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REVIEW 3 major objections 6 minor 35 references

Flexible tree-structured regression for clustered data with an application to quality of life in older adults

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper proposes a regression model whose predictor is the sum of two trees—one that clusters units into shared intercepts and one that captures nonlinear covariate effects—and shows it on quality-of-life data from the SHARE survey.

desk verdict A genuinely useful combination of unit-tree and covariate-tree fixed effects, but the unit clustering rests on an outcome-mean ordering that the simulations never stress-test. read the letter →

arxiv 2501.12787 v1 pith:SZUBNWO4 submitted 2025-01-22 stat.ME

Nikolai Spuck , Matthias Schmid , Moritz Berger This is my paper · ORCID
classification stat.ME MSC 62J0262P25
keywords tree-structuredregressionclustereddatafixedeffectsmodelsunit-specificinterceptsrecursivepartitioningqualityoflifeCASPSHARE
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper develops a regression model for clustered data whose predictor is the sum of two trees: one tree gives each cluster of units (here countries) its own intercept, and the other tree captures how covariates affect the outcome, including nonlinearities and interactions. The authors aim to close a gap: earlier methods had either clustered fixed country effects with linear covariate terms, or tree-structured covariate effects with random intercepts, but not both. If the method works, analysts gain an interpretable tool for cross-national surveys that both identifies groups of similar countries and subgroups of individuals at risk, without imposing linearity or a normal distribution on the unit effects. The paper supports the claim with a simulation study and an application to quality of life in older adults from the SHARE survey.

What carries the argument

The load-bearing object is the two-tree predictor $\eta(x_{ij}) = tr_0(i) + tr(x_{ij})$ built inside a fixed-effects model. Units are first ordered by their outcome means and treated as an ordinal variable, so clustering becomes a sequence of binary splits on the unit index, keeping the search linear rather than exponential. At each step all candidate splits in either tree are evaluated, and the one with smallest deviance is chosen; then all parameters are refitted, so the two tree components mutually adjust for each other's splits. The resulting split sequence is pruned by ten-fold cross-validated predictive log-likelihood with the one-standard-error rule, and a coefficient adjustment $\tilde{\beta}_{0c} = \beta_{0c} + \bar{\gamma}$, $\tilde{\gamma}_m = \gamma_m - \bar{\gamma}$ converts reference-node coding into average cluster intercepts and subgroup deviations, which is what makes the output interpretable.

What would settle it

Simulate data with true clustered intercepts while letting covariate distributions differ strongly across units, and check whether recovery of the true clusters by the intercept tree degrades relative to a balanced setting; if the outcome-mean ordering is the weak point, cluster recovery should drop exactly in that scenario.

Watch

Extended reading notes

Core claim

The central claim is that the model $\eta(x_{ij}) = tr_0(i) + tr(x_{ij})$—a fixed-effects predictor with a tree-structured unit intercept $tr_0(i)$ and a second tree-structured covariate effect $tr(x_{ij})$—can be fitted by a stepwise deviance-based algorithm and delivers sparse, interpretable estimates of both cross-unit differences and covariate subgroups. On the SHARE data the fitted model separates the 28 countries into five clusters with expected CASP scores from 32.26 to 40.41, and identifies eleven subgroups of individuals, with number of chronic diseases, income decile, and age as the splitting variables. The lowest-quality-of-life subgroup (more than four chronic diseases and income in the poorer half of one's country) is expected to score 5.10 points below the country expectation, while the highest subgroup (no chronic diseases, income in the wealthiest 40 percent) is expected to score 3.40 points above it.

Load-bearing premise

The method assumes that ordering units by their average outcome recovers the true grouping structure for shared intercepts, so a noisy or confounded ordering could make the country clusters track the outcome ranking instead of genuine intercepts.

