title: “SEM Modeling of the Influence of Lecturer-Student Relationships on Students’ Academic Performance Using CFA Analysis” short-title: “Beamer Slides” author: “Gatiari Dwi Panefi, Metha Nailis Sa’adah, Anisa Khaynun Najwa” short-author: “J & M Doe” date: ‘June 06, 2025’ # 05 31, 2025 (Main Slide) short-date: ‘06/06/2025’ # 05/31/2025 (Lower Right) institute: “Universitas Negeri Surabaya” short-institute: “” department: “Fakultas Matematika dan Ilmu Pengetahuan Alam” # Institute must be defined license: “” section-titles: false # Provides slide headings safe-columns: true # Enables special latex macros for columns. output: uiucthemes::beamer_illinois — — title: “SEM Modeling of the Influence of Lecturer-Student Relationships on Students’ Academic Performance Using CFA Analysis” author: Gatiari Dwi Panefi; Metha Nailis Sa’adah; Anisa Khaynun Najwa; Brilliyanda Annisatulrohmah date: “2025-06-06” output: html_document: default pdf_document: default —
Load Dataset
df <-read.csv("dataset_uas_bersih (1).csv")
head(df,3)## AGE GDR UNAME DEPT INTRCT ASSIS AGOALS POSTV APER ONLIMP TotalSum OVRL SUPPO
## 1 2 1 16 15 3 3 3 4 4 3 54 1 5
## 2 2 2 16 15 2 4 3 4 3 1 52 1 4
## 3 2 2 16 15 1 3 2 3 3 1 49 1 4
## ONLN
## 1 2
## 2 4
## 3 31) Data Understanding
# Load library
library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.4.3## Warning: package 'ggplot2' was built under R version 4.4.3## Warning: package 'tibble' was built under R version 4.4.3## Warning: package 'tidyr' was built under R version 4.4.3## Warning: package 'readr' was built under R version 4.4.3## Warning: package 'purrr' was built under R version 4.4.3## Warning: package 'dplyr' was built under R version 4.4.3## Warning: package 'stringr' was built under R version 4.4.3## Warning: package 'forcats' was built under R version 4.4.3## Warning: package 'lubridate' was built under R version 4.4.3## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.0.4
## ── 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 errorslibrary(psych)## Warning: package 'psych' was built under R version 4.4.3##
## Attaching package: 'psych'
##
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha# Lihat struktur data
str(df)## 'data.frame': 395 obs. of 14 variables:
