Implemetation of Structural Equation Modeling on Student Stress Factors Dataset
Halilatunnisa (130) & Faishal Muflih Irfanu Tsaqib (170)
2026-05-22
1 Install and Load Library
2 Preprocessing Data
2.1 Load Data
data <- read.csv("StressLevelDataset.csv", header = TRUE)
cat("Number of rows (respondents):", nrow(data), "\n")## Number of rows (respondents): 1100## Number of columns (variables): 21##
## Column names:## [1] "anxiety_level" "self_esteem"
## [3] "mental_health_history" "depression"
## [5] "headache" "blood_pressure"
## [7] "sleep_quality" "breathing_problem"
## [9] "noise_level" "living_conditions"
## [11] "safety" "basic_needs"
## [13] "academic_performance" "study_load"
## [15] "teacher_student_relationship" "future_career_concerns"
## [17] "social_support" "peer_pressure"
## [19] "extracurricular_activities" "bullying"
## [21] "stress_level"## anxiety_level self_esteem mental_health_history depression headache
## 1 14 20 0 11 2
## 2 15 8 1 15 5
## 3 12 18 1 14 2
## 4 16 12 1 15 4
## 5 16 28 0 7 2
## blood_pressure sleep_quality breathing_problem noise_level living_conditions
## 1 1 2 4 2 3
## 2 3 1 4 3 1
## 3 1 2 2 2 2
## 4 3 1 3 4 2
## 5 3 5 1 3 2
## safety basic_needs academic_performance study_load
## 1 3 2 3 2
## 2 2 2 1 4
## 3 3 2 2 3
## 4 2 2 2 4
## 5 4 3 4 3
## teacher_student_relationship future_career_concerns social_support
## 1 3 3 2
## 2 1 5 1
## 3 3 2 2
## 4 1 4 1
## 5 1 2 1
## peer_pressure extracurricular_activities bullying stress_level
## 1 3 3 2 1
## 2 4 5 5 2
## 3 3 2 2 1
## 4 4 4 5 2
## 5 5 0 5 12.2 Cek Missing Value
## Total NA in dataset: 0## Percentage of NA per column:## anxiety_level self_esteem
## 0 0
## mental_health_history depression
## 0 0
## headache blood_pressure
## 0 0
## sleep_quality breathing_problem
## 0 0
## noise_level living_conditions
## 0 0
## safety basic_needs
## 0 0
## academic_performance study_load
## 0 0
## teacher_student_relationship future_career_concerns
## 0 0
## social_support peer_pressure
## 0 0
## extracurricular_activities bullying
## 0 0
## stress_level
## 02.3 Remove Duplicate Data
duplicate_rows <- data[duplicated(data), ]
cat("Number of duplicate rows:", nrow(duplicate_rows), "\n")## Number of duplicate rows: 0if (nrow(duplicate_rows) > 0) {
data <- data[!duplicated(data), ]
cat("Duplicates removed. Remaining rows:", nrow(data), "\n")
} else {
cat("No duplicates found, data remains intact.\n")
}## No duplicates found, data remains intact.2.4 Convert Variables to Numeric
data_numeric <- data
for (col in colnames(data_numeric)) {
if (!is.numeric(data_numeric[[col]])) {
data_numeric[[col]] <- as.numeric(as.factor(data_numeric[[col]]))
}
}
cat("All columns successfully converted to numeric.\n")## All columns successfully converted to numeric.## anxiety_level self_esteem
## "integer" "integer"
## mental_health_history depression
## "integer" "integer"
## headache blood_pressure
## "integer" "integer"
## sleep_quality breathing_problem
## "integer" "integer"
## noise_level living_conditions
## "integer" "integer"
## safety basic_needs
## "integer" "integer"
## academic_performance study_load
## "integer" "integer"
## teacher_student_relationship future_career_concerns
## "integer" "integer"
## social_support peer_pressure
## "integer" "integer"
## extracurricular_activities bullying
## "integer" "integer"
## stress_level
## "integer"2.5 Invert Variabel Negatif
Columns depression and bullying have reversed meanings: high scores = bad condition. To maintain consistency with the constructs (high scores = good condition), both variables are inverted.
## Range before inversion:## depression: 0 27## bullying : 0 5max_dep <- max(data_numeric$depression)
max_bul <- max(data_numeric$bullying)
data_numeric$depression_inv <- (max_dep + 1) - data_numeric$depression
data_numeric$bullying_inv <- (max_bul + 1) - data_numeric$bullying
max_ap <- max(data_numeric$academic_performance)
data_numeric$academic_performance_inv <-
(max_ap + 1) - data_numeric$academic_performance
max_mh <- max(data_numeric$mental_health_history)
data_numeric$mental_health_history_inv <-
(max_mh + 1) - data_numeric$mental_health_history
max_extra <- max(data_numeric$extracurricular_activities)
data_numeric$extra_inv <- (max_extra + 1) - data_numeric$extracurricular_activities
cat("Range after inversion:\n")## Range after inversion:## depression_inv: 1 28## bullying_inv : 1 62.6 Z-Score Normalization
Only the 13 indicators used in SEM are normalized. The stress_level column (classification label) is not included.
sem_columns <- c(
# X1 - Academic Stress
"anxiety_level", "study_load", "academic_performance_inv",
"future_career_concerns", "peer_pressure",
# X2 - Social Support
"social_support", "teacher_student_relationship",
"extra_inv", "bullying_inv",
# Y - Psychological Well-Being
"self_esteem", "depression_inv",
"sleep_quality", "mental_health_history_inv"
)
data_sem <- data_numeric[, sem_columns]
data_z <- as.data.frame(lapply(data_sem, function(x) {
(x - mean(x, na.rm = TRUE)) / sd(x, na.rm = TRUE)
}))
cat("Dimensions of data_z:", nrow(data_z), "rows x", ncol(data_z), "columns\n")## Dimensions of data_z: 1100 rows x 13 columns## anxiety_level study_load academic_performance_inv future_career_concerns
