What Montenegro’s PISA 2022 data says about the north, and what it cannot say

About half of the north’s disadvantage is socio-economic composition. The other half is not explained by who the students are or by which type of school they attend, and the largest divide in the data is not regional at all.

Dr Milos Kankaras | ORCID 0000-0002-3190-7751 | Center for Psychology, Podgorica | PISA 2022 country notes, Western Balkans | August 2026

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Summary

Montenegro’s 15-year-olds averaged 405.6 score points in mathematics in PISA 2022. That single number is what the international report is built to deliver, and it is where most national discussion of PISA begins and ends. This note asks a different question of the same data, one the international volumes are not structured to answer: how large is the gap between Montenegro’s regions, and what is it actually made of.

What the data shows.

• Students in the north scored 25.0 points below students in the central region (2.5). Roughly half of that gap is socio-economic composition: net of the PISA index the gap is 13.2 points (2.6), and it remains clearly different from zero.
• The remaining gap is not explained by which school programmes northern students attend either. Adjusting for programme as well as socio-economic status leaves 16.0 points (2.5).
• The largest structural divide in the data is not regional. Students in gimnazija programmes outscored students in vocational programmes by 79.0 points (2.3), and by 67.4 points once socio-economic status is held constant, for the 53.5% of the cohort in vocational programmes.
• The mathematics anxiety index quoted alongside these gaps was tested for measurement equivalence across the same groups before being compared. It passed at the strict level under two different estimators.

This note is an independent contribution alongside the work of Montenegro’s national PISA centre, not a commentary on it. It uses only data the OECD has made public, and it is written so that every estimate in it can be reproduced. Comments and corrections from the national centre are welcome.

Why this question

Every country in PISA receives, on release day, a rank, a headline and an international report written for eighty education systems at once. What almost no country receives is an analysis of its own data at the resolution its own policy debate operates at. Montenegro’s debate is not about where it sits between Serbia and Croatia. It is about the north, about vocational schooling, and about whether the differences everyone quotes are real.

Those questions can be answered from data that already exists. The PISA 2022 Public Use Files have been openly downloadable since May 2024, they contain every Montenegrin student record, and Montenegro paid for their collection. What they require is the analytical machinery to handle them properly: plausible values, replicate weights, and a willingness to test whether a comparison is measurement-supported before making it.

Regions here are taken from the explicit sampling strata the OECD publishes for Montenegro, which cross school programme with north, central and south. That is the national centre’s own design variable rather than a grouping invented by an outside analyst. It should be read as an analytical breakdown rather than official regional statistics, because Montenegro is not regionally adjudicated in PISA and the OECD publishes no separate regional estimates.

The data, and how it was handled

5,793 students in 63 schools, representing a weighted population of 6,340 15-year-olds, from the OECD’s PISA 2022 student and school Public Use Files. National mean in mathematics: 405.6 points (SE 1.1).

Achievement is imputed rather than measured, so estimates are pooled by Rubin’s rules over all ten plausible values. The sample is clustered in schools, so standard errors come from the 80 Fay-adjusted replicate weights the OECD ships for the purpose. Omitting either understates the uncertainty, usually by a factor of two or more.

Source: OECD, PISA 2022 Results (Volume I and II) Country Note: Montenegro, published 5 December 2023, https://www.oecd.org/en/publications/pisa-2022-results-volume-i-and-ii-country-notes_ed6fbcc5-en/montenegro_84d80839-en.html

The regional gap, and what survives adjustment

The three regions are far apart, on a scale where the national standard deviation is 81.6 points.

The obvious explanation is family background, and it is partly right. The north is markedly more disadvantaged, at -0.54 on the PISA index against -0.10 in the centre, and each one-unit increase in that index is worth 29.3 score points (1.4) nationally. Adjusting for it removes about half the gap and leaves the rest standing.

The south is the more surprising half of the picture. Its socio-economic profile is close to the centre’s, at -0.07 against -0.10, so adjustment barely moves its advantage: 10.5 points unadjusted, 9.5 net of socio-economic status. Whatever is happening in the south is not a socio-economic story.

A second candidate explanation is that the north simply has a different mix of school programmes. Holding programme constant as well does not shrink the northern gap; it widens it slightly, to 16.0 points below the centre, while the southern advantage widens to 14.0 points.

