Model of vocational student achievement from academic self-efficacy and learning motivation

Covariance-Based SEM (lavaan) for Education and Learning

Field: Education and LearningLevel: Doctoral dissertation (S3)Method: Covariance-Based SEM (lavaan)

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Testing the path from academic self-efficacy to learning motivation to academic achievement with covariance-based SEM and model fit indices (the analysis is illustrated with synthetic data). Covariance-based SEM (CB-SEM) with lavaan estimates the measurement and structural models together and judges how well the model reproduces the data covariance matrix. It suits theses that test a theory (for example TAM or TPB) with Likert questionnaires and reasonably large samples.

Model of vocational student achievement from academic self-efficacy and learning motivation: result sheet

Project info

Field of studyEducation and Learning
LevelDoctoral dissertation (S3)
Method typeSEM and Psychometrics
Estimated build time± 7 working days
Toolslavaan::sem, lavaan::fitMeasures, lavaan::standardizedSolution, lavaan::lavInspect, ggplot2
PriceUS$28 - US$178

Research goal

Testing the path from academic self-efficacy to learning motivation to academic achievement with covariance-based SEM and model fit indices (the analysis is illustrated with synthetic data).

Variables

Role	Variable	Unit
Main	Academic achievement	Likert 1-5
Supporting 1	Academic self-efficacy	Likert 1-5
Supporting 2	Learning motivation	Likert 1-5

Example result

0.972CFI (robust)
0.963TLI (robust)
0.052RMSEA (robust)
0.046SRMR
0.203Std. indirect effect
<0.001Indirect p-value

The model fits the data well (CFI = 0.972, TLI = 0.963, RMSEA = 0.052, SRMR = 0.046). Academic self-efficacy has a significant direct effect on Academic achievement (beta = 0.200, p = 0.008), and the indirect effect through Learning motivation is 0.203 (p < 0.001). The model explains 31.0% of the variance in Academic achievement.

Computed from illustrative synthetic data, not from a real study.

About Covariance-Based SEM (lavaan)

Covariance-based SEM (CB-SEM) with lavaan estimates the measurement and structural models together and judges how well the model reproduces the data covariance matrix. It suits theses that test a theory (for example TAM or TPB) with Likert questionnaires and reasonably large samples.

Steps

1Prepare the Likert item data, one column per item
2Write the model syntax: measurement (=~), structural (~) and indirect effects (:=)
3Estimate with lavaan::sem using the MLR estimator, which is robust to non-normality
4Assess model fit with CFI, TLI, RMSEA and SRMR
5Check the standardised loading of every item
6Report standardised path coefficients, p-values, R2 and the indirect effect

Assumptions to check

The model is specified from theory and is identified
The sample is large enough (usually at least 200 respondents)
Five-category Likert items are treated as continuous with a robust correction (MLR)
Item residuals are uncorrelated unless specified

Reading and reporting the results

The model fits when CFI and TLI exceed 0.90 (preferably 0.95) and RMSEA and SRMR are below 0.08. Then report standardised loadings, standardised path coefficients with p-values, R2 of the endogenous constructs and the indirect effect a*b to conclude on the mediator.

Example R code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

Show code

# Contoh kode R: Covariance-Based SEM (lavaan)
suppressPackageStartupMessages({
  library(ggplot2)
  library(patchwork)
  library(lavaan)
})
set.seed(42)
# ---- Gaya grafik ----
pal <- c("#1f6feb", "#e8590c", "#2f9e44", "#ae3ec9", "#f59f00")
warna <- list(bg = "#f4f6fa", panel = "#ffffff", teks = "#1f2933", redup = "#5f6b78", grid = "#e3e8ee", bar = "#1d3557")
tata <- 1
theme_set(theme_minimal(base_size = 11) + theme(legend.position = "bottom"))