## 1 0.4799895 -0.4725849 -0.1606629 0.2294460
## 2 0.6434534 1.0474249 1.2531706 1.5371694
## 3 0.1530617 0.2874200 0.5462539 -0.4244157
## peer_pressure social_support teacher_student_relationship extra_inv
## 1 0.1862492 0.1127876 0.2540977 -0.1641743
## 2 0.8878731 -0.8415689 -1.1903852 -1.5750470
## 3 0.1862492 0.1127876 0.2540977 0.5412621
## bullying_inv self_esteem depression_inv sleep_quality
## 1 0.4031938 0.24849937 0.2013010 -0.4262512
## 2 -1.5563636 -1.09309234 -0.3163638 -1.0720865
## 3 0.4031938 0.02490076 -0.1869476 -0.4262512
## mental_health_history_inv
## 1 0.9851107
## 2 -1.0141915
## 3 -1.01419153 Exploration and Descriptive Statistics
3.1 Statistical Summary
## Descriptive Statistics (before normalization)## anxiety_level study_load academic_performance_inv
## Min. : 0.00 Min. :0.000 Min. :1.000
## 1st Qu.: 6.00 1st Qu.:2.000 1st Qu.:2.000
## Median :11.00 Median :2.000 Median :4.000
## Mean :11.06 Mean :2.622 Mean :3.227
## 3rd Qu.:16.00 3rd Qu.:3.000 3rd Qu.:4.000
## Max. :21.00 Max. :5.000 Max. :6.000
## future_career_concerns peer_pressure social_support
## Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:1.000 1st Qu.:2.000 1st Qu.:1.000
## Median :2.000 Median :2.000 Median :2.000
## Mean :2.649 Mean :2.735 Mean :1.882
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:3.000
## Max. :5.000 Max. :5.000 Max. :3.000
## teacher_student_relationship extra_inv bullying_inv self_esteem
## Min. :0.000 Min. :1.000 Min. :1.000 Min. : 0.00
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:11.00
## Median :2.000 Median :3.500 Median :3.000 Median :19.00
## Mean :2.648 Mean :3.233 Mean :3.383 Mean :17.78
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:5.000 3rd Qu.:26.00
## Max. :5.000 Max. :6.000 Max. :6.000 Max. :30.00
## depression_inv sleep_quality mental_health_history_inv
## Min. : 1.00 Min. :0.00 Min. :1.000
## 1st Qu.: 9.00 1st Qu.:1.00 1st Qu.:1.000
## Median :16.00 Median :2.50 Median :2.000
## Mean :15.44 Mean :2.66 Mean :1.507
## 3rd Qu.:22.00 3rd Qu.:4.00 3rd Qu.:2.000
## Max. :28.00 Max. :5.00 Max. :2.0003.2 Skewness And Kurtosis
## mean sd skew kurtosis min max
## anxiety_level 11.06 6.12 -0.08 -1.10 0 21
## study_load 2.62 1.32 0.23 -0.67 0 5
## academic_performance_inv 3.23 1.42 -0.18 -1.07 1 6
## future_career_concerns 2.65 1.53 0.20 -1.30 0 5
## peer_pressure 2.73 1.43 0.19 -1.01 0 5
## social_support 1.88 1.05 -0.18 -1.44 0 3
## teacher_student_relationship 2.65 1.39 0.20 -0.91 0 5
## extra_inv 3.23 1.42 -0.14 -1.04 1 6
## bullying_inv 3.38 1.53 -0.17 -1.28 1 6
## self_esteem 17.78 8.95 -0.40 -1.07 0 30
## depression_inv 15.45 7.73 -0.22 -0.99 1 28
## sleep_quality 2.66 1.55 0.18 -1.32 0 5
## mental_health_history_inv 1.51 0.50 -0.03 -2.00 1 2
4 Assumption Testing
4.1 Multivariate Normality Test (Mardia)
Mardia’s test is used to determine whether the data meet the multivariate normality assumption required in CB-SEM.
mardia_result <- mardia(data_z, plot = FALSE)
cat("Mardia Skewness :", round(mardia_result$skew, 4), "\n")## Mardia Skewness : 10214.72## Mardia Kurtosis : 173.3041## p-value Skewness : 0## p-value Kurtosis : 0if (mardia_result$p.skew > 0.05 & mardia_result$p.kurt > 0.05) {
cat("Conclusion: The data MEET the multivariate normality assumption (p > 0.05)\n")
} else {
cat("Conclusion: The data DO NOT meet multivariate normality.\n")
cat("Note: SEM can still proceed due to the large sample size (n=1100).\n")
cat("Robust estimators (MLR) may be considered.\n")
}## Conclusion: The data DO NOT meet multivariate normality.
## Note: SEM can still proceed due to the large sample size (n=1100).
## Robust estimators (MLR) may be considered.4.2 Sampling Adequacy Test (KMO)
r_matrix <- cor(data_z, use = "complete.obs")
kmo_result <- KMO(r_matrix)
cat("Overall MSA (KMO):", round(kmo_result$MSA, 4), "\n\n")## Overall MSA (KMO): 0.9741## KMO for each variable:## anxiety_level study_load
## 0.9787 0.9831
## academic_performance_inv future_career_concerns
## 0.9783 0.9766
## peer_pressure social_support
## 0.9782 0.9474
## teacher_student_relationship extra_inv
## 0.9629 0.9818
## bullying_inv self_esteem
## 0.9742 0.9657
## depression_inv sleep_quality
## 0.9783 0.9750
## mental_health_history_inv
## 0.9835if (kmo_result$MSA >= 0.5) {
cat("Conclusion: KMO ≥ 0.5 — sampling adequacy is satisfied\n")
} else {
cat("Conclusion: KMO < 0.5 — sampling adequacy is not satisfied\n")
}## Conclusion: KMO ≥ 0.5 — sampling adequacy is satisfied4.3 Multicollinearity Test (VIF)
data_z_clean <- na.omit(data_z)
model_vif <- lm(
self_esteem ~ anxiety_level + study_load + academic_performance_inv +
future_career_concerns + peer_pressure +
social_support + teacher_student_relationship +
extra_inv + bullying_inv +
depression_inv + sleep_quality,
data = data_z_clean
)
vif_values <- vif(model_vif)
cat("VIF values:\n")## VIF values:## anxiety_level study_load
## 3.028 1.852
## academic_performance_inv future_career_concerns
## 2.447 3.132
## peer_pressure social_support
## 2.345 2.126
## teacher_student_relationship extra_inv
## 2.894 2.319
## bullying_inv depression_inv
## 3.019 2.973
## sleep_quality
## 2.954if (length(problematic) == 0) {
cat("Conclusion: All VIF values are < 5 — no problematic multicollinearity\n")
} else {
cat("VIF > 5 found in variables:", names(problematic), "\n")
}## Conclusion: All VIF values are < 5 — no problematic multicollinearityNote: Safe VIF values are < 3.3 (strict) or < 5 (moderate). Values above 5 require attention, and above 10 are problematic.
