Work-Leisure (Q9A - Q2A)
F3 -> Financial Discipline (Q3A - Q1A)
F4 -> Self-Reliance (Q6A - Q11A)
library(psych)
fa.diagram(factors2)
residuals <- factors2$residual
residuals <- as.matrix(residuals[upper.tri(residuals)])
highresiduals <- abs(residuals) > 0.05
head(highresiduals)## [,1]
## [1,] FALSE
## [2,] FALSE
## [3,] FALSE
## [4,] FALSE
## [5,] FALSE
## [6,] FALSEsum(highresiduals)/nrow(residuals)## [1] 0.01470588head(factors2$scores)## MR1 MR2 MR3 MR4
## [1,] 0.6600824 0.8878537 0.04478136 0.03914653
## [2,] -0.4275908 -1.4535593 0.58208279 0.50479973
## [3,] -0.5698184 -0.2746627 -0.64392475 0.50933862
## [4,] 0.9194183 0.7515384 0.58109507 0.95065175
## [5,] -1.4894063 1.1462971 0.14256054 -1.15459613
## [6,] -0.7630665 1.2964196 -0.83266448 -1.10128591print(factors2$weights)## MR1 MR2 MR3 MR4
## Q1A 0.0037222748 -0.0856051701 0.15115211 0.085331172
## Q2A -0.0223718461 -0.1435261210 0.04779496 0.129077737
## Q3A 0.0037802471 0.0052559880 0.21241574 0.016846232
## Q5A 0.0035949828 0.0005757773 0.11399277 0.017232075
## Q6A 0.0478562495 -0.0385010541 -0.01852301 0.406440681
## Q7A -0.0031480263 0.0210188093 0.14491478 0.001148358
## Q8A 0.0003228938 -0.0211155590 0.13881583 0.015948707
## Q9A -0.0099524071 0.4328790239 0.02042869 -0.042827037
## Q10A 0.4059750981 -0.0122786950 -0.02225333 0.036307740
## Q11A 0.0392680786 0.0139193763 0.07599667 0.289982785
## Q12A 0.0078931905 -0.0387901283 0.14860369 0.013242708
## Q13A -0.1122640880 0.0295161368 0.01754068 -0.017043320
## Q14A -0.0194638286 0.0152363661 0.11160444 0.032429960
## Q15A -0.0328859611 0.3520586454 0.02784484 0.024572379
## Q16A 0.0781886654 0.0117393066 0.16348446 -0.029164505
## Q17A 0.3867711804 -0.0263986840 0.05106735 0.085638368
## Q19A 0.0513935796 -0.0160249147 0.19838069 0.066390322mydata$F1_Meri <- factors2$scores[ ,1]
mydata$F2_Work <- factors2$scores[ ,2]
mydata$F3_FinD <- factors2$scores[ ,3]
mydata$F4_Self <- factors2$scores[ ,4]
print(mydata[100,])## Q1A Q2A Q3A Q4A Q5A Q6A Q7A Q8A Q9A Q10A Q11A Q12A Q13A Q14A Q15A Q16A Q17A
## 100 4 2 5 5 5 4 5 5 2 4 5 4 1 5 2 5 5
## Q18A Q19A F1_Meri F2_Work F3_FinD F4_Self
## 100 5 5 0.9517155 -1.369416 1.579608 1.448549F1_Meri <- mydata[,c("Q10A", "Q17A", "Q13A")]
head(F1_Meri)## Q10A Q17A Q13A
## 1 5 5 2
## 2 2 4 4
## 3 3 3 3
## 4 5 5 2
## 5 2 2 5
## 6 3 3 4library(psych)
alpha(F1_Meri,
check.keys = TRUE)## Warning in alpha(F1_Meri, check.keys = TRUE): Some items were negatively correlated with the first principal component and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: alpha(x = F1_Meri, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.8 0.8 0.75 0.58 4.1 0.0095 3.6 1.2 0.52
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.78 0.8 0.82
## Duhachek 0.78 0.8 0.82
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Q10A 0.68 0.68 0.52 0.52 2.1 0.0174 NA 0.52
## Q17A 0.66 0.66 0.50 0.50 2.0 0.0183 NA 0.50
## Q13A- 0.84 0.84 0.72 0.72 5.2 0.0088 NA 0.72
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Q10A 1349 0.87 0.87 0.80 0.70 3.8 1.4
## Q17A 1349 0.87 0.88 0.81 0.71 3.7 1.3
## Q13A- 1349 0.80 0.79 0.59 0.55 3.2 1.4
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## Q10A 0.11 0.11 0.10 0.27 0.41 0
## Q17A 0.10 0.11 0.12 0.30 0.37 0
## Q13A 0.22 0.28 0.12 0.21 0.17 0Factor analysis was conducted using the minimum residual method on 19 standardized indicators (n = 1350). The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy confirmed the appropriateness of the analysis, with an overall KMO value of 0.92, and individual MSA values all above 0.82, indicating strong suitability for factor analysis.
Based on the parallel analysis and eigenvalues, we determined a four-factor solution using oblique rotation (Oblimin method). The following four factors were identified based on their pattern loadings:
Factor 1 (λ₁ = 2.08): Meritocracy (Q10A - Q13A).
Factor 2 (λ₂ = 1.80): Work-Leisure Balance (Q9A - Q2A).
Factor 3 (λ₃ = 1.40): Financial Discipline (Q3A - Q1A).
Factor 4 (λ₄ = 1.28): Self-Reliances (Q6A - Q11A).
These factors explain 57.8% of the variation in the data. The reliability of F1 was assessed using Cronbach’s alpha, indicating acceptable reliability (α > 0.8).