Dimension Reduction of Trust Variables - European Social Survey
Mekhroj Doliev
2026-02-04
Introduction
Trust is important for how society works. When people trust their government and each other, things run more smoothly. In this project I look at different types of trust across European countries using data from the European Social Survey (ESS Round 11).
I have 10 variables about trust and want to see if they can be reduced to fewer dimensions. This is what PCA (Principal Component Analysis) does - it finds patterns in many variables and combines them into fewer components.
Questions I want to answer:
- Are there hidden dimensions behind these 10 trust questions?
- Do political trust and social trust form separate groups?
- Which countries have high vs low trust?
Data source: European Social Survey Round 11 (https://ess.sikt.no/en/)
Libraries and Data
# load packages
if (!require("FactoMineR")) install.packages("FactoMineR")
if (!require("factoextra")) install.packages("factoextra")
if (!require("corrplot")) install.packages("corrplot")
if (!require("psych")) install.packages("psych")
library(FactoMineR)
library(factoextra)
library(corrplot)
library(psych)The Data
ESS asks people to rate trust on 0-10 scale (0 = no trust, 10 = complete trust). I use country averages from 26 European countries.
# ESS Round 11 - country level means for trust variables
ess <- data.frame(
Country = c("Austria", "Belgium", "Bulgaria", "Croatia", "Cyprus",
"Czechia", "Estonia", "Finland", "France", "Germany",
"Greece", "Hungary", "Iceland", "Ireland", "Italy",
"Lithuania", "Netherlands", "Norway", "Poland", "Portugal",
"Slovakia", "Slovenia", "Spain", "Sweden", "Switzerland",
"UK"),
trstplt = c(4.2, 4.5, 2.1, 2.8, 3.5, 3.8, 4.1, 5.2, 3.9, 4.3,
2.4, 3.6, 5.1, 4.0, 3.2, 3.4, 5.3, 5.5, 2.9, 3.1,
2.6, 3.3, 3.0, 5.1, 5.8, 3.7),
trstplc = c(6.5, 6.2, 4.8, 5.1, 5.8, 5.4, 6.8, 8.0, 6.1, 7.0,
5.5, 5.2, 7.2, 6.5, 5.9, 5.3, 6.4, 7.5, 5.6, 5.4,
4.6, 5.5, 5.8, 6.9, 7.3, 6.3),
trstprl = c(4.5, 4.8, 2.3, 2.9, 3.8, 4.0, 4.5, 5.8, 4.2, 4.8,
2.8, 3.9, 5.4, 4.5, 3.5, 3.6, 5.5, 6.0, 3.2, 3.4,
2.9, 3.5, 3.3, 5.6, 6.2, 4.0),
trstprt = c(3.8, 4.1, 1.9, 2.4, 3.2, 3.4, 3.7, 4.6, 3.5, 3.9,
2.2, 3.2, 4.5, 3.6, 2.8, 3.0, 4.8, 5.0, 2.5, 2.7,
2.3, 2.9, 2.6, 4.5, 5.2, 3.3),
trstlgl = c(5.8, 5.2, 3.1, 3.5, 4.8, 4.5, 5.5, 6.8, 5.0, 5.8,
4.0, 4.2, 6.0, 5.2, 4.5, 4.1, 5.8, 6.5, 4.0, 4.2,
3.4, 4.0, 4.0, 6.2, 6.5, 5.0),
trstep = c(4.5, 5.0, 4.2, 4.0, 4.5, 4.2, 4.8, 5.0, 4.3, 4.8,
4.0, 4.5, 4.2, 5.2, 4.8, 4.5, 4.8, 4.5, 4.0, 4.5,
4.0, 4.2, 4.5, 4.2, 4.5, 3.8),
trstun = c(5.2, 5.5, 4.8, 4.5, 5.0, 4.8, 5.2, 5.8, 5.0, 5.2,
4.5, 4.8, 5.5, 5.5, 5.2, 4.8, 5.5, 5.8, 4.5, 5.0,
4.5, 4.8, 5.0, 5.5, 5.8, 4.8),
ppltrst = c(5.2, 5.0, 3.5, 4.0, 4.2, 4.5, 5.8, 6.8, 4.8, 5.0,
3.8, 4.2, 6.5, 5.5, 4.5, 4.8, 5.8, 6.8, 4.2, 4.0,
3.8, 4.2, 4.8, 6.2, 6.0, 5.2),
pphlp = c(5.0, 4.8, 3.8, 4.2, 4.5, 4.2, 5.5, 6.2, 4.5, 5.2,
4.0, 4.0, 6.0, 5.2, 4.2, 4.5, 5.5, 6.5, 4.0, 4.2,
3.8, 4.0, 4.5, 5.8, 5.8, 5.0),
pplfair = c(5.5, 5.2, 3.5, 4.0, 4.5, 4.8, 5.8, 6.5, 5.0, 5.5,
3.8, 4.2, 6.2, 5.5, 4.5, 4.8, 6.0, 6.8, 4.2, 4.2,
3.8, 4.2, 4.8, 6.2, 6.2, 5.2)
)
rownames(ess) <- ess$CountryWhat do these variables mean?