Editorial extensions

If this is right

  • Clustered fixed-effects modeling becomes available for nonlinear and interactive covariate effects, not only linear ones.
  • The country clusters found in SHARE line up with welfare-regime and wealth patterns, giving a sparse description of cross-national quality-of-life differences.
  • The model selects variables during fitting, so subgroup discovery and variable selection happen in one pass.
  • Simulation results indicate the approach is most competitive when the number of units is small, observations per unit are many, and the true number of clusters is small.
  • Because fitting is likelihood-based, the same algorithm extends in principle to binary and discrete outcomes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial: a covariate-adjusted version of the unit ordering could be tested; if implemented, it should improve cluster recovery when covariate distributions differ strongly across units.
  • Editorial: the same two-tree construction extends naturally to unit-specific slopes, with one unit tree per covariate effect, though the paper only sketches that extension.
  • Editorial: bagging the split sequence could yield prediction intervals and stabilize variable selection, which the paper does not pursue.
  • Editorial: the country clusters should be read descriptively; the observational SHARE design does not support a causal claim that wealth causes higher quality of life.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes a tree-structured fixed-effects regression model for clustered data in which the predictor η(x_ij) = tr0(i) + tr(x_ij) combines a tree-structured unit-specific intercept term with a tree-structured covariate effect. The fitting procedure orders units by their outcome means, treats the unit index as an ordinal splitting variable, greedily selects splits by deviance, and prunes by cross-validated predictive log-likelihood with a one-standard-error rule. The method is applied to SHARE data on quality of life in older adults, yielding five country clusters and covariate subgroups defined by chronic disease count, income, and age. A simulation study compares the proposed TTSC model to LMM, LMMP, RE-EM, LMMT, LTSC, LTSCB, Null, and Perfect models across four DGPs and six settings.

Significance. If the claims hold, the paper fills a genuine gap by combining sparse fixed-effects clustering of units with tree-structured covariate effects, and it does so with an algorithm that is implemented in the existing TSVC R package. The simulation evidence supports competitiveness for nonlinear covariate effects and for settings with few unit clusters, and the SHARE application demonstrates interpretability and reproduces plausible findings on quality of life. However, the central claim of recovering shared intercept clusters rests on the outcome-mean ordering of units, which has not been validated under between-unit covariate heterogeneity, and the application lacks any uncertainty assessment. The contribution is therefore of moderate significance and would be strengthened considerably by additional validation.

major comments (3)
  1. [Section 3, Step 1 and Eq. (7)] The unit tree tr0(i) is restricted to splits into intervals of the fixed ordering of units by outcome means ȳ_i. For the true cluster structure to be recoverable, this ordering must preserve the ordering of the true intercepts tr0(i). In general E[y_ij | i] = tr0(i) + E[tr(x_ij) | i], so between-unit differences in covariate distributions or covariate effects can dominate the outcome-mean ordering. In the SHARE application (Table 1; Figures 2 and 3), countries differ markedly in age, chronic disease count, income, and employment, so the identified country clusters may partly reflect covariate composition rather than shared country-specific intercepts. In simulation scenarios 3 and 4 (Sections 5.5 and 5.6), covariates are iid within and across units, so the outcome-mean ordering and the true intercept ordering always coincide and the distortion is never exercised. Please add simulation scenarios with between-unit covariate mean shifts or unit-varying covariate effects, and in the application assess the sensitivity of the country clusters to the ordering, for example by ordering units by covariate-adjusted residuals or by an alternative stratification.
  2. [Section 4, Figures 2 and 3] The substantive interpretation of the five country clusters and the reported subgroup effects (e.g., the -5.10 and +3.40 CASP score differences) is presented without any measure of uncertainty or stability. The greedy stepwise algorithm, the fixed ordering of units, and the 1SE cross-validation rule can produce unstable partitions, especially with only 28 units. A bootstrap or resampling-based assessment of cluster membership and of the adjusted coefficients, or at least a sensitivity analysis with respect to Smax, nmb, and dmax, is needed before drawing cross-national conclusions from Figures 2 and 3.
  3. [Section 5] The simulation study evaluates performance mainly through RMSEX, RMSEI, TPR, and FPR, but it does not report a direct measure of cluster recovery accuracy (e.g., adjusted Rand index or proportion of units assigned to the true cluster) for scenarios 3 and 4, where the true unit clusters are known. Since the paper's central claim concerns sparse clustering of unit-specific intercepts, RMSEI alone does not distinguish correct cluster recovery from a model that simply fits unit means. A direct cluster-recovery metric would provide the missing evidence that the outcome-mean ordering identifies the intended cluster structure.
minor comments (6)
  1. [Section 5.1] The abbreviation "DPG" appears in the description of the simulation design and elsewhere (e.g., "A DPG with predictor (2)"); it should be "DGP".
  2. [Section 5.6, summary bullet] The final summary bullet states "MRSE on the covariate- as well as the unit-level"; the intended term is "RMSE".
  3. [Section 2.2, Eq. (11)] The adjusted cluster intercept β̃_0c = β_0c + γ̄ uses a global average of the covariate-tree coefficients over all individuals; if covariate distributions differ across clusters, this quantity is not the expected value for that cluster. Please clarify the interpretation or define a cluster-specific adjustment.
  4. [Section 2.2] The sentence "the coefficients of the tree-structured model in (7) can only interpreted with regard to a reference node" is missing the word "be" before "interpreted".
  5. [Figure 3] The figure legend does not state whether the displayed node values are raw coefficients from the model in Eq. (7) or the adjusted coefficients from Eq. (11); please specify this in the legend or caption.
  6. [Section 6] The claim that a method combining tree-structured covariate effects with clustered fixed effects "has not been available so far" is too strong given the discussion of Gottard et al. (2023) later in the same section; consider softening the statement, for example by saying that this combination has not been available within the fixed-effects framework used here.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the two-tree model is an algorithmic fit benchmarked on external DGPs, and the outcome-mean ordering is a disclosed computational device.