The policy reading is narrow and defensible. About half of the north’s measured disadvantage is the socio-economic composition of the region. The other half is a difference in what happens to comparable students in comparable programmes, and it is the part a regional policy instrument could in principle move.

The divide that is larger than the regional one

Regional debate is loud, but the data puts a bigger number somewhere else. The distance between gimnazija and vocational programmes is three times the north to centre gap.

Socio-economic selection into the two tracks is real and accounts for part of it, but only part: net of the index the gap is still 67.4 points, roughly four fifths of a national standard deviation.

Two cautions before anyone reaches for a conclusion. This is a selection difference as much as a school-effect difference, and PISA cannot separate the two: students are not randomly assigned to tracks and prior attainment is not measured. And it is measured at age 15, when tracking has only recently taken effect, so it says nothing directly about what the two tracks add over their full duration.

Can this comparison be trusted? A measurement audit

Test scores are placed on a common scale by design. Questionnaire indices are not. Comparing an index across groups assumes the items mean the same thing in every group being compared, and that assumption is testable. It is usually not tested.

The obvious index to attach to these findings is mathematics anxiety, which PISA 2022 measures with six items and which is the most quoted explanatory variable in the mathematics cycle. Before comparing it across regions and programmes, it was put through a staged measurement-invariance cascade.

Measurement invariance of the mathematics anxiety block across region. N = 4,787. Estimator MLR. Decision rule after Chen (2007).

Strict invariance held across regions, and a separate run reached the same verdict across school programmes. Because a continuous estimator on four-category items can in principle distort this verdict, the whole cascade was refitted with a categorical estimator on pairwise-present data, and it reached strict invariance again in both groupings. The conclusion does not depend on the estimator.

One honest qualification belongs with that result. Absolute fit of the single-factor model is mediocre in every group, with RMSEA around 0.14 at the configural stage. Invariance means the model is equally imperfect everywhere, which is what licenses the comparison. It does not mean the index is a clean unidimensional measure of one thing.

What follows

Three statements are supported by the analysis above and are narrow enough to defend under questioning.

• The north’s disadvantage is real and is only about half compositional. A policy response aimed purely at socio-economic disadvantage would address roughly half of the measured gap and leave the rest untouched.
• The vocational to gimnazija gap is the largest single structure in Montenegro’s 15-year-old attainment distribution, it is not mainly explained by who enters each track, and it applies to more than half the cohort.
• Mathematics anxiety differs by programme rather than by region, and that comparison has been shown to be measurement-supported rather than assumed.

The natural next question, which this note does not answer, is what happens to the northern gap inside programmes and inside schools, and whether it is concentrated in particular strata. That requires the school-level file and a multilevel decomposition, which is a larger piece of work than a note.

What this note does not claim

• No trend statement. Comparing 2022 with an earlier cycle requires the published link error for that cycle pair to be carried in the variance. No such comparison is made here.
• No causal claim. Every difference is an association measured at one point in time. “Net of ESCS” means one measured index is held constant, not that other things are equal.
• The invariance cascade is fitted without the replicate-weight design, which is standard practice and is stated rather than left implicit.
• No official regional statistics. Montenegro is not regionally adjudicated in PISA, so the regional breakdown uses the OECD’s published sampling strata, which is a sound analytical basis but is not an official regional estimate.
• Limited precision in small cells. The regional samples rest on 63 schools in total, and the smallest programme group has 66 students. The confidence intervals should be read rather than the point estimates.

Method and reproducibility

Data: OECD PISA 2022 Public Use Files, downloaded from webfs.oecd.org on 6 August 2026. Point estimates pooled over ten plausible values by Rubin’s rules; sampling variance from 80 Fay-adjusted replicate weights with a Fay factor of 0.5, computed per plausible value and averaged; imputation variance inflated by (1 + 1/M). Invariance tested as a staged configural, metric, scalar and strict cascade in lavaan with full-information estimation for the rotated questionnaire design, plus a categorical sensitivity re-run on pairwise-present data.

Subgroups are derived from variables the OECD codes identically in every participating system, so this note was produced without country-specific recoding. Where a country’s own sampling strata carry a more policy-relevant structure, that structure is used instead and the note says so.

Enquiries about reproducing the analysis are welcome at milos@centerforpsychology.me. Commissioning the equivalent for another country is consulting work, handled by AdriaMont Consulting DOO at milos@adriamont.me.

All country notes in this series