# ---- Data sintetis: 12 butir Likert 1-5 dari tiga konstruk laten ----
n <- 200
a <- runif(1, 0.4, 0.7)                                         # jalur X1 -> X2 (mediator)
b <- runif(1, 0.3, 0.55)                                        # jalur X2 -> Y
cp <- runif(1, 0.1, 0.35)                                       # jalur langsung X1 -> Y
e_x1 <- rnorm(n)
e_x2 <- a * e_x1 + rnorm(n, 0, sqrt(1 - a^2))
e_y <- as.numeric(scale(cp * e_x1 + b * e_x2 + rnorm(n, 0, runif(1, 0.55, 0.75))))
# butir Likert: muatan acak 0.65-0.9, ambang diacak agar rata-rata butir sekitar 3.4-3.8
likert <- function(eta, k) {
  sapply(seq_len(k), function(j) {
    l <- runif(1, 0.65, 0.9)
    s <- l * eta + rnorm(length(eta), 0, sqrt(1 - l^2))
    findInterval(s, sort(c(-2, -1.1, -0.2, 0.9) + runif(1, -0.3, 0.2))) + 1
  })
}
# butir Y ke-4 sedikit ikut dipengaruhi X1 (muatan silang kecil) agar kecocokan model realistis, tidak sempurna
d <- data.frame(likert(e_x1, 4), likert(e_x2, 4), likert(e_y, 3),
                likert(as.numeric(scale(e_y + runif(1, 0.25, 0.5) * e_x1)), 1))
names(d) <- c(paste0("academic_self_efficacy", "_", 1:4), paste0("learning_motivation", "_", 1:4), paste0("academic_achievement", "_", 1:4))
write.csv(d, "data_contoh.csv", row.names = FALSE)

# ---- Spesifikasi model: pengukuran (=~), struktural (~), efek tidak langsung (:=) ----
model <- paste0(
  "academic_self_efficacy =~ ", paste(names(d)[1:4], collapse = " + "), "\n",
  "learning_motivation =~ ", paste(names(d)[5:8], collapse = " + "), "\n",
  "academic_achievement =~ ", paste(names(d)[9:12], collapse = " + "), "\n",
  "learning_motivation ~ a*academic_self_efficacy\n",
  "academic_achievement ~ b*learning_motivation + c*academic_self_efficacy\n",
  "tidak_langsung := a*b\n",
  "total := c + a*b\n")
cat(model)
fit <- sem(model, data = d, estimator = "MLR")                  # ML robust (data Likert diperlakukan kontinu)
print(summary(fit, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE))

# ---- Indeks kecocokan model (versi robust, cadangan versi biasa) ----
fm <- fitMeasures(fit, c("cfi.robust", "tli.robust", "rmsea.robust", "srmr", "cfi", "tli", "rmsea"))
pilih <- function(r, s) if (is.finite(fm[[r]])) fm[[r]] else fm[[s]]
idx <- c(CFI = pilih("cfi.robust", "cfi"), TLI = pilih("tli.robust", "tli"),
         RMSEA = pilih("rmsea.robust", "rmsea"), SRMR = fm[["srmr"]])
print(round(idx, 3))

# ---- Koefisien terstandar ----
ss <- standardizedSolution(fit)
jalur <- ss[ss$op == "~", ]
ambil <- function(lhs, rhs) jalur[jalur$lhs == lhs & jalur$rhs == rhs, ]
j_a <- ambil("learning_motivation", "academic_self_efficacy"); j_b <- ambil("academic_achievement", "learning_motivation"); j_c <- ambil("academic_achievement", "academic_self_efficacy")
tl <- ss[ss$op == ":=" & ss$lhs == "tidak_langsung", ]
muat <- ss[ss$op == "=~", ]
r2 <- lavInspect(fit, "rsquare")
print(jalur[, c("lhs", "rhs", "est.std", "se", "pvalue")]); print(tl)