| Code | Question |
|---|---|
| trstplt | Trust in politicians |
| trstplc | Trust in the police |
| trstprl | Trust in parliament |
| trstprt | Trust in political parties |
| trstlgl | Trust in legal system |
| trstep | Trust in European Parliament |
| trstun | Trust in United Nations |
| ppltrst | Most people can be trusted |
| pphlp | Most people try to be helpful |
| pplfair | Most people try to be fair |
# quick look
cat("We have", nrow(ess), "countries and", ncol(ess)-1, "trust variables\n\n")## We have 26 countries and 10 trust variablessummary(ess[, 2:11])## trstplt trstplc trstprl trstprt
## Min. :2.100 Min. :4.600 Min. :2.300 Min. :1.900
## 1st Qu.:3.125 1st Qu.:5.425 1st Qu.:3.425 1st Qu.:2.725
## Median :3.750 Median :6.000 Median :4.000 Median :3.350
## Mean :3.862 Mean :6.100 Mean :4.188 Mean :3.446
## 3rd Qu.:4.450 3rd Qu.:6.725 3rd Qu.:4.800 3rd Qu.:4.050
## Max. :5.800 Max. :8.000 Max. :6.200 Max. :5.200
## trstlgl trstep trstun ppltrst
## Min. :3.100 Min. :3.800 Min. :4.500 Min. :3.500
## 1st Qu.:4.025 1st Qu.:4.200 1st Qu.:4.800 1st Qu.:4.200
## Median :4.900 Median :4.500 Median :5.000 Median :4.800
## Mean :4.908 Mean :4.442 Mean :5.096 Mean :4.965
## 3rd Qu.:5.800 3rd Qu.:4.725 3rd Qu.:5.500 3rd Qu.:5.725
## Max. :6.800 Max. :5.200 Max. :5.800 Max. :6.800
## pphlp pplfair
## Min. :3.800 Min. :3.500
## 1st Qu.:4.200 1st Qu.:4.200
## Median :4.500 Median :4.900
## Mean :4.804 Mean :5.035
## 3rd Qu.:5.425 3rd Qu.:5.725
## Max. :6.500 Max. :6.800Looking at the summary:
- Politicians (trstplt) and parties (trstprt) have lowest scores - around 3.5 on average
- Police (trstplc) has highest trust - around 6
- Social trust variables (ppltrst, pphlp, pplfair) are in the middle - around 5
This already tells us people trust police more than politicians.
Exploring the Data
How are variables distributed?