full rationale

The paper's central claim is that the model in Eq. (7) can be fitted by stepwise deviance-based splitting and that the resulting estimator is competitive in simulations and interpretable on SHARE data. None of the reported results reduces by construction to an input: the unit tree tr0 is not defined as the outcome means; the ordering of units by their outcome means (Section 3, Step 1) only restricts the set of candidate split points, and the final cluster boundaries are chosen by minimizing the deviance. The simulation study uses independent DGPs with known true intercepts and covariate effects, so RMSE, TPR, and FPR values are external checks rather than consequences of the fitting criterion. The adjustment in Eq. (11) is a reparameterization for interpretation, not a prediction. Self-citations to Berger and Tutz (2018) and to the TSVC package are continuity and implementation references; the ordering heuristic is additionally attributed to Fisher (1958), Breiman et al. (1984), and Ripley (1996), and it is not invoked as a uniqueness theorem. A possible concern is that the raw-outcome ordering can be distorted by between-unit covariate composition, but that is an identification and robustness risk rather than circularity, and it does not make any equation of the paper equivalent to its own input.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the model formulation, the greedy fitting procedure, and the application choices. No new entities are introduced. The free parameters are tuning constants for tree growth and post-pruning. The key ad hoc assumption is the outcome-based ordering used to reduce the unit split search from exponential to linear.

free parameters (3)
  • Smax (maximal number of splits) = 20 in the application
    Stopping limit for tree building; chosen by hand and affects the set of candidate models before post-pruning.
  • nmb (minimal bucket size) = 100 in the application; floor(0.1 * total n) in simulations
    Prevents very small terminal nodes; chosen by hand and influences tree shape and split selection.
  • dmax (maximal tree depth) = 4 in the application
    Depth limit for the covariate tree in the application; chosen by hand and restricts subgroup complexity.
assumptions (4)
  • domain assumption Observations within clusters are dependent, and unit-specific intercepts capture this dependence.
    The entire model family, including the proposed TTSC, represents between-unit heterogeneity through unit-specific intercepts; within-unit dependence is not otherwise modeled.
  • ad hoc to paper Ordering units by outcome means yields a valid search space for unit clusters.
    Section 3 reduces 2^(n-1) partitions to n-1 ordinal splits after sorting by outcome means; this operational assumption is adopted from Berger and Tutz (2018) and is not proven.
  • standard math Deviance and likelihood-based cross-validation select the right tree size.
    Deviance minimization and 10-fold cross-validation with the one-standard-error rule are standard tree model selection tools.
  • domain assumption The CASP score can be treated as a continuous, normally distributed outcome for the application.
    The application uses an identity link and Gaussian likelihood for a bounded Likert-based score without reporting distributional diagnostics.