5 CFA — Academic Stress (X1)
Construct: AcademicStress
Indicators: anxiety_level,
study_load, academic_performance_inv,
future_career_concerns, peer_pressure
model_cfa_x1 <- '
AcademicStress =~ anxiety_level + study_load + academic_performance_inv +
future_career_concerns + peer_pressure
'
fit_x1 <- cfa(
model_cfa_x1,
data = data_z,
std.lv = TRUE,
estimator = "MLR"
)5.1 CFA X1 Summary
## lavaan 0.6-21 ended normally after 18 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
##
## Number of observations 1100
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7.155 2.829
## Degrees of freedom 5 5
## P-value (Chi-square) 0.209 0.726
## Scaling correction factor 2.529
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 2919.113 1186.203
## Degrees of freedom 10 10
## P-value 0.000 0.000
## Scaling correction factor 2.461
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.999 1.000
## Tucker-Lewis Index (TLI) 0.999 1.004
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.004
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -6345.682 -6345.682
## Scaling correction factor 1.440
## for the MLR correction
## Loglikelihood unrestricted model (H1) -6342.104 -6342.104
## Scaling correction factor 1.803
## for the MLR correction
##
## Akaike (AIC) 12711.363 12711.363
## Bayesian (BIC) 12761.394 12761.394
## Sample-size adjusted Bayesian (SABIC) 12729.631 12729.631
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.020 0.000
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.050 0.015
## P-value H_0: RMSEA <= 0.050 0.953 1.000
## P-value H_0: RMSEA >= 0.080 0.000 0.000
##
## Robust RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.049
## P-value H_0: Robust RMSEA <= 0.050 0.955
## P-value H_0: Robust RMSEA >= 0.080 0.002
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.008 0.008
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AcademicStress =~
## anxiety_level 0.845 0.020 42.624 0.000 0.845 0.845
## study_load 0.689 0.023 29.851 0.000 0.689 0.690
## acdmc_prfrmnc_ 0.755 0.021 36.288 0.000 0.755 0.755
## ftr_crr_cncrns 0.851 0.019 45.542 0.000 0.851 0.852
## peer_pressure 0.769 0.020 37.802 0.000 0.769 0.769
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .anxiety_level 0.285 0.026 11.157 0.000 0.285 0.285
## .study_load 0.524 0.034 15.317 0.000 0.524 0.525
## .acdmc_prfrmnc_ 0.429 0.032 13.616 0.000 0.429 0.430
## .ftr_crr_cncrns 0.275 0.029 9.540 0.000 0.275 0.275
## .peer_pressure 0.408 0.031 13.307 0.000 0.408 0.408
## AcademicStress 1.000 1.000 1.0005.2 Fit Indices CFA X1
fi_x1 <- fitMeasures(fit_x1, c("chisq", "df", "pvalue", "cfi", "tli", "rmsea", "srmr"))
print(round(fi_x1, 4))## chisq df pvalue cfi tli rmsea srmr
## 7.155 5.000 0.209 0.999 0.999 0.020 0.008cfi_x1 <- fitMeasures(fit_x1, "cfi")
tli_x1 <- fitMeasures(fit_x1, "tli")
rmsea_x1 <- fitMeasures(fit_x1, "rmsea")
srmr_x1 <- fitMeasures(fit_x1, "srmr")
eval_x1 <- data.frame(
Index = c("CFI", "TLI", "RMSEA", "SRMR"),
Value = round(c(cfi_x1, tli_x1, rmsea_x1, srmr_x1), 4),
Target = c("≥ 0.90", "≥ 0.90", "< 0.08", "< 0.08"),
Status = c(
ifelse(cfi_x1 >= 0.90, "PASS", "FAIL"),
ifelse(tli_x1 >= 0.90, "PASS", "FAIL"),
ifelse(rmsea_x1 < 0.08, "PASS", "FAIL"),
ifelse(srmr_x1 < 0.08, "PASS", "FAIL")
)
)
print(eval_x1)## Index Value Target Status
## cfi CFI 0.9993 ≥ 0.90 PASS
## tli TLI 0.9985 ≥ 0.90 PASS
## rmsea RMSEA 0.0198 < 0.08 PASS
## srmr SRMR 0.0081 < 0.08 PASS5.3 CFA X1 Loading Factors
std_x1 <- standardizedSolution(fit_x1)
loading_x1 <- std_x1[std_x1$op == "=~", c("rhs", "est.std", "se", "pvalue")]
colnames(loading_x1) <- c("Indicator", "Std.Loading", "SE", "p-value")
loading_x1$Evaluation <- ifelse(
abs(loading_x1$Std.Loading) >= 0.70, "Ideal (≥0.70)",
ifelse(abs(loading_x1$Std.Loading) >= 0.50, "Acceptable (0.50–0.70)", "Weak (<0.50)")
)
loading_x1$Std.Loading <- round(loading_x1$Std.Loading, 4)
loading_x1$SE <- round(loading_x1$SE, 4)
loading_x1$`p-value` <- round(loading_x1$`p-value`, 4)
print(loading_x1[, 1:3])## Indicator Std.Loading SE
## 1 anxiety_level 0.846 0.015
## 2 study_load 0.690 0.020
## 3 academic_performance_inv 0.755 0.018
## 4 future_career_concerns 0.852 0.016
## 5 peer_pressure 0.769 0.018## Indicator Evaluation
## 1 anxiety_level Ideal (≥0.70)
## 2 study_load Acceptable (0.50–0.70)
## 3 academic_performance_inv Ideal (≥0.70)
## 4 future_career_concerns Ideal (≥0.70)
## 5 peer_pressure Ideal (≥0.70)5.4 Composite Reliability and AVE X1
calculate_CR_AVE <- function(fit) {
std <- standardizedSolution(fit)
lambda <- std$est.std[std$op == "=~"]
theta <- 1 - lambda^2
CR <- sum(lambda)^2 / (sum(lambda)^2 + sum(theta))
AVE <- sum(lambda^2) / (sum(lambda^2) + sum(theta))
return(list(CR = CR, AVE = AVE))
}
cr_ave_x1 <- calculate_CR_AVE(fit_x1)
alpha_x1 <- psych::alpha(data_z[, c("anxiety_level", "study_load",
"academic_performance_inv",
"future_career_concerns", "peer_pressure")])
rel_x1 <- data.frame(
Measure = c("Composite Reliability (CR)", "AVE", "Cronbach's Alpha"),
Value = round(c(cr_ave_x1$CR, cr_ave_x1$AVE, alpha_x1$total$raw_alpha), 4),
Target = c("≥ 0.70", "≥ 0.50", "≥ 0.70"),
Status = c(
ifelse(cr_ave_x1$CR >= 0.70, "PASS", "FAIL"),
ifelse(cr_ave_x1$AVE >= 0.50, "PASS", "FAIL"),
ifelse(alpha_x1$total$raw_alpha >= 0.70, "PASS", "FAIL")
)
)
print(rel_x1)## Measure Value Target Status
## 1 Composite Reliability (CR) 0.8884 ≥ 0.70 PASS
## 2 AVE 0.6156 ≥ 0.50 PASS
## 3 Cronbach's Alpha 0.8870 ≥ 0.70 PASS5.5 CFA X1 Path Diagram
semPaths(
object = fit_x1,
what = "path",
whatLabels = "std",
style = "ram",
layout = "tree",
rotation = 2,
sizeMan = 7,
sizeLat = 8,
edge.label.cex = 1.2,
label.cex = 1.1,
color = list(lat = "#AED6F1", man = "#A9DFBF"),
mar = c(3, 3, 3, 3)
)
title(main = "CFA — Academic Stress (X1)", cex.main = 1.3, font.main = 2)
6 CFA — Social Support (X2)
Construct: SocialSupport
Indicators: social_support,
teacher_student_relationship,
extracurricular_activities, bullying_inv
model_cfa_x2 <- '
SocialSupport =~ social_support + teacher_student_relationship +
extra_inv + bullying_inv
'
fit_x2 <- cfa(
model_cfa_x2,
data = data_z,
std.lv = TRUE,
estimator = "MLR"
)6.1 CFA X2 Summary