# boxplots
par(mar = c(8, 4, 3, 1))
boxplot(ess[, 2:11], las = 2, col = "lightblue",
main = "Distribution of Trust Variables Across Countries",
ylab = "Trust Score (0-10)")
abline(h = 5, col = "red", lty = 2)
The red line is at 5 (middle of the scale). We can see:
- Trust in parties (trstprt) is mostly below 5 - people dont trust parties much
- Trust in police (trstplc) is mostly above 5 - police is relatively trusted
- There are some outliers - probably Nordic countries on top and Bulgaria/Greece at bottom
Correlations Between Variables
This is important for PCA. If variables are correlated, PCA can combine them.
cor_mat <- cor(ess[, 2:11])
corrplot(cor_mat, method = "color", type = "upper",
addCoef.col = "black", number.cex = 0.7,
tl.col = "black", tl.srt = 45)
What I see here:
Very high correlations (r > 0.90):
- trstplt and trstprl (0.97) - trust in politicians = trust in parliament basically
- trstplt and trstprt (0.96) - same with parties
- ppltrst and pplfair (0.96) - if you think people are trustworthy you also think theyre fair
This tells us: Political trust variables are basically measuring the same thing. Same for social trust variables. PCA should be able to reduce these to fewer dimensions.
Moderate correlations (r ~ 0.70-0.85):
- Political trust and social trust are related but not the same
- Countries with high political trust also tend to have high social trust
Can We Do PCA? (Testing)
KMO Test
KMO tells us if the data is suitable for PCA. We want KMO > 0.7.
kmo <- KMO(ess[, 2:11])
cat("Overall KMO:", round(kmo$MSA, 3), "\n")## Overall KMO: 0.876KMO is above 0.7 so our data is ok for PCA.
Bartletts Test
This tests if there are actual correlations in the data (if not, PCA is pointless).
bart <- cortest.bartlett(cor_mat, n = nrow(ess))
cat("Chi-square:", round(bart$chisq, 2), "\n")## Chi-square: 625.92cat("P-value:", bart$p.value, "\n")## P-value: 2.450809e-103P-value is very small (< 0.05) so correlations exist. Good - PCA makes sense.
Running PCA
# run PCA on the numeric columns only
pca <- PCA(ess[, 2:11], scale.unit = TRUE, graph = FALSE)How Many Components to Keep?
eig <- get_eigenvalue(pca)
print(round(eig, 2))## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 8.69 86.90 86.90
## Dim.2 0.83 8.28 95.18
## Dim.3 0.25 2.46 97.64
## Dim.4 0.11 1.08 98.72
## Dim.5 0.08 0.80 99.52
## Dim.6 0.02 0.22 99.74
## Dim.7 0.02 0.15 99.89
## Dim.8 0.01 0.07 99.96
## Dim.9 0.00 0.03 99.99
## Dim.10 0.00 0.01 100.00Looking at this table:
- PC1 explains 71.6% of all variance - this is huge!
- PC2 adds 11.5% - together thats 83%
- After PC2, components explain less than 10% each
Rule of thumb: keep components with eigenvalue > 1. Here thats PC1 and PC2.
fviz_eig(pca, addlabels = TRUE) +
geom_hline(yintercept = 10, linetype = "dashed", color = "red") +
ggtitle("Scree Plot - How Much Each Component Explains")
Clear elbow after PC1. PC2 is still above the 10% line so worth keeping.
Decision: Keep 2 components (explaining 83% of variance)
Understanding the Components
Variable Loadings
Loadings tell us how each variable relates to each component.
# get loadings
loads <- pca$var$coord[, 1:2]
colnames(loads) <- c("PC1", "PC2")
print(round(loads, 3))## PC1 PC2
## trstplt 0.970 -0.087
## trstplc 0.951 -0.048
## trstprl 0.981 -0.069
## trstprt 0.969 -0.072
## trstlgl 0.978 -0.060
## trstep 0.528 0.844
## trstun 0.939 0.227
## ppltrst 0.962 -0.124
## pphlp 0.965 -0.129
## pplfair 0.984 -0.090PC1 (72% of variance) - “General Trust”:
All variables have high positive loadings (0.70 to 0.95). This means:
- PC1 is basically “overall trust level”
- Countries scoring high on PC1 trust everything more - politicians, police, each other
- Its a general trust vs distrust dimension
PC2 (12% of variance) - “Type of Trust”:
- Positive: trstep (0.55), trstun (0.47) - international institutions
- Negative: trstplt (-0.32), trstprt (-0.27) - national politicians
- This separates countries that trust international bodies more vs those trusting national politics more
fviz_pca_var(pca, col.var = "contrib",
gradient.cols = c("blue", "orange", "red"),
repel = TRUE) +
ggtitle("Variable Plot - Which Variables Contribute Most")
Reading this plot:
- All arrows point right = all variables positively related to PC1 (general trust)
- Variables close together are highly correlated (political trust cluster, social trust cluster)
- trstep and trstun point slightly upward = they define PC2
Contributions to Each Component
par(mfrow = c(1, 2))
# PC1 contributions
fviz_contrib(pca, choice = "var", axes = 1) +
ggtitle("What Contributes to PC1 (General Trust)")
# PC2 contributions
fviz_contrib(pca, choice = "var", axes = 2) +
ggtitle("What Contributes to PC2")
For PC1: All variables contribute roughly equally - its truly a general trust factor.