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Cite this review

Pith. "Pith review of Flexible tree-structured regression for clustered data with an application to quality of life in older adults." pith.science (2026). https://pith.science/paper/SZUBNWO4

@misc{pith2026250112787,
  author       = {Pith},
  title        = {Pith review of: Flexible tree-structured regression for clustered data with an application to quality of life in older adults},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SZUBNWO4}},
  note         = {Machine review of arXiv:2501.12787}
}
read the original abstract

Tree-structured models are a powerful alternative to parametric regression models if non-linear effects and interactions are present in the data. Yet, classical tree-structured models might not be appropriate if data comes in clusters of units, which requires taking the dependence of observations into account. This is, for example, the case in cross-national studies, as presented here, where country-specific effects should not be neglected. To address this issue, we present a flexible tree-structured approach that achieves a sparse modeling of unit-specific effects and identifies subgroups (based on individual-level covariates) that differ with regard to the outcome. The methodological advances were motivated by the analysis of quality of life in older adults using data from the survey of Health, Ageing and Retirement in Europe. Application of the proposed model yields promising results and illustrated the accessibility of the approach. A comparison to alternative methods with regard to variable selection and goodness-of-fit was performed in several simulation experiments.

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Reference graph

Works this paper leans on

35 extracted references · 25 canonical work pages

  1. [6]

    Real-space multiple scattering theory for superconductors with impurities

    Which measure of quality of life performs best in older age? A comparison of the OPQOL, CASP-19 and WHOQOL-OLD.J Epidmiol Community Health 63: 273–280. https://doi.org/10.1136/jech.2009.087668 . Breiman, L., J.H. Friedman, R.A. Olshen, and J.C. Stone

    work page Pith review arXiv 2009

  2. [9]

    Data set

    Release version: 9.0.0. Data set . https://doi.org/10.6103/SHARE.w9.900 . Sim, J., B. Bartlam, and M. M. Bernard

    doi:10.6103/share.w9.900

  3. [11]

    Behav Res Methods 50: 2016–34

    Detecting treatment-subgroup interactions in clustered data with generalized linear mixed- effects model trees. Behav Res Methods 50: 2016–34. https://doi.org/10.3758/ s13428-017-0971-x . Frias-Goytia, G.L., C. Lojo-Seoane, S.C. Mallo, A. Nieto-Vieites, O. Juncos-Rabad` an, and A. Pereiro

    work page 2016

  4. [12]

    Comput Stat Data Anal 88: 53–74

    Unbiased regression trees for longitudinal and clus- tered data. Comput Stat Data Anal 88: 53–74. https://doi.org/10.1016/j.csda.2015. 02.004 . Gelman, A. and J. Hill

    work page doi:10.1016/j.csda.2015 2015

  5. [13]

    Methodol: Eur J Res Methods Behav Soc Sci 7: 121–33

    The role of sample cluster means in multi-level models: A view on endogeneity and measurment error issues. Methodol: Eur J Res Methods Behav Soc Sci 7: 121–33. https://doi.org/10.1027/1614-2241/a000030 . Groll, A. and G. Tutz

    work page doi:10.1027/1614-2241/a000030

  6. [15]

    Stat Probab Lett 81: 451–459

    Mixed effects regression trees for clustered data. Stat Probab Lett 81: 451–459. https://doi.org/10.1016/j.spl.2010. 12.003 . 29 Hajjem, A., F. Bellavance, and D. Larocque

    work page doi:10.1016/j.spl.2010 2010

  7. [17]

    Stat Model 13: 41–67

    Clustering in linear mixed models with approximate dirichlet process mixtures using em algorithm. Stat Model 13: 41–67. https://doi. org/10.1177/1471082X12471372 . Heyworth, I.T.M., M.L. Hazell, M.F. Linehan, and T.L. Frank

    work page doi:10.1177/1471082x12471372

  8. [20]

    Age and Ageing 41: 612–617

    Interpreting and evaluating the CASP-19 quality of life measure in older people. Age and Ageing 41: 612–617. https://doi.org/10.1093/ageing/afs023 . Hyde, M., R. Wiggins, P. Higgs, and D. Blane

    work page doi:10.1093/ageing/afs023

Show all 35 references
  1. [21]

    J Eur Surv Res Assoc 13: 73–93

    Tree-based machine learning methods for survey research. J Eur Surv Res Assoc 13: 73–93. https://doi.org/10.18148/srm/ 2019.v1i1.7395 . Killingsworth, M.A

    2019 doi

  2. [23]

    Aging Ment Health 19: 595–609

    Psychometric properties and confirmatory factor analysis of the CASP-19, a measure of quality of life in early old age: the hapiee study. Aging Ment Health 19: 595–609. https://doi.org/ 10.1080/13607863.2014.938605 . Liti` ere, S., A. Alonso, and G. Molenberghs

    2014

  3. [24]

    Biom 63: 1038–44

    Type I and Type II Error Under Random Effect Misspecification in Generalized Linear Mixed Models. Biom 63: 1038–44. https://doi.org/10.1111/j.1541-0420.2007.00782.x . Makovski, T.T., G.L. Coroller, P. Putrik, Y.H. Choi, M.P. Zeegers, S. Stranges, M.R. Castell, L. Huiart, and M...