## $ AGE : int 2 2 2 2 2 2 2 2 2 2 ...
## $ GDR : int 1 2 2 2 1 1 1 1 1 2 ...
## $ UNAME : int 16 16 16 21 8 16 16 26 6 17 ...
## $ DEPT : int 15 15 15 47 17 15 15 9 15 5 ...
## $ INTRCT : int 3 2 1 3 3 1 5 3 2 2 ...
## $ ASSIS : int 3 4 3 2 5 3 2 3 2 4 ...
## $ AGOALS : int 3 3 2 2 3 3 2 1 3 3 ...
## $ POSTV : int 4 4 3 4 4 3 2 2 3 4 ...
## $ APER : int 4 3 3 3 3 3 1 3 3 3 ...
## $ ONLIMP : int 3 1 1 1 1 3 3 3 3 3 ...
## $ TotalSum: int 54 52 49 43 57 46 42 41 45 51 ...
## $ OVRL : int 1 1 1 2 0 2 2 2 2 1 ...
## $ SUPPO : int 5 4 4 3 5 3 2 3 3 3 ...
## $ ONLN : int 2 4 3 4 2 2 1 3 5 3 ...# Statistik deskriptif
summary(df)## AGE GDR UNAME DEPT INTRCT
## Min. :2.00 Min. :1.000 Min. : 0.00 Min. : 0.0 Min. :1.000
## 1st Qu.:2.00 1st Qu.:1.000 1st Qu.:16.00 1st Qu.:15.0 1st Qu.:3.000
## Median :2.00 Median :1.000 Median :16.00 Median :18.0 Median :4.000
## Mean :2.01 Mean :1.309 Mean :18.21 Mean :22.6 Mean :3.463
## 3rd Qu.:2.00 3rd Qu.:2.000 3rd Qu.:20.00 3rd Qu.:29.0 3rd Qu.:4.000
## Max. :3.00 Max. :3.000 Max. :45.00 Max. :51.0 Max. :5.000
## ASSIS AGOALS POSTV APER
## 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.:2.000
## Median :4.000 Median :3.000 Median :4.000 Median :2.000
## Mean :3.395 Mean :3.372 Mean :3.552 Mean :2.603
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:3.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## ONLIMP TotalSum OVRL SUPPO
## Min. :1.000 Min. :27.00 Min. :0.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:43.00 1st Qu.:0.000 1st Qu.:3.000
## Median :2.000 Median :53.00 Median :1.000 Median :4.000
## Mean :2.314 Mean :50.07 Mean :1.167 Mean :3.299
## 3rd Qu.:3.000 3rd Qu.:57.00 3rd Qu.:2.000 3rd Qu.:4.000
## Max. :5.000 Max. :65.00 Max. :3.000 Max. :5.000
## ONLN
## Min. :1.000
## 1st Qu.:2.000
## Median :3.000
## Mean :2.724
## 3rd Qu.:3.000
## Max. :5.000# Cek missing value
colSums(is.na(df))## AGE GDR UNAME DEPT INTRCT ASSIS AGOALS POSTV
## 0 0 0 0 0 0 0 0
## APER ONLIMP TotalSum OVRL SUPPO ONLN
## 0 0 0 0 0 0install.packages(“tidyverse”)
2) Cek Deskriptif dan Korelasi antar Indikator
library(psych)
# Daftar semua indikator
indikator <- c("INTRCT", "ASSIS", "SUPPO", # TeacherSupport
"AGOALS", "POSTV", "APER", # GoalOrientation
"ONLN", "ONLIMP", # OnlineLearningExp
"TotalSum", "OVRL") # AcademicPerformance
# Deskriptif
describe(df[indikator])## vars n mean sd median trimmed mad min max range skew kurtosis
## INTRCT 1 395 3.46 1.15 4 3.55 1.48 1 5 4 -0.57 -0.52
## ASSIS 2 395 3.39 1.12 4 3.48 1.48 1 5 4 -0.64 -0.34
## SUPPO 3 395 3.30 1.18 4 3.37 1.48 1 5 4 -0.58 -0.60
## AGOALS 4 395 3.37 1.18 3 3.43 1.48 1 5 4 -0.28 -0.77
## POSTV 5 395 3.55 1.17 4 3.65 1.48 1 5 4 -0.58 -0.50
## APER 6 395 2.60 0.98 2 2.57 1.48 1 5 4 0.51 -0.10
## ONLN 7 395 2.72 1.03 3 2.71 1.48 1 5 4 0.31 -0.46
## ONLIMP 8 395 2.31 0.90 2 2.30 1.48 1 5 4 -0.04 -0.85
## TotalSum 9 395 50.07 8.90 53 50.69 7.41 27 65 38 -0.63 -0.76
## OVRL 10 395 1.17 0.96 1 1.09 1.48 0 3 3 0.49 -0.67
## se
## INTRCT 0.06
## ASSIS 0.06
## SUPPO 0.06
## AGOALS 0.06
## POSTV 0.06
## APER 0.05
## ONLN 0.05
## ONLIMP 0.05
## TotalSum 0.45
## OVRL 0.05# Korelasi antar indikator
cor(df[indikator], use = "complete.obs")## INTRCT ASSIS SUPPO AGOALS POSTV