## lavaan 0.6-21 ended normally after 15 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 8
##
## Number of observations 1100
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 67.759 34.602
## Degrees of freedom 2 2
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.958
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 2074.587 877.586
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 2.364
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.968 0.963
## Tucker-Lewis Index (TLI) 0.905 0.888
##
## Robust Comparative Fit Index (CFI) 0.969
## Robust Tucker-Lewis Index (TLI) 0.907
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5237.914 -5237.914
## Scaling correction factor 1.492
## for the MLR correction
## Loglikelihood unrestricted model (H1) -5204.035 -5204.035
## Scaling correction factor 1.586
## for the MLR correction
##
## Akaike (AIC) 10491.829 10491.829
## Bayesian (BIC) 10531.853 10531.853
## Sample-size adjusted Bayesian (SABIC) 10506.443 10506.443
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.173 0.122
## 90 Percent confidence interval - lower 0.139 0.097
## 90 Percent confidence interval - upper 0.209 0.148
## P-value H_0: RMSEA <= 0.050 0.000 0.000
## P-value H_0: RMSEA >= 0.080 1.000 0.997
##
## Robust RMSEA 0.170
## 90 Percent confidence interval - lower 0.123
## 90 Percent confidence interval - upper 0.222
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.999
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.031 0.031
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SocialSupport =~
## social_support 0.758 0.019 40.759 0.000 0.758 0.759
## tchr_stdnt_rlt 0.837 0.023 36.284 0.000 0.837 0.838
## extra_inv 0.735 0.026 28.384 0.000 0.735 0.735
## bullying_inv 0.798 0.025 31.345 0.000 0.798 0.798
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .social_support 0.424 0.032 13.107 0.000 0.424 0.425
## .tchr_stdnt_rlt 0.298 0.024 12.540 0.000 0.298 0.298
## .extra_inv 0.459 0.042 10.862 0.000 0.459 0.460
## .bullying_inv 0.363 0.042 8.591 0.000 0.363 0.363
## SocialSupport 1.000 1.000 1.0006.2 CFA X2 Fit Indices
fi_x2 <- fitMeasures(fit_x2, c("chisq", "df", "pvalue", "cfi", "tli", "rmsea", "srmr"))
print(round(fi_x2, 4))## chisq df pvalue cfi tli rmsea srmr
## 67.759 2.000 0.000 0.968 0.905 0.173 0.031cfi_x2 <- fitMeasures(fit_x2, "cfi")
tli_x2 <- fitMeasures(fit_x2, "tli")
rmsea_x2 <- fitMeasures(fit_x2, "rmsea")
srmr_x2 <- fitMeasures(fit_x2, "srmr")
eval_x2 <- data.frame(
Index = c("CFI", "TLI", "RMSEA", "SRMR"),
Value = round(c(cfi_x2, tli_x2, rmsea_x2, srmr_x2), 4),
Target = c("≥ 0.90", "≥ 0.90", "< 0.08", "< 0.08"),
Status = c(
ifelse(cfi_x2 >= 0.90, "PASS", "FAIL"),
ifelse(tli_x2 >= 0.90, "PASS", "FAIL"),
ifelse(rmsea_x2 < 0.08, "PASS", "FAIL"),
ifelse(srmr_x2 < 0.08, "PASS", "FAIL")
)
)
print(eval_x2)## Index Value Target Status
## cfi CFI 0.9682 ≥ 0.90 PASS
## tli TLI 0.9046 ≥ 0.90 PASS
## rmsea RMSEA 0.1729 < 0.08 FAIL
## srmr SRMR 0.0314 < 0.08 PASS| Although the RMSEA value exceeded the recommended threshold, the model still demonstrated acceptable fit based on other indices such as CFI, TLI, and SRMR. The elevated RMSEA may be influenced by the small degrees of freedom (df = 2), which is known to inflate RMSEA values in simple CFA models. |
6.3 CFA X2 Loading Factors
std_x2 <- standardizedSolution(fit_x2)
loading_x2 <- std_x2[std_x2$op == "=~", c("rhs", "est.std", "se", "pvalue")]
colnames(loading_x2) <- c("Indicator", "Std.Loading", "SE", "p-value")
loading_x2$Evaluation <- ifelse(
abs(loading_x2$Std.Loading) >= 0.70, "Ideal (≥0.70)",
ifelse(abs(loading_x2$Std.Loading) >= 0.50, "Acceptable (0.50–0.70)", "Weak (<0.50)")
)
loading_x2$Std.Loading <- round(loading_x2$Std.Loading, 4)
loading_x2$SE <- round(loading_x2$SE, 4)
loading_x2$`p-value` <- round(loading_x2$`p-value`, 4)
print(loading_x2[, 1:3])## Indicator Std.Loading SE
## 1 social_support 0.759 0.019
## 2 teacher_student_relationship 0.838 0.015
## 3 extra_inv 0.735 0.026
## 4 bullying_inv 0.798 0.025## Indicator Evaluation
## 1 social_support Ideal (≥0.70)
## 2 teacher_student_relationship Ideal (≥0.70)
## 3 extra_inv Ideal (≥0.70)
## 4 bullying_inv Ideal (≥0.70)6.4 Composite Reliability and AVE X2
cr_ave_x2 <- calculate_CR_AVE(fit_x2)
alpha_x2 <- psych::alpha(data_z[, c(
"social_support",
"teacher_student_relationship",
"extra_inv",
"bullying_inv"
)])
rel_x2 <- data.frame(
Measure = c("Composite Reliability (CR)", "AVE", "Cronbach's Alpha"),
Value = round(c(cr_ave_x2$CR, cr_ave_x2$AVE, alpha_x2$total$raw_alpha), 4),
Target = c("≥ 0.70", "≥ 0.50", "≥ 0.70"),
Status = c(
ifelse(cr_ave_x2$CR >= 0.70, "PASS", "FAIL"),
ifelse(cr_ave_x2$AVE >= 0.50, "PASS", "FAIL"),
ifelse(alpha_x2$total$raw_alpha >= 0.70, "PASS", "FAIL")
)
)
print(rel_x2)## Measure Value Target Status
## 1 Composite Reliability (CR) 0.8637 ≥ 0.70 PASS
## 2 AVE 0.6137 ≥ 0.50 PASS
## 3 Cronbach's Alpha 0.8629 ≥ 0.70 PASS6.5 CFA X2 Path Diagram
semPaths(
object = fit_x2,
what = "path",
whatLabels = "std",
style = "ram",
layout = "tree",
rotation = 2,
sizeMan = 7,
sizeLat = 8,
edge.label.cex = 1.2,
label.cex = 1.1,
color = list(lat = "#F9E79F", man = "#FDEBD0"),
mar = c(3, 3, 3, 3)
)
title(main = "CFA — Social Support (X2)", cex.main = 1.3, font.main = 2)
7 CFA — Psychological Well-Being (Y)
model_cfa_y <- '
PsychologicalWellBeing =~ self_esteem +
depression_inv +
sleep_quality +
mental_health_history_inv
'
fit_y <- cfa(
model_cfa_y,
data = data_z,
std.lv = TRUE,
estimator = "MLR"
)7.1 CFA Y Summary
## lavaan 0.6-21 ended normally after 17 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 8
##
## Number of observations 1100
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 2.464 1.181
## Degrees of freedom 2 2
## P-value (Chi-square) 0.292 0.554
## Scaling correction factor 2.086
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 2303.929 1108.938
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 2.078
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 0.999 1.002
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.002
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5090.597 -5090.597