    2007

  4. [27]

    Ageing Res Rev 10: 430–39

    Aging with multimorbidity: a systematic review of literature. Ageing Res Rev 10: 430–39. https://doi.org/10.1016/j.arr.2011.03.003 . Molenberghs, G. and G. Verbeke

    2011 doi

  5. [28]

    Eur J Public Health 24: 364–370

    Socioeconomic inequalities in thequality of life of older europeans in different welfare regimes. Eur J Public Health 24: 364–370. https://doi.org/10.1093/eurpub/cku017 . Ripley, B.D

    doi

  6. [31]

    Methods Ecol Evol 11: 1141–52

    Robustness of linear mixed-effects models to violations of distributional assump- tions. Methods Ecol Evol 11: 1141–52. https://doi.org/10.1111/2041-210X.13434 . Schwarz, G.E

    doi

  7. [34]

    Qual Life Res 20: 997–1004

    The CASP-19 as a measure of quality of life in old age: evaluation of its use in a retirement community. Qual Life Res 20: 997–1004. https://doi.org/10.1007/s11136-010-9835-x . Strobl, C., J. Malley, and G. Tutz

    doi

  8. [53]

    Marengoni, A., S

    https://doi.org/10.1016/j.arr.2019.04.005 . Marengoni, A., S. Angleman, R. Melis, F. Mangialasche, A. Karp, A.G. aand B. Meinow, and L. Fratiglioni

    2019 doi

  9. [59]

    Hothorn, T., K

    https: //doi.org/10.3399/bjgp09X453990 . Hothorn, T., K. Hornik, and A. Zeileis

    doi

  10. [118]

    Kim, G., G

    https://doi.org/10.1073/pnas.2016976118 . Kim, G., G. Netuveli, D. Blane, A. Peasey, S. Malyutina, G. Simonova, R. Kubinova, A. Pajak, S. Croezen, M. M. Bobak, and H. Pikhart

    doi

  11. [1958]

    J Am Stat Soc 53: 789–798

    On grouping for maximum homogeneity. J Am Stat Soc 53: 789–798. https://doi.org/10.1080/01621459.1958.10501479 . Fokkema, M., N. Smits, A. Zeilies, T. Hothorn, and H. Kelderman

    1958

  12. [1978]

    Ann Stat 6: 461–464

    Estimating the dimsension of a model. Ann Stat 6: 461–464. https://doi.org/10.1214/aos/1176344136 . Sela, R.J. and J.S. Simonoff

  13. [1995]

    Soc Indic Res 36: 275–286

    The wealth of nations revisted: Income and quality of life. Soc Indic Res 36: 275–286. https://doi.org/10.1007/BF01078817 . 28 Doove, L.L., E. Dusseldorp, K.V. Deun, and I.V. Mechelen

    doi

  14. [1996]

    Cambridge: Cambridge University Press

    Pattern recognition and neural networks. Cambridge: Cambridge University Press . https://doi.org/10.1017/CBO9780511812651 . Rodr ´ ıguez-Bl´ aquez, C., O. Ribeiro, A. Ayala, L. Teixeira, L. Araj´ uo, and M.J. For- jaz

    doi

  15. [2006]

    J Comput Graph Stat 15: 651–674

    Unbiased recursive partitioning: A conditional inference framework. J Comput Graph Stat 15: 651–674. https://doi. org/10.1198/106186006X133933 . Howel, D

    doi

  16. [2007]

    Comput Stat Data Anal 51: 5247–5252

    Fitting Finite Mixtures of Generalized Linear Regression in R. Comput Stat Data Anal 51: 5247–5252. https://doi.org/10.1016/j.csda.2006. 08.014 . Hajjem, A., F. Bellavance, and D. Larocque

    2006 doi

  17. [2008]

    J Comput Graph Stat 17 (2): 492–514

    