Spatial pattern of junior secondary enrolment across districts and the role of distance to school

Spatial Autocorrelation and Spatial Regression (sf, spdep) for Education and Learning

Field: Education and LearningLevel: Doctoral dissertation (S3)Method: Spatial Autocorrelation and Spatial Regression (sf, spdep)

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Testing spatial autocorrelation of junior secondary GER and the effect of mean distance to school and poor population with spatial regression using synthetic data for demonstration. Spatial analysis tests whether values in neighbouring areas are similar (Moran's I and LISA) and then models them with a spatial lag regression. It suits theses based on area level data such as districts, regencies or villages.

Spatial pattern of junior secondary enrolment across districts and the role of distance to school: result sheet

Project info

Field of studyEducation and Learning
LevelDoctoral dissertation (S3)
Method typeData Exploration
Estimated build time± 7 working days
Toolssf::st_make_grid, spdep::poly2nb, spdep::moran.test, spdep::localmoran, spatialreg::lagsarlm, ggplot2::geom_sf
PriceUS$31 - US$191

Research goal

Testing spatial autocorrelation of junior secondary GER and the effect of mean distance to school and poor population with spatial regression using synthetic data for demonstration.

Variables

Role	Variable	Unit
Main	Junior secondary GER	%
Supporting 1	Mean distance to school	km
Supporting 2	Poor population	%

Example result

0.47Moran's I (Y)
<0.001Moran's I p-value
0.379Rho (spatial lag)
<0.001LR test p-value
312.038AIC OLS
294.486AIC spatial lag

Moran's I for Junior secondary GER across 117 district units is 0.470 (p < 0.001), indicating spatial clustering; LISA flags 19 High-High units. The spatial lag model gives rho = 0.379 with an LR test p < 0.001 and AIC 294.5 versus 312.0 for OLS, so the spatial model is preferred.

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

About Spatial Autocorrelation and Spatial Regression (sf, spdep)

Spatial analysis tests whether values in neighbouring areas are similar (Moran's I and LISA) and then models them with a spatial lag regression. It suits theses based on area level data such as districts, regencies or villages.

Steps

1Prepare the area polygons (sf) and join the attribute data
2Build queen neighbours (spdep::poly2nb) and row-standardised weights (nb2listw)
3Test global autocorrelation with Moran's I (moran.test)
4Compute LISA (localmoran) and map High-High, Low-Low and outlier clusters
5Fit OLS and check the Lagrange multiplier tests (lm.RStests)
6Fit the spatial lag model (spatialreg::lagsarlm) and compare it with OLS by AIC and the LR test

Assumptions to check

The neighbour definition (queen) and spatial weights match the process studied
Errors of the spatial lag model are normal with constant variance
No areas lack neighbours, or they are handled with zero.policy

Reading and reporting the results

Report Moran's I with its p-value and the number of areas in each LISA cluster. For the model, report rho, the predictor coefficients, and the AIC and LR comparison with OLS; a significant positive rho means an area's value is driven partly by its neighbours.

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: Spatial Autocorrelation and Spatial Regression (sf, spdep)
suppressPackageStartupMessages({
  library(ggplot2)
  library(patchwork)
  library(sf)
  library(spdep)
  library(spatialreg)
})
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"))

# ---- Wilayah sintetis: sel grid 5 km (CRS UTM 49S) yang dipangkas menjadi bentuk wilayah tak beraturan ----
kotak <- sf::st_as_sfc(sf::st_bbox(c(xmin = 500000, ymin = 9100000, xmax = 570000, ymax = 9160000), crs = sf::st_crs(32749)))
sel <- sf::st_make_grid(kotak, cellsize = 5000, square = TRUE)
pusat_sel <- sf::st_coordinates(sf::st_centroid(sel))
u <- (pusat_sel[, 1] - 535000) / 33000
v <- (pusat_sel[, 2] - 9130000) / 28000
fase <- runif(1, 0, 2 * pi)
batas <- 1 + 0.22 * sin(3 * atan2(v, u) + fase) + 0.1 * cos(5 * atan2(v, u))
peta <- sf::st_sf(wilayah = NA_character_, geometry = sel[u^2 + v^2 < batas])
peta$wilayah <- sprintf("W%03d", seq_len(nrow(peta)))
xy <- sf::st_coordinates(sf::st_centroid(sf::st_geometry(peta)))
peta$koord_x <- round(xy[, 1]); peta$koord_y <- round(xy[, 2])

# ---- Matriks bobot spasial: tetangga queen, standarisasi baris ----
nb <- spdep::poly2nb(peta, queen = TRUE)
lw <- spdep::nb2listw(nb, style = "W", zero.policy = TRUE)
print(summary(nb))

# ---- Data sintetis: Y mengikuti proses SAR, Y = (I - rho W)^-1 (X b + e) ----
m <- nrow(peta)
W <- spdep::listw2mat(lw)
tren <- as.numeric(scale(xy[, 1] * runif(1, -1, 1) + xy[, 2] * runif(1, -1, 1)))
z1 <- 0.6 * tren + rnorm(m, 0, 0.8)                     # X1 sedikit berpola spasial
z2 <- rnorm(m)
rho_benar <- runif(1, 0.45, 0.7)
b1 <- runif(1, 0.5, 0.8); b2 <- runif(1, 0.2, 0.45) * sample(c(-1, 1), 1)
zy <- as.numeric(solve(diag(m) - rho_benar * W, b1 * z1 + b2 * z2 + rnorm(m, 0, runif(1, 0.5, 0.7))))
positif <- function(x, mu) if (mu > 0) pmax(x, 0.05 * mu) else x   # cegah nilai negatif yang tidak wajar
peta$junior_secondary_ger <- round(positif(100 + 15 * as.numeric(scale(zy)), 100), 3)
peta$mean_distance_to_school <- round(positif(50 + 10 * as.numeric(scale(z1)), 50), 3)
peta$poor_population <- round(positif(30 + 6 * z2, 30), 3)
d <- sf::st_drop_geometry(peta)                          # kolom geometri tidak ditulis ke CSV
write.csv(d, "data_contoh.csv", row.names = FALSE)