## INTRCT 1.00000000 0.51607567 0.495608854 0.4857521 0.452059477
## ASSIS 0.51607567 1.00000000 0.493156549 0.4255121 0.449788847
## SUPPO 0.49560885 0.49315655 1.000000000 0.4942149 0.521719999
## AGOALS 0.48575206 0.42551215 0.494214869 1.0000000 0.479583198
## POSTV 0.45205948 0.44978885 0.521719999 0.4795832 1.000000000
## APER 0.19866187 0.14755251 0.151042828 0.1691870 0.118592442
## ONLN 0.24859880 0.22203786 0.180870163 0.1573818 0.143608285
## ONLIMP 0.01109519 0.04022891 0.007057476 -0.0336558 0.006172282
## TotalSum 0.68903554 0.68273201 0.710643708 0.6496873 0.684651704
## OVRL -0.66798830 -0.65586027 -0.654392965 -0.6294986 -0.641065462
## APER ONLN ONLIMP TotalSum OVRL
## INTRCT 0.19866187 0.2485988 0.011095185 0.6890355 -0.6679883
## ASSIS 0.14755251 0.2220379 0.040228909 0.6827320 -0.6558603
## SUPPO 0.15104283 0.1808702 0.007057476 0.7106437 -0.6543930
## AGOALS 0.16918700 0.1573818 -0.033655796 0.6496873 -0.6294986
## POSTV 0.11859244 0.1436083 0.006172282 0.6846517 -0.6410655
## APER 1.00000000 0.4174204 0.083777242 0.4022924 -0.3528001
## ONLN 0.41742039 1.0000000 0.117840169 0.4403749 -0.4186176
## ONLIMP 0.08377724 0.1178402 1.000000000 0.1569401 -0.1636682
## TotalSum 0.40229245 0.4403749 0.156940058 1.0000000 -0.9489979
## OVRL -0.35280007 -0.4186176 -0.163668156 -0.9489979 1.00000003) Exploratory Factor Analysis
# 1. Install & load paket yang diperlukan
install.packages("psych")## Warning: package 'psych' is in use and will not be installedlibrary(psych)
# 2. Buat dataframe hanya dengan indikator yang digunakan
data_efa <- df[, c("INTRCT", "ASSIS", "SUPPO", "AGOALS", "POSTV", "ONLN", "TotalSum")]
# 3. Cek KMO dan Bartlett's Test
KMO(data_efa)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = data_efa)
## Overall MSA = 0.8
## MSA for each item =
## INTRCT ASSIS SUPPO AGOALS POSTV ONLN TotalSum
## 0.91 0.88 0.87 0.89 0.84 0.49 0.70cortest.bartlett(cor(data_efa), n = nrow(data_efa))## $chisq
## [1] 1389.309
##
## $p.value
## [1] 1.835468e-281
##
## $df
## [1] 21# 4. Scree Plot untuk jumlah faktor optimal
fa.parallel(data_efa, fa = "fa")## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = 2 and the number of components = NA# 5. Jalankan EFA (misal 3 faktor berdasarkan scree)
fa_result <- fa(data_efa, nfactors = 3, rotate = "varimax")## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefullyprint(fa_result$loadings)##
## Loadings:
## MR1 MR3 MR2
## INTRCT 0.429 0.890 0.135
## ASSIS 0.596 0.269 0.152
## SUPPO 0.702 0.206
## AGOALS 0.623 0.232
## POSTV 0.690 0.167
## ONLN 0.127 0.847
## TotalSum 0.892 0.292 0.353
##
## MR1 MR3 MR2
## SS loadings 2.708 1.083 0.898
## Proportion Var 0.387 0.155 0.128
## Cumulative Var 0.387 0.542 0.670# 6. Lihat hasil dan interpretasi
fa.diagram(fa_result)
4) Measure Model CFA
library(lavaan)## Warning: package 'lavaan' was built under R version 4.4.3## This is lavaan 0.6-19
## lavaan is FREE software! Please report any bugs.##
## Attaching package: 'lavaan'## The following object is masked from 'package:psych':
##
## cor2covmodel_cfa <- '
AcademicPerformance =~ ASSIS + SUPPO + AGOALS + POSTV
TeacherInteraction =~ INTRCT
OnlineLearningExperience =~ ONLN
'fit_cfa <- cfa(model_cfa, data = df)
summary(fit_cfa, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6-19 ended normally after 22 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 13