## Scaling correction factor 1.201
## for the MLR correction
## Loglikelihood unrestricted model (H1) -5089.364 -5089.364
## Scaling correction factor 1.378
## for the MLR correction
##
## Akaike (AIC) 10197.193 10197.193
## Bayesian (BIC) 10237.218 10237.218
## Sample-size adjusted Bayesian (SABIC) 10211.808 10211.808
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.015 0.000
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.063 0.035
## P-value H_0: RMSEA <= 0.050 0.853 0.994
## P-value H_0: RMSEA >= 0.080 0.008 0.000
##
## Robust RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.074
## P-value H_0: Robust RMSEA <= 0.050 0.833
## P-value H_0: Robust RMSEA >= 0.080 0.034
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.005 0.005
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv
## PsychologicalWellBeing =~
## self_esteem 0.818 0.021 39.909 0.000 0.818
## depression_inv 0.847 0.021 41.157 0.000 0.847
## sleep_quality 0.818 0.020 41.878 0.000 0.818
## mntl_hlth_hst_ 0.737 0.016 47.078 0.000 0.737
## Std.all
##
## 0.819
## 0.847
## 0.818
## 0.737
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .self_esteem 0.329 0.027 12.276 0.000 0.329 0.330
## .depression_inv 0.282 0.027 10.569 0.000 0.282 0.282
## .sleep_quality 0.330 0.030 11.009 0.000 0.330 0.331
## .mntl_hlth_hst_ 0.456 0.023 19.775 0.000 0.456 0.456
## PsychlgclWllBn 1.000 1.000 1.0007.2 CFA Y Fit Indices
fi_y <- fitMeasures(
fit_y,
c("chisq", "df", "pvalue", "cfi", "tli", "rmsea", "srmr")
)
print(round(fi_y, 4))## chisq df pvalue cfi tli rmsea srmr
## 2.465 2.000 0.292 1.000 0.999 0.015 0.005cfi_y <- fitMeasures(fit_y, "cfi")
tli_y <- fitMeasures(fit_y, "tli")
rmsea_y <- fitMeasures(fit_y, "rmsea")
srmr_y <- fitMeasures(fit_y, "srmr")
eval_y <- data.frame(
Index = c("CFI", "TLI", "RMSEA", "SRMR"),
Value = round(c(cfi_y, tli_y, rmsea_y, srmr_y), 4),
Target = c("≥ 0.90", "≥ 0.90", "< 0.08", "< 0.08"),
Status = c(
ifelse(cfi_y >= 0.90, "PASS", "FAIL"),
ifelse(tli_y >= 0.90, "PASS", "FAIL"),
ifelse(rmsea_y < 0.08, "PASS", "FAIL"),
ifelse(srmr_y < 0.08, "PASS", "FAIL")
)
)
print(eval_y)## Index Value Target Status
## cfi CFI 0.9998 ≥ 0.90 PASS
## tli TLI 0.9994 ≥ 0.90 PASS
## rmsea RMSEA 0.0145 < 0.08 PASS
## srmr SRMR 0.0053 < 0.08 PASS| Although the RMSEA value may be slightly high, the model can still be considered acceptable if supported by strong CFI, TLI, and SRMR values. Small degrees of freedom may inflate RMSEA values in simple CFA models. |
7.3 CFA Y Loading Factors
std_y <- standardizedSolution(fit_y)
loading_y <- std_y[
std_y$op == "=~",
c("rhs", "est.std", "se", "pvalue")
]
colnames(loading_y) <- c(
"Indicator",
"Std.Loading",
"SE",
"p-value"
)
loading_y$Evaluation <- ifelse(
abs(loading_y$Std.Loading) >= 0.70,
"Ideal (≥0.70)",
ifelse(
abs(loading_y$Std.Loading) >= 0.50,
"Acceptable (0.50–0.70)",
"Weak (<0.50)"
)
)
loading_y$Std.Loading <- round(loading_y$Std.Loading, 4)
loading_y$SE <- round(loading_y$SE, 4)
loading_y$`p-value` <- round(loading_y$`p-value`, 4)
print(loading_y[, 1:3])## Indicator Std.Loading SE
## 1 self_esteem 0.819 0.016
## 2 depression_inv 0.847 0.015
## 3 sleep_quality 0.818 0.017
## 4 mental_health_history_inv 0.737 0.016## Indicator Evaluation
## 1 self_esteem Ideal (≥0.70)
## 2 depression_inv Ideal (≥0.70)
## 3 sleep_quality Ideal (≥0.70)
## 4 mental_health_history_inv Ideal (≥0.70)7.4 Composite Reliability and AVE Y
cr_ave_y <- calculate_CR_AVE(fit_y)
alpha_y <- psych::alpha(data_z[, c(
"self_esteem",
"depression_inv",
"sleep_quality",
"mental_health_history_inv"
)])
rel_y <- data.frame(
Measure = c(
"Composite Reliability (CR)",
"AVE",
"Cronbach's Alpha"
),
Value = round(c(
cr_ave_y$CR,
cr_ave_y$AVE,
alpha_y$total$raw_alpha
), 4),
Target = c("≥ 0.70", "≥ 0.50", "≥ 0.70"),
Status = c(
ifelse(cr_ave_y$CR >= 0.70, "PASS", "FAIL"),
ifelse(cr_ave_y$AVE >= 0.50, "PASS", "FAIL"),
ifelse(alpha_y$total$raw_alpha >= 0.70, "PASS", "FAIL")
)
)
print(rel_y)## Measure Value Target Status
## 1 Composite Reliability (CR) 0.8812 ≥ 0.70 PASS
## 2 AVE 0.6503 ≥ 0.50 PASS
## 3 Cronbach's Alpha 0.8805 ≥ 0.70 PASS7.5 CFA Y Path Diagram
semPaths(
object = fit_y,
what = "path",
whatLabels = "std",
style = "ram",
layout = "tree",
rotation = 2,
sizeMan = 7,
sizeLat = 8,
edge.label.cex = 1.2,
label.cex = 1.1,
color = list(
lat = "#D7BDE2",
man = "#F5EEF8"
),
mar = c(3, 3, 3, 3)
)
title(
main = "CFA — Psychological Well-Being (Y)",
cex.main = 1.3,
font.main = 2
)
8 Measurement Model
8.1 Full Measurement Model
measurement_model <- '
# Latent Variables
AcademicStress =~ anxiety_level +
study_load +
academic_performance_inv +
future_career_concerns +
peer_pressure
SocialSupport =~ social_support +
teacher_student_relationship +
extra_inv +
bullying_inv
PsychologicalWellBeing =~ self_esteem +
depression_inv +
sleep_quality +
mental_health_history_inv
'
fit_measurement <- cfa(
measurement_model,
data = data_z,
std.lv = TRUE,
estimator = "MLR"
)8.2 Measurement Model Summary
## lavaan 0.6-21 ended normally after 28 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 29
##
## Number of observations 1100
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 340.122 136.554
## Degrees of freedom 62 62
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 2.491
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 11173.583 4608.024
## Degrees of freedom 78 78
## P-value 0.000 0.000
## Scaling correction factor 2.425
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.975 0.984
## Tucker-Lewis Index (TLI) 0.968 0.979
##
## Robust Comparative Fit Index (CFI) 0.983
## Robust Tucker-Lewis Index (TLI) 0.979
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -14867.588 -14867.588
## Scaling correction factor 1.384
## for the MLR correction
## Loglikelihood unrestricted model (H1) -14697.527 -14697.527
## Scaling correction factor 2.138
## for the MLR correction
##
## Akaike (AIC) 29793.176 29793.176
## Bayesian (BIC) 29938.265 29938.265
## Sample-size adjusted Bayesian (SABIC) 29846.154 29846.154
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.064 0.033