# ---- Autokorelasi spasial global (Moran's I) dan lokal (LISA) ----
mi <- spdep::moran.test(peta$junior_secondary_ger, lw, zero.policy = TRUE)
print(mi)
lisa <- spdep::localmoran(peta$junior_secondary_ger, lw, zero.policy = TRUE)
zy_std <- as.numeric(scale(peta$junior_secondary_ger))
lag_y <- spdep::lag.listw(lw, zy_std, zero.policy = TRUE)
p_lisa <- lisa[, 5]
peta$lisa <- ifelse(p_lisa >= 0.05, "Not significant",
                    ifelse(zy_std > 0 & lag_y > 0, "High-High", ifelse(zy_std < 0 & lag_y < 0, "Low-Low",
                           ifelse(zy_std > 0, "High-Low", "Low-High"))))
print(table(peta$lisa))

# ---- Regresi OLS, uji pengganda Lagrange, dan model spasial lag (SAR) ----
ols <- lm(junior_secondary_ger ~ mean_distance_to_school + poor_population, data = peta)
print(summary(ols))
print(spdep::lm.morantest(ols, lw, zero.policy = TRUE))
rs <- spdep::lm.RStests(ols, lw, test = c("RSerr", "RSlag", "adjRSerr", "adjRSlag"), zero.policy = TRUE)
print(rs)
sar <- spatialreg::lagsarlm(junior_secondary_ger ~ mean_distance_to_school + poor_population, data = peta, listw = lw, zero.policy = TRUE)
print(summary(sar))
rho <- as.numeric(sar$rho)
lr <- 2 * (as.numeric(logLik(sar)) - as.numeric(logLik(ols)))
p_lr <- pchisq(lr, df = 1, lower.tail = FALSE)
aic_ols <- AIC(ols); aic_sar <- AIC(sar)


# ---- Grafik ----
tema_peta <- theme(axis.text = element_blank(), axis.title = element_blank(), panel.grid = element_blank())
p1 <- ggplot(peta) +
  geom_sf(aes(fill = junior_secondary_ger), colour = warna$panel, linewidth = 0.25) +
  scale_fill_gradient(low = warna$grid, high = pal[1], name = NULL) +
  coord_sf(datum = NA) +
  labs(title = "Choropleth map", subtitle = paste0("junior_secondary_ger", " by ", tolower("Group"))) +
  tema_peta + theme(legend.key.width = unit(0.5, "lines"))
warna_lisa <- c("High-High" = pal[2], "Low-Low" = pal[1], "High-Low" = pal[5], "Low-High" = pal[4], "Not significant" = warna$grid)
peta$lisa <- factor(peta$lisa, levels = names(warna_lisa))
p2 <- ggplot(peta) +
  geom_sf(aes(fill = lisa), colour = warna$panel, linewidth = 0.25, show.legend = TRUE) +
  scale_fill_manual(values = warna_lisa, drop = FALSE, name = NULL) +
  coord_sf(datum = NA) +
  labs(title = "LISA cluster map (p < 0.05)", subtitle = "Queen contiguity, row-standardised W") +
  tema_peta + theme(legend.key.size = unit(0.6, "lines"))
dm <- data.frame(z = zy_std, lag = lag_y, lisa = peta$lisa)
p3 <- ggplot(dm, aes(z, lag)) +
  geom_hline(yintercept = 0, colour = warna$redup, linetype = "dashed") +
  geom_vline(xintercept = 0, colour = warna$redup, linetype = "dashed") +
  geom_point(aes(colour = lisa), size = 1.8, alpha = 0.85, show.legend = FALSE) +
  geom_smooth(method = "lm", formula = y ~ x, se = FALSE, colour = warna$teks, linewidth = 0.9) +
  scale_colour_manual(values = replace(warna_lisa, "Not significant", warna$redup)) +
  labs(title = sprintf("Moran scatterplot (I = %.3f)", mi$estimate[1]), x = "junior_secondary_ger (z-score)", y = "Spatial lag of z")
p1 <- wrap_elements(full = p1)   # peta berasio tetap: isi penuh sel tata letak
p2 <- wrap_elements(full = p2)
p_hasil <- if (tata == 1) ((p1 | p2) / p3) + plot_layout(heights = c(1.25, 1)) else
  (p3 | (p1 / p2)) + plot_layout(widths = c(1, 1.1))

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$31

excl. 11% VAT

Duration: 7 working days

Output: R files + result figures

Deliverables

Fully commented R code (.R) for Spatial Autocorrelation and Spatial Regression (sf, spdep)
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$88

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$191

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. Spatial Autocorrelation and Spatial Regression (sf, spdep) 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$31, Package 2 (your data analysis and interpretation) US$88 and Package 3 (full guidance) US$191, excluding 11% VAT. Larger datasets, extra methods or tight deadlines adjust the quote after a short consultation.

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