##
## Number of observations 395
##
## Model Test User Model:
##
## Test statistic 9.189
## Degrees of freedom 8
## P-value (Chi-square) 0.327
##
## Model Test Baseline Model:
##
## Test statistic 653.678
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.998
## Tucker-Lewis Index (TLI) 0.997
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3343.075
## Loglikelihood unrestricted model (H1) -3338.481
##
## Akaike (AIC) 6712.150
## Bayesian (BIC) 6763.876
## Sample-size adjusted Bayesian (SABIC) 6722.627
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.019
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.064
## P-value H_0: RMSEA <= 0.050 0.839
## P-value H_0: RMSEA >= 0.080 0.008
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.020
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv
## AcademicPerformance =~
## ASSIS 1.000 0.759
## SUPPO 1.133 0.095 11.903 0.000 0.861
## AGOALS 1.048 0.094 11.190 0.000 0.796
## POSTV 1.049 0.093 11.298 0.000 0.796
## TeacherInteraction =~
## INTRCT 1.000 1.152
## OnlineLearningExperience =~
## ONLN 1.000 1.030
## Std.all
##
## 0.679
## 0.731
## 0.674
## 0.682
##
## 1.000
##
## 1.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AcademicPerformance ~~
## TeacherIntrctn 0.615 0.068 9.091 0.000 0.703 0.703
## OnlnLrnngExprn 0.199 0.047 4.247 0.000 0.254 0.254
## TeacherInteraction ~~
## OnlnLrnngExprn 0.295 0.062 4.795 0.000 0.249 0.249
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ASSIS 0.675 0.059 11.442 0.000 0.675 0.539
## .SUPPO 0.644 0.061 10.516 0.000 0.644 0.465
## .AGOALS 0.760 0.066 11.505 0.000 0.760 0.545
## .POSTV 0.727 0.064 11.386 0.000 0.727 0.534
## .INTRCT 0.000 0.000 0.000
## .ONLN 0.000 0.000 0.000
## AcademcPrfrmnc 0.576 0.082 6.992 0.000 1.000 1.000
## TeacherIntrctn 1.327 0.094 14.053 0.000 1.000 1.000
## OnlnLrnngExprn 1.061 0.075 14.053 0.000 1.000 1.0005) Uji Kecocokan Model CFA
- Lihat Chi-square, CFI, TLI, RMSEA, confident interval, SRMR ## 6) Visualisasi Model CFA
library(lavaan)
library(semPlot)## Warning: package 'semPlot' was built under R version 4.4.3# Contoh model CFA sederhana
model <- '
AcademicPerformance =~ ASSIS + SUPPO + AGOALS + POSTV
TeacherInteraction =~ INTRCT
OnlineLearningExperience =~ ONLN
'
fit <- cfa(model, data = df)
# Visualisasi path diagram
semPaths(fit, whatLabels = "std", layout = "tree", edge.label.cex = 1.2,
sizeMan = 6, sizeLat = 10, residuals = FALSE,
title = TRUE, curve = 1, nCharNodes = 0)
semPaths(fit,
whatLabels = "std",
residuals = TRUE,
nCharNodes = 7,
edge.label.cex = 1.2,
layout = "spring",
color = list(lat = "lightblue", man = "pink"),
sizeMan = 6, sizeLat = 10,
edge.color = "black")
7) Evaluasi Validitas dan Reliabilitas Konstruk
- Validitas Konvergen
- Validitas Diskriminan
- Composite Reliablity
- Cronbach’s Alpha install.packages(“semTools”)
library(semTools)## Warning: package 'semTools' was built under R version 4.4.3## ## ################################################################################# This is semTools 0.5-7## All users of R (or SEM) are invited to submit functions or ideas for functions.## #################################################################################