## 90 Percent confidence interval - lower 0.057 0.028
## 90 Percent confidence interval - upper 0.071 0.038
## P-value H_0: RMSEA <= 0.050 0.000 1.000
## P-value H_0: RMSEA >= 0.080 0.000 0.000
##
## Robust RMSEA 0.052
## 90 Percent confidence interval - lower 0.040
## 90 Percent confidence interval - upper 0.064
## P-value H_0: Robust RMSEA <= 0.050 0.365
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.023 0.023
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv
## AcademicStress =~
## anxiety_level 0.836 0.018 47.515 0.000 0.836
## study_load 0.689 0.020 34.406 0.000 0.689
## acdmc_prfrmnc_ 0.780 0.018 44.429 0.000 0.780
## ftr_crr_cncrns 0.846 0.016 54.216 0.000 0.846
## peer_pressure 0.763 0.018 41.685 0.000 0.763
## SocialSupport =~
## social_support 0.717 0.013 53.602 0.000 0.717
## tchr_stdnt_rlt 0.804 0.018 43.483 0.000 0.804
## extra_inv 0.769 0.018 43.863 0.000 0.769
## bullying_inv 0.831 0.016 52.328 0.000 0.831
## PsychologicalWellBeing =~
## self_esteem 0.820 0.018 46.838 0.000 0.820
## depression_inv 0.834 0.018 46.240 0.000 0.834
## sleep_quality 0.827 0.016 53.344 0.000 0.827
## mntl_hlth_hst_ 0.741 0.012 61.332 0.000 0.741
## Std.all
##
## 0.836
## 0.689
## 0.780
## 0.846
## 0.763
##
## 0.717
## 0.804
## 0.769
## 0.832
##
## 0.820
## 0.834
## 0.827
## 0.741
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AcademicStress ~~
## SocialSupport -1.003 0.011 -90.052 0.000 -1.003 -1.003
## PsychlgclWllBn -1.005 0.009 -105.878 0.000 -1.005 -1.005
## SocialSupport ~~
## PsychlgclWllBn 0.995 0.011 93.449 0.000 0.995 0.995
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .anxiety_level 0.301 0.020 15.220 0.000 0.301 0.301
## .study_load 0.525 0.030 17.462 0.000 0.525 0.525
## .acdmc_prfrmnc_ 0.391 0.024 16.362 0.000 0.391 0.391
## .ftr_crr_cncrns 0.284 0.023 12.305 0.000 0.284 0.284
## .peer_pressure 0.417 0.028 14.794 0.000 0.417 0.418
## .social_support 0.485 0.029 16.659 0.000 0.485 0.486
## .tchr_stdnt_rlt 0.353 0.022 16.294 0.000 0.353 0.354
## .extra_inv 0.408 0.028 14.632 0.000 0.408 0.408
## .bullying_inv 0.308 0.025 12.518 0.000 0.308 0.308
## .self_esteem 0.327 0.021 15.799 0.000 0.327 0.327
## .depression_inv 0.304 0.020 15.199 0.000 0.304 0.304
## .sleep_quality 0.315 0.023 13.447 0.000 0.315 0.316
## .mntl_hlth_hst_ 0.450 0.018 25.167 0.000 0.450 0.451
## AcademicStress 1.000 1.000 1.000
## SocialSupport 1.000 1.000 1.000
## PsychlgclWllBn 1.000 1.000 1.000## AcdmcS SclSpp PsycWB
## AcademicStress 1.000
## SocialSupport -1.003 1.000
## PsychologicalWellBeing -1.005 0.995 1.0009 Structural Model (SEM)
9.1 SEM Model
model_sem <- '
# Measurement Model
AcademicStress =~ anxiety_level +
study_load +
academic_performance_inv +
future_career_concerns +
peer_pressure
SocialSupport =~ social_support +
teacher_student_relationship +
extra_inv +
bullying_inv
PsychologicalWellBeing =~ self_esteem +
depression_inv +
sleep_quality +
mental_health_history_inv
# Structural Model
PsychologicalWellBeing ~ AcademicStress + SocialSupport
'
fit_sem <- sem(
model_sem,
data = data_z,
std.lv = TRUE,
estimator = "MLR"
)
inspect(fit_sem, "converged")## [1] FALSE9.2 SEM Summary
## lavaan 0.6-21 did NOT end normally after 2304 iterations
## ** WARNING ** Estimates below are most likely unreliable
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 29
##
## Number of observations 1100
##
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv
## AcademicStress =~
## anxiety_level 0.837 NA 0.837
## study_load 0.689 NA 0.689
## acdmc_prfrmnc_ 0.780 NA 0.780
## ftr_crr_cncrns 0.847 NA 0.847
## peer_pressure 0.764 NA 0.764
## SocialSupport =~
## social_support 0.715 NA 0.715
## tchr_stdnt_rlt 0.801 NA 0.801
## extra_inv 0.768 NA 0.768
## bullying_inv 0.829 NA 0.829
## PsychologicalWellBeing =~
## self_esteem 0.000 NA 0.820
## depression_inv 0.000 NA 0.834
## sleep_quality 0.000 NA 0.827
## mntl_hlth_hst_ 0.000 NA 0.740
## Std.all
##
## 0.837
## 0.690
## 0.781
## 0.847
## 0.764
##
## 0.715
## 0.802
## 0.768
## 0.829
##
## 0.821
## 0.834
## 0.827
## 0.741
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv
## PsychologicalWellBeing ~
## AcademicStress -13587.695 NA -0.445
## SocialSupport 16920.625 NA 0.554
## Std.all
##
## -0.445
## 0.554
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AcademicStress ~~
## SocialSupport -1.004 NA -1.004 -1.004
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .anxiety_level 0.299 NA 0.299 0.299
## .study_load 0.524 NA 0.524 0.524
## .acdmc_prfrmnc_ 0.390 NA 0.390 0.390
## .ftr_crr_cncrns 0.282 NA 0.282 0.282
## .peer_pressure 0.416 NA 0.416 0.416
## .social_support 0.488 NA 0.488 0.489
## .tchr_stdnt_rlt 0.357 NA 0.357 0.357
## .extra_inv 0.410 NA 0.410 0.410
## .bullying_inv 0.312 NA 0.312 0.312
## .self_esteem 0.326 NA 0.326 0.327
## .depression_inv 0.304 NA 0.304 0.304
## .sleep_quality 0.316 NA 0.316 0.316
## .mntl_hlth_hst_ 0.451 NA 0.451 0.451
## AcademicStress 1.000 1.000 1.000
## SocialSupport 1.000 1.000 1.000
## .PsychlgclWllBn 1.000 0.000 0.000
##
## R-Square:
## Estimate
## anxiety_level 0.701
## study_load 0.476
## acdmc_prfrmnc_ 0.610
## ftr_crr_cncrns 0.718
## peer_pressure 0.584
## social_support 0.511
## tchr_stdnt_rlt 0.643
## extra_inv 0.590
## bullying_inv 0.688
## self_esteem 0.673
## depression_inv 0.696
## sleep_quality 0.684
## mntl_hlth_hst_ 0.549
## PsychlgclWllBn 1.0009.3 SEM Goodness of Fit
if(inspect(fit_sem, "converged")) {
fit_sem_indices <- fitMeasures(
fit_sem,
c(
"chisq",
"df",
"pvalue",
"cfi",
"tli",
"rmsea",
"srmr"
)
)
print(round(fit_sem_indices, 4))
cfi_sem <- fitMeasures(fit_sem, "cfi")
tli_sem <- fitMeasures(fit_sem, "tli")
rmsea_sem <- fitMeasures(fit_sem, "rmsea")
srmr_sem <- fitMeasures(fit_sem, "srmr")
eval_sem <- data.frame(
Index = c("CFI", "TLI", "RMSEA", "SRMR"),
Value = round(c(cfi_sem, tli_sem, rmsea_sem, srmr_sem), 4),
Target = c("≥ 0.90", "≥ 0.90", "< 0.08", "< 0.08"),
Status = c(
ifelse(cfi_sem >= 0.90, "PASS", "FAIL"),
ifelse(tli_sem >= 0.90, "PASS", "FAIL"),
ifelse(rmsea_sem < 0.08, "PASS", "FAIL"),
ifelse(srmr_sem < 0.08, "PASS", "FAIL")
)
)
print(eval_sem)
} else {
cat("SEM model did not converge.\n")
cat("Fit indices cannot be calculated.\n")
cat("Possible causes:\n")
cat("- Multicollinearity between latent variables\n")
cat("- Correlation between constructs too high\n")
cat("- Model misspecification\n")
}## SEM model did not converge.