# ---- Grafik ----
singkat <- function(s, w = 18) {                                # nama konstruk pendek untuk grafik
  k <- strsplit(s, " ")[[1]]
  if (nchar(s) > w) k <- k[!tolower(k) %in% c("of", "to", "the", "and", "for", "in", "on", "with")]
  i <- length(k)
  while (nchar(paste(k, collapse = " ")) > w && i >= 1) {
    if (nchar(k[i]) > 5) k[i] <- paste0(substr(k[i], 1, 4), ".")
    i <- i - 1
  }
  substr(paste(k, collapse = " "), 1, w)
}
nm_k <- make.unique(unname(sapply(c("academic_self_efficacy", "learning_motivation", "academic_achievement"), singkat)), sep = " ")
bintang <- function(p) ifelse(p < 0.001, "***", ifelse(p < 0.01, "**", ifelse(p < 0.05, "*", " ns")))
elips <- function(x0, y0, rx = 0.74, ry = 0.3, id = 1) {
  t_ <- seq(0, 2 * pi, length.out = 60)
  data.frame(x = x0 + rx * cos(t_), y = y0 + ry * sin(t_), id = id)
}
pos <- data.frame(x = c(0, 1.6, 3.2), y = c(0, 1.25, 0), lab = nm_k)
de <- do.call(rbind, lapply(1:3, function(i) elips(pos$x[i], pos$y[i], id = i)))
# kotak indikator: X1 di kiri bawah, X2 di atas, Y di kanan bawah
ind <- data.frame(x = c(-0.9, -0.3, 0.3, 0.9, 0.7, 1.3, 1.9, 2.5, 2.3, 2.9, 3.5, 4.1),
                  y = rep(c(-0.95, 2.35, -0.95), each = 4), grup = rep(1:3, each = 4),
                  lab = paste0(rep(c("X1.", "M.", "Y."), each = 4), rep(1:4, 3)))
ind$xl <- pos$x[ind$grup]; ind$yl <- pos$y[ind$grup] + ifelse(ind$grup == 2, 0.3, -0.3)
st <- data.frame(x = c(0.45, 2.15, 0.78), y = c(0.3, 0.95, 0), xend = c(1.05, 2.75, 2.42), yend = c(1.0, 0.3, 0),
                 lab = sprintf("%.2f%s", c(j_a$est.std, j_b$est.std, j_c$est.std), bintang(c(j_a$pvalue, j_b$pvalue, j_c$pvalue))),
                 lx = c(0.55, 2.65, 1.6), ly = c(0.78, 0.78, -0.14))
p1 <- ggplot() +
  geom_segment(data = ind, aes(xl, yl, xend = x, yend = y + ifelse(grup == 2, -0.15, 0.15)), colour = warna$redup,
               linewidth = 0.4, arrow = arrow(length = unit(0.07, "inches"), type = "closed")) +
  geom_tile(data = ind, aes(x, y), width = 0.5, height = 0.3, fill = warna$panel, colour = warna$redup, linewidth = 0.4) +
  geom_text(data = ind, aes(x, y, label = lab), colour = warna$teks, size = 2.6) +
  geom_segment(data = st, aes(x, y, xend = xend, yend = yend), colour = warna$teks, linewidth = 0.9,
               arrow = arrow(length = unit(0.13, "inches"), type = "closed")) +
  geom_text(data = st, aes(lx, ly, label = lab), colour = warna$teks, fontface = "bold", size = 3.3) +
  geom_polygon(data = de, aes(x, y, group = id, fill = factor(id)), show.legend = FALSE) +
  scale_fill_manual(values = pal[1:3]) +
  geom_text(data = pos, aes(x, y, label = lab), colour = warna$panel, fontface = "bold", size = 3) +
  annotate("text", x = 1.6, y = -1.38, size = 3, colour = warna$teks,
           label = sprintf("Std. indirect = %.3f%s   R2 = %.2f", tl$est.std, bintang(tl$pvalue), r2[["academic_achievement"]])) +
  coord_cartesian(xlim = c(-1.25, 4.45), ylim = c(-1.5, 2.6)) +
  theme_void() + theme(plot.background = element_rect(fill = warna$panel, colour = NA),
                       plot.title = element_text(face = "bold", colour = warna$teks, margin = margin(4, 0, 4, 6))) +
  labs(title = "Standardised structural model (MLR)")
df <- data.frame(indeks = factor(names(idx), levels = names(idx)), nilai = unname(idx),
                 ambang = c(0.9, 0.9, 0.08, 0.08), arah = c("Higher is better", "Higher is better", "Lower is better", "Lower is better"))
p2 <- ggplot(df, aes(indeks, nilai, fill = arah)) +
  geom_col(width = 0.6) +
  geom_errorbar(aes(ymin = ambang, ymax = ambang), width = 0.8, linetype = "dashed", colour = warna$teks, linewidth = 0.6) +
  geom_text(aes(label = sprintf("%.3f", nilai)), vjust = -0.4, colour = warna$teks, size = 3) +
  facet_wrap(~arah, scales = "free") +
  scale_fill_manual(values = pal[4:5], guide = "none") +
  scale_y_continuous(expand = expansion(mult = c(0, 0.15))) +
  labs(title = "Fit indices vs cut-offs (dashed)", x = NULL, y = "Value")
muat$konstruk <- factor(nm_k[match(muat$lhs, c("academic_self_efficacy", "learning_motivation", "academic_achievement"))], levels = nm_k)
muat$butir <- factor(ind$lab, levels = rev(ind$lab))
p3 <- ggplot(muat, aes(est.std, butir, colour = konstruk)) +
  geom_vline(xintercept = 0.7, linetype = "dashed", colour = warna$redup) +
  geom_segment(aes(x = 0, xend = est.std, yend = butir), linewidth = 0.9) +
  geom_point(size = 2.6) +
  geom_text(aes(label = sprintf("%.2f", est.std)), hjust = -0.35, size = 2.6, colour = warna$teks) +
  scale_colour_manual(values = pal[1:3], name = NULL) +
  scale_x_continuous(limits = c(0, 1.1), breaks = seq(0, 1, 0.25)) +
  labs(title = "Standardised loadings", x = "Loading", y = NULL)
p_hasil <- if (tata == 1) p1 / (p2 | p3) + plot_layout(heights = c(1.15, 1)) else p1 | (p2 / p3)