## Attaching package: 'semTools'## The following objects are masked from 'package:psych':
##
## reliability, skew## The following object is masked from 'package:readr':
##
## clipboard# Hitung reliabilitas (alpha, omega, dll)
compRel <- compRelSEM(fit)
# Hitung AVE untuk tiap konstruk
ave <- AVE(fit)# Tampilkan hasil reliabilitas
print(compRel)## AcademicPerformance
## 0.787# Tampilkan hasil AVE
print(ave)## AcademicPerformance
## 0.4798) SEM
library(lavaan)
model_sem <- '
# Measurement model
AcademicPerformance =~ ASSIS + SUPPO + AGOALS + POSTV
TeacherInteraction =~ INTRCT
OnlineLearningExperience =~ ONLN
# Structural model
TeacherInteraction ~ OnlineLearningExperience
AcademicPerformance ~ TeacherInteraction
'
# Estimasi model SEM
fit_sem <- sem(model_sem, data = df, estimator = "ML")
# Ringkasan hasil
summary(fit_sem, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE)## lavaan 0.6-19 ended normally after 26 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 12
##
## Number of observations 395
##
## Model Test User Model:
##
## Test statistic 12.597
## Degrees of freedom 9
## P-value (Chi-square) 0.182
##
## Model Test Baseline Model:
##
## Test statistic 653.678
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.994
## Tucker-Lewis Index (TLI) 0.991
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3344.779
## Loglikelihood unrestricted model (H1) -3338.481
##
## Akaike (AIC) 6713.559
## Bayesian (BIC) 6761.305
## Sample-size adjusted Bayesian (SABIC) 6723.229
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.032
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.069
## P-value H_0: RMSEA <= 0.050 0.748
## P-value H_0: RMSEA >= 0.080 0.014
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.031
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv
## AcademicPerformance =~
## ASSIS 1.000 0.756
## SUPPO 1.138 0.096 11.849 0.000 0.861
## AGOALS 1.054 0.094 11.157 0.000 0.797
## POSTV 1.055 0.094 11.271 0.000 0.798
## TeacherInteraction =~
## INTRCT 1.000 1.152
## OnlineLearningExperience =~
## ONLN 1.000 1.030
## Std.all
##
## 0.676
## 0.732
## 0.675
## 0.684
##
## 1.000
##
## 1.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## TeacherInteraction ~
## OnlnLrnngExprn 0.278 0.055 5.101 0.000 0.249 0.249
## AcademicPerformance ~
## TeacherIntrctn 0.461 0.039 11.867 0.000 0.702 0.702
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .ASSIS 0.680 0.059 11.465 0.000 0.680 0.543
## .SUPPO 0.643 0.061 10.491 0.000 0.643 0.465
## .AGOALS 0.758 0.066 11.476 0.000 0.758 0.544
## .POSTV 0.724 0.064 11.346 0.000 0.724 0.532
## .INTRCT 0.000 0.000 0.000
## .ONLN 0.000 0.000 0.000
## .AcademcPrfrmnc 0.290 0.046 6.363 0.000 0.507 0.507
## .TeacherIntrctn 1.245 0.089 14.053 0.000 0.938 0.938
## OnlnLrnngExprn 1.061 0.075 14.053 0.000 1.000 1.000
##
## R-Square:
## Estimate
## ASSIS 0.457
## SUPPO 0.535
## AGOALS 0.456
## POSTV 0.468
## INTRCT 1.000
## ONLN 1.000
## AcademcPrfrmnc 0.493
## TeacherIntrctn 0.0629) Uji Kecocokan Model SEM
Chi-Square, CFI, TLI, RMSEA ## 10) Visualisasi Plot SEM
library(semPlot)
semPaths(fit_sem,
what = "path",
whatLabels = "par",
style = "ram",
layout = "tree",
rotation = 2,
sizeMan = 7,
sizeLat = 7,
color = "lightblue",
edge.label.cex = 1.2,
label.cex = 1.3)
## 11) Interpretasi dan Kesimpulan