## Fit indices cannot be calculated.
## Possible causes:
## - Multicollinearity between latent variables
## - Correlation between constructs too high
## - Model misspecification9.4 Hypothesis Testing
sem_paths <- standardizedSolution(fit_sem)
hypothesis_result <- sem_paths[
sem_paths$op == "~",
c("lhs", "rhs", "est.std", "z", "pvalue")
]
colnames(hypothesis_result) <- c(
"Dependent",
"Independent",
"Std.Estimate",
"Z-value",
"p-value"
)
hypothesis_result$Decision <- ifelse(
hypothesis_result$`p-value` < 0.05,
"Significant",
"Not Significant"
)
hypothesis_result$Std.Estimate <- round(
hypothesis_result$Std.Estimate,
4
)
hypothesis_result$`Z-value` <- round(
hypothesis_result$`Z-value`,
4
)
hypothesis_result$`p-value` <- round(
hypothesis_result$`p-value`,
4
)
print(hypothesis_result)## Dependent Independent Std.Estimate Z.value p.value Decision
## 14 PsychologicalWellBeing AcademicStress -0.445 NA NA NA
## 15 PsychologicalWellBeing SocialSupport 0.554 NA NA NA9.5 R-Square
## anxiety_level study_load
## 0.701 0.476
## academic_performance_inv future_career_concerns
## 0.610 0.718
## peer_pressure social_support
## 0.584 0.511
## teacher_student_relationship extra_inv
## 0.643 0.590
## bullying_inv self_esteem
## 0.688 0.673
## depression_inv sleep_quality
## 0.696 0.684
## mental_health_history_inv PsychologicalWellBeing
## 0.549 1.0009.6 SEM Path Diagram
semPaths(
object = fit_sem,
what = "std",
whatLabels = "std",
style = "ram",
layout = "tree",
rotation = 2,
sizeLat = 9,
sizeMan = 6,
edge.label.cex = 1.1,
label.cex = 1,
residuals = FALSE,
intercepts = FALSE,
mar = c(4, 4, 4, 4),
color = list(
lat = "#85C1E9",
man = "#D5F5E3"
)
)
title(
main = "Structural Equation Modeling (SEM)",
cex.main = 1.4,
font.main = 2
)
9.7 Interpretation of Hypothesis
## Interpretation of Structural Relationships# Academic Stress - Psychological Well-Being
p1 <- hypothesis_result$`p-value`[1]
if(!is.na(p1) && p1 < 0.05){
cat(
"Academic Stress significantly influences Psychological Well-Being.\n"
)
} else {
cat(
"Academic Stress does not significantly influence Psychological Well-Being.\n"
)
}## Academic Stress does not significantly influence Psychological Well-Being.# Social Support - Psychological Well-Being
p2 <- hypothesis_result$`p-value`[2]
if(!is.na(p2) && p2 < 0.05){
cat(
"Social Support significantly influences Psychological Well-Being.\n"
)
} else {
cat(
"Social Support does not significantly influence Psychological Well-Being.\n"
)
}## Social Support does not significantly influence Psychological Well-Being.| The convergence issue in the full SEM model cannot be resolved simply by modifying the code or estimation method. Therefore, in addition to using the full SEM model, this study also explores an alternative approach by splitting the analysis into two separate structural models, namely H1 and H2. This approach was adopted to determine whether the convergence problem was caused by the simultaneous use of multiple latent constructs within a single SEM model. |
10 Structural Model H1
10.1 Academic Stress - Psychological Well-Being
model_h1 <- '
AcademicStress =~ anxiety_level +
study_load +
academic_performance_inv +
future_career_concerns +
peer_pressure
PsychologicalWellBeing =~ self_esteem +
depression_inv +
sleep_quality +
mental_health_history_inv
PsychologicalWellBeing ~ AcademicStress
'
fit_h1 <- sem(
model_h1,
data = data_z,
std.lv = TRUE,
estimator = "MLR"
)
inspect(fit_h1, "converged")## [1] FALSE10.2 H1 Summary
## lavaan 0.6-21 did NOT end normally after 1384 iterations
## ** WARNING ** Estimates below are most likely unreliable
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 19
##
## Number of observations 1100
##
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv
## AcademicStress =~
## anxiety_level 0.841 NA 0.841
## study_load 0.694 NA 0.694
## acdmc_prfrmnc_ 0.771 NA 0.771
## ftr_crr_cncrns 0.846 NA 0.846
## peer_pressure 0.766 NA 0.766
## PsychologicalWellBeing =~
## self_esteem 0.001 NA 0.817
## depression_inv 0.001 NA 0.835
## sleep_quality 0.001 NA 0.828
## mntl_hlth_hst_ 0.001 NA 0.746
## Std.all
##
## 0.841
## 0.695
## 0.771
## 0.847
## 0.766
##
## 0.818
## 0.836
## 0.828
## 0.747
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv
## PsychologicalWellBeing ~
## AcademicStress -1150.603 NA -1.000
## Std.all
##
## -1.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .anxiety_level 0.292 NA 0.292 0.292
## .study_load 0.517 NA 0.517 0.517
## .acdmc_prfrmnc_ 0.405 NA 0.405 0.406
## .ftr_crr_cncrns 0.283 NA 0.283 0.283
## .peer_pressure 0.412 NA 0.412 0.413
## .self_esteem 0.331 NA 0.331 0.331
## .depression_inv 0.301 NA 0.301 0.302
## .sleep_quality 0.314 NA 0.314 0.314
## .mntl_hlth_hst_ 0.442 NA 0.442 0.442
## AcademicStress 1.000 1.000 1.000
## .PsychlgclWllBn 1.000 0.000 0.000
##
## R-Square:
## Estimate
## anxiety_level 0.708
## study_load 0.483
## acdmc_prfrmnc_ 0.594
## ftr_crr_cncrns 0.717
## peer_pressure 0.587
## self_esteem 0.669
## depression_inv 0.698
## sleep_quality 0.686
## mntl_hlth_hst_ 0.558
## PsychlgclWllBn 1.00010.3 H1 Fit Indices
if(inspect(fit_h1, "converged")) {
fit_h1_indices <- fitMeasures(
fit_h1,
c(
"chisq",
"df",
"pvalue",
"cfi",
"tli",
"rmsea",
"srmr"
)
)
print(round(fit_h1_indices, 4))
} else {
cat("H1 model did not converge.\n")
cat("Fit indices cannot be calculated.\n")
}## H1 model did not converge.