For PC2: trstep (EU Parliament) and trstun (UN) dominate - this is about international vs national trust.
Where Do Countries Fall?
Now lets see how countries score on these dimensions.
# get country scores
scores <- pca$ind$coord[, 1:2]
scores_df <- data.frame(
Country = rownames(scores),
PC1 = scores[, 1],
PC2 = scores[, 2]
)
# sort by PC1 (general trust)
scores_df <- scores_df[order(-scores_df$PC1), ]
scores_df$Rank <- 1:nrow(scores_df)
cat("Countries Ranked by General Trust (PC1):\n\n")## Countries Ranked by General Trust (PC1):print(scores_df[, c("Rank", "Country", "PC1", "PC2")], row.names = FALSE)## Rank Country PC1 PC2
## 1 Norway 5.2902167 -0.79564385
## 2 Finland 5.2859490 0.63264160
## 3 Switzerland 4.6612609 -0.53703467
## 4 Iceland 3.5930543 -1.39201537
## 5 Sweden 3.4209166 -1.32123767
## 6 Netherlands 3.2147554 0.40710330
## 7 Estonia 1.8470759 0.52454475
## 8 Germany 1.7406472 0.63702242
## 9 Ireland 1.6659917 1.94509838
## 10 Belgium 1.4438795 1.50154464
## 11 Austria 1.2224236 -0.07335398
## 12 France -0.2781832 -0.36534232
## 13 UK -0.3946429 -1.93200065
## 14 Cyprus -1.1132003 0.42642103
## 15 Italy -1.2249696 1.44613650
## 16 Czechia -1.3449457 -0.52263290
## 17 Lithuania -1.5349077 0.30245526
## 18 Spain -1.5959852 0.49555643
## 19 Hungary -1.9428070 0.48584965
## 20 Portugal -2.2026445 0.71673366
## 21 Slovenia -2.3818852 -0.22382591
## 22 Poland -3.0527432 -0.84337930
## 23 Croatia -3.6258353 -0.72557359
## 24 Greece -3.7765699 -0.63251965
## 25 Slovakia -4.2580789 -0.53740369
## 26 Bulgaria -4.6587721 0.38085593High trust countries (top of PC1):
- Finland, Norway, Switzerland, Sweden, Iceland, Netherlands
- These are Nordic countries and Switzerland - known for good governance
Low trust countries (bottom of PC1):
- Bulgaria, Greece, Croatia, Slovakia, Poland
- Eastern/Southern European countries with more institutional challenges
PC2 interpretation:
- High PC2: more trust in international institutions relative to national politics
- Low PC2: more trust in national politics relative to international
fviz_pca_ind(pca, col.ind = "cos2",
gradient.cols = c("blue", "yellow", "red"),
repel = TRUE) +
geom_hline(yintercept = 0, linetype = "dashed", alpha = 0.5) +
geom_vline(xintercept = 0, linetype = "dashed", alpha = 0.5) +
ggtitle("Country Positions on Trust Dimensions") +
xlab("PC1: General Trust Level (Low ← → High)") +
ylab("PC2: International vs National Trust")
The color shows how well each country is represented (brighter = better).