print(p_hasil)

The project file you can download

The original project file is available. It is not just the picture above: you get the working R project. It can be downloaded after payment, and we send it by WhatsApp or email.

ZIP: analisis.R + data_contoh.csv + BACA-DULU.txt

What is inside the ZIP

The complete analysis script (analisis.R), commented step by step, ready to run in RStudio.
A sample dataset (data_contoh.csv) so the script runs straight away.
A short guide (BACA-DULU.txt): which packages to install, how to run it and how to swap in your own data.

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

Package 1

Code and Explanation

US$28

excl. 11% VAT

Duration: 7 working days

Output: R files + result figures

Deliverables

Fully commented R code (.R) for Covariance-Based SEM (lavaan)
Example data and step-by-step run instructions
Ready-to-use result figures and metrics table
Short explanation of the method, its assumptions and how to read the results

Choose Package 1

Package 2 · most chosen

Your Data Analysis + Interpretation

US$81

excl. 11% VAT

Duration: 13 working days

Output: Code + analysis + interpretation notes

Includes all of Package 1, plus

Adapting the code to your own research dataset (CSV or Excel)
Assumption checks, result validation and data cleaning
Tables and figures formatted for your manuscript
Interpretation notes for the methods and discussion sections, for you to write up in your own words

Choose Package 2

Package 3

Full Guidance

US$178

excl. 11% VAT

Duration: 18-21 working days

Output: Code + analysis + guidance until ready to present

Includes all of Packages 1 & 2, plus

Comparison against one alternative method with the reasoning for the choice
Two 60-minute online coaching sessions so you fully understand the code and results
Revisions following your supervisor feedback (up to 3 rounds)
Practice Q&A to prepare for your seminar and defence
Full documentation (README, R package list (sessionInfo)) so the results can be reproduced

Choose Package 3

Payment: 50% down payment before work starts, balance after the deliverables are handed over
Tax: Prices exclude 11% VAT
Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions

Do I get the real project file?

Yes. The original project file is a ZIP containing the complete analisis.R script, a data_contoh.csv sample dataset and a BACA-DULU.txt guide. It can be downloaded after payment, and we send it by WhatsApp or email. For your own data (Package 2 and 3) the script is adapted to your dataset.

Is this suitable for a Doctoral dissertation (S3)?

Yes. Covariance-Based SEM (lavaan) is commonly used at this level in Education and Learning. We adapt the analysis to your research question, your own data and your supervisor's requirements.

Is the result sheet real data?

No. The sheet is computed from illustrative synthetic data so you can see the kind of output R Studio gives. For your order we run the same method on your own data.

Will I understand the code?

That is the point of the packages. Every script is commented, and Package 3 includes two coaching sessions plus practice questions so you can explain the method and the results at your seminar and defence.

How is the price decided?

Each project has three packages: Package 1 (code and explanation) US$28, Package 2 (your data analysis and interpretation) US$81 and Package 3 (full guidance) US$178, excluding 11% VAT. Larger datasets, extra methods or tight deadlines adjust the quote after a short consultation.

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