## Fit indices cannot be calculated.10.4 H1 Hypothesis Test
h1_paths <- standardizedSolution(fit_h1)
h1_result <- h1_paths[
h1_paths$op == "~",
c("lhs", "rhs", "est.std", "z", "pvalue")
]
colnames(h1_result) <- c(
"Dependent",
"Independent",
"Std.Estimate",
"Z-value",
"p-value"
)
h1_result$Decision <- ifelse(
h1_result$`p-value` < 0.05,
"Significant",
"Not Significant"
)
h1_result$Std.Estimate <- round(h1_result$Std.Estimate, 4)
h1_result$`Z-value` <- round(h1_result$`Z-value`, 4)
h1_result$`p-value` <- round(h1_result$`p-value`, 4)
print(h1_result)## Dependent Independent Std.Estimate Z.value p.value Decision
## 10 PsychologicalWellBeing AcademicStress -1 NA NA NA10.5 H1 R-Square
## anxiety_level study_load academic_performance_inv
## 0.708 0.483 0.594
## future_career_concerns peer_pressure self_esteem
## 0.717 0.588 0.669
## depression_inv sleep_quality mental_health_history_inv
## 0.698 0.686 0.558
## PsychologicalWellBeing
## 1.00010.6 H1 Path Diagram
semPaths(
object = fit_h1,
what = "std",
whatLabels = "std",
style = "ram",
layout = "tree",
rotation = 2,
sizeLat = 9,
sizeMan = 6,
edge.label.cex = 1.1,
label.cex = 1,
residuals = FALSE,
intercepts = FALSE,
mar = c(4, 4, 4, 4),
color = list(
lat = "#85C1E9",
man = "#D5F5E3"
)
)
title(
main = "H1: Academic Stress - Psychological Well-Being",
cex.main = 1.3,
font.main = 2
)
11 Structural Model H2
11.2 H2 Summary
## lavaan 0.6-21 ended normally after 74 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 17
##
## Number of observations 1100
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 195.218 84.289
## Degrees of freedom 19 19
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 2.316
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 6071.858 2695.830
## Degrees of freedom 28 28
## P-value 0.000 0.000
## Scaling correction factor 2.252
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.971 0.976
## Tucker-Lewis Index (TLI) 0.957 0.964
##
## Robust Comparative Fit Index (CFI) 0.975
## Robust Tucker-Lewis Index (TLI) 0.963
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -9544.337 -9544.337
## Scaling correction factor 1.297
## for the MLR correction
## Loglikelihood unrestricted model (H1) -9446.728 -9446.728
## Scaling correction factor 1.835
## for the MLR correction
##
## Akaike (AIC) 19122.674 19122.674
## Bayesian (BIC) 19207.726 19207.726
## Sample-size adjusted Bayesian (SABIC) 19153.730 19153.730
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.092 0.056
## 90 Percent confidence interval - lower 0.080 0.048
## 90 Percent confidence interval - upper 0.104 0.064
## P-value H_0: RMSEA <= 0.050 0.000 0.107
## P-value H_0: RMSEA >= 0.080 0.955 0.000
##
## Robust RMSEA 0.085
## 90 Percent confidence interval - lower 0.067
## 90 Percent confidence interval - upper 0.104
## P-value H_0: Robust RMSEA <= 0.050 0.001
## P-value H_0: Robust RMSEA >= 0.080 0.693
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.027 0.027
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv
## SocialSupport =~
## social_support 0.741 0.013 55.829 0.000 0.741
## tchr_stdnt_rlt 0.814 0.019 43.501 0.000 0.814
## extra_inv 0.761 0.019 39.908 0.000 0.761
## bullying_inv 0.814 0.018 45.282 0.000 0.814
## PsychologicalWellBeing =~
## self_esteem 0.080 0.090 0.894 0.371 0.826
## depression_inv 0.081 0.091 0.893 0.372 0.839
## sleep_quality 0.080 0.089 0.893 0.372 0.822
## mntl_hlth_hst_ 0.071 0.079 0.894 0.371 0.732
## Std.all
##
## 0.741
## 0.815
## 0.761
## 0.814
##
## 0.826
## 0.839
## 0.823
## 0.732
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv
## PsychologicalWellBeing ~
## SocialSupport 10.253 11.557 0.887 0.375 0.995
## Std.all
##
## 0.995
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .social_support 0.451 0.028 15.836 0.000 0.451 0.451
## .tchr_stdnt_rlt 0.336 0.020 16.486 0.000 0.336 0.336
## .extra_inv 0.420 0.031 13.524 0.000 0.420 0.420
## .bullying_inv 0.337 0.029 11.828 0.000 0.337 0.338
## .self_esteem 0.317 0.021 14.862 0.000 0.317 0.317
## .depression_inv 0.296 0.022 13.354 0.000 0.296 0.296
## .sleep_quality 0.323 0.025 12.708 0.000 0.323 0.323
## .mntl_hlth_hst_ 0.464 0.020 22.655 0.000 0.464 0.464
## SocialSupport 1.000 1.000 1.000
## .PsychlgclWllBn 1.000 0.009 0.009
##
## R-Square:
## Estimate
## social_support 0.549
## tchr_stdnt_rlt 0.664
## extra_inv 0.580
## bullying_inv 0.662
## self_esteem 0.683
## depression_inv 0.704
## sleep_quality 0.677
## mntl_hlth_hst_ 0.536
## PsychlgclWllBn 0.99111.3 H2 Fit Indices
fit_h2_indices <- fitMeasures(
fit_h2,
c(
"chisq",
"df",
"pvalue",
"cfi",
"tli",
"rmsea",
"srmr"
)
)
print(round(fit_h2_indices, 4))## chisq df pvalue cfi tli rmsea srmr
## 195.218 19.000 0.000 0.971 0.957 0.092 0.02711.4 H2 Hypothesis Test
h2_paths <- standardizedSolution(fit_h2)
h2_result <- h2_paths[
h2_paths$op == "~",
c("lhs", "rhs", "est.std", "z", "pvalue")
]
colnames(h2_result) <- c(
"Dependent",
"Independent",
"Std.Estimate",
"Z-value",
"p-value"
)
h2_result$Decision <- ifelse(
h2_result$`p-value` < 0.05,
"Significant",
"Not Significant"
)
h2_result$Std.Estimate <- round(h2_result$Std.Estimate, 4)
h2_result$`Z-value` <- round(h2_result$`Z-value`, 4)
h2_result$`p-value` <- round(h2_result$`p-value`, 4)
print(h2_result)## Dependent Independent Std.Estimate Z.value p.value Decision
## 9 PsychologicalWellBeing SocialSupport 0.995 94.165 0 Significant11.5 H2 R-Square
## social_support teacher_student_relationship
## 0.549 0.664
## extra_inv bullying_inv
## 0.580 0.662
## self_esteem depression_inv
## 0.683 0.704
## sleep_quality mental_health_history_inv
## 0.677 0.536
## PsychologicalWellBeing
## 0.99111.6 H2 Path Diagram
semPaths(
object = fit_h2,
what = "std",
whatLabels = "std",
style = "ram",
layout = "tree",
rotation = 2,
sizeLat = 9,
sizeMan = 6,
edge.label.cex = 1.1,
label.cex = 1,
residuals = FALSE,
intercepts = FALSE,
mar = c(4, 4, 4, 4),
color = list(
lat = "#F5B7B1",
man = "#FDEDEC"
)
)
title(
main = "H2: Social Support - Psychological Well-Being",
cex.main = 1.3,
font.main = 2
)
| After a second attempt was made to split the model into H1 and H2, convergence issues persisted, particularly in the H1 model, which still failed to converge. This suggests that the primary issue lies not in the syntax or the program code used, but rather in the characteristics of the dataset itself. All variables in StressLevelDataset.csv were designed to predict stress levels linearly, resulting in very high correlations among the variables. Consequently, latent constructs such as Academic Stress, Social Support, and Psychological Well-Being become very difficult to empirically distinguish. This condition is evident from latent correlations approaching ±1, indicating high multicollinearity and a lack of discriminant validity among constructs. Therefore, the SEM model becomes statistically unstable, and the model parameters cannot be estimated properly. |
Multivariate Analysis Last Task, Data Science UNESA 2024
11.1 Social Support - Psychological Well-Being