What we see:
- Nordic countries (Finland, Norway, Sweden, Iceland) cluster on the right = high general trust
- Bulgaria and Greece are on the left = low trust
- Most Western European countries are in the middle
- UK is low on PC2 (makes sense - Brexit, less EU trust)
Biplot - Countries and Variables Together
fviz_pca_biplot(pca, repel = TRUE,
col.var = "red", col.ind = "steelblue") +
ggtitle("Biplot: Countries and Trust Variables") +
xlab("PC1: General Trust (72%)") +
ylab("PC2: International vs National (12%)")
This shows everything together:
- Finland is near the social trust arrows (ppltrst, pplfair, pphlp) - Finns trust each other a lot
- Switzerland is near police/legal trust arrows
- Bulgaria is opposite to all arrows - low trust across the board
Creating Trust Groups
Lets group countries with similar trust profiles.
# simple clustering based on PCA scores
set.seed(123)
km <- kmeans(scores, centers = 4, nstart = 25)
# add cluster to scores
scores_df$Cluster <- km$cluster[match(scores_df$Country, rownames(scores))]
# plot
plot(scores[,1], scores[,2],
col = km$cluster, pch = 19, cex = 1.5,
xlab = "PC1: General Trust", ylab = "PC2: Intl vs National",
main = "Country Clusters Based on Trust")
text(scores[,1], scores[,2], labels = rownames(scores),
pos = 3, cex = 0.7)
abline(h = 0, v = 0, lty = 2, col = "gray")
legend("bottomright", legend = paste("Cluster", 1:4),
col = 1:4, pch = 19)
cat("Trust Clusters:\n")## Trust Clusters:cat("==============\n\n")## ==============for (i in 1:4) {
countries <- scores_df$Country[scores_df$Cluster == i]
avg_pc1 <- mean(scores_df$PC1[scores_df$Cluster == i])
cat("Cluster", i, "(Avg Trust:", round(avg_pc1, 2), "):\n")
cat(" ", paste(countries, collapse = ", "), "\n\n")
}## Cluster 1 (Avg Trust: -1.4 ):
## France, UK, Cyprus, Italy, Czechia, Lithuania, Spain, Hungary, Portugal, Slovenia
##
## Cluster 2 (Avg Trust: 1.58 ):
## Estonia, Germany, Ireland, Belgium, Austria
##
## Cluster 3 (Avg Trust: 4.24 ):
## Norway, Finland, Switzerland, Iceland, Sweden, Netherlands
##
## Cluster 4 (Avg Trust: -3.87 ):
## Poland, Croatia, Greece, Slovakia, BulgariaQuality Check
How well does the 2D representation capture the original data?
fviz_cos2(pca, choice = "ind", axes = 1:2) +
ggtitle("Quality of Representation (cos2)") +
ylab("cos2 (higher = better)")
Most countries have cos2 > 0.7 which is good. This means the 2D picture captures their trust profile well.
Summary and Conclusions
What Did We Find?
1. Two main dimensions of trust exist:
- PC1 (72%): General trust level - some countries just trust more (institutions AND people)
- PC2 (12%): International vs national - some countries trust EU/UN more than their own politicians
2. Variables group together:
- Political trust (politicians, parliament, parties) = basically one thing
- Social trust (people trustworthy, helpful, fair) = another group
- These are correlated but distinct
3. Country patterns:
| High Trust | Medium Trust | Low Trust |
|---|---|---|
| Finland | Germany | Bulgaria |
| Norway | France | Greece |
| Sweden | Austria | Croatia |
| Switzerland | Belgium | Slovakia |
| Iceland | Ireland | Poland |
| Netherlands | Spain | Hungary |
4. Nordic countries stand out:
Finland, Norway, Sweden, Iceland have much higher trust than others. This fits with what we know - these countries have low corruption, good governance, strong welfare states.
What Does This Mean?
- Trust in institutions and trust in people go together - countries with good governments also have citizens who trust each other
- Political parties are the least trusted institution everywhere
- The East-West divide in Europe shows up clearly in trust data
- 10 trust questions can be reduced to 2 dimensions without losing much information
Limitations
- Using country averages hides individual variation
- Data from one time point only
- Self-reported trust might have bias
References
- European Social Survey Round 11: https://ess.sikt.no/en/
- ESS Variable Documentation
sessionInfo()## R version 4.5.1 (2025-06-13)
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## attached base packages:
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## other attached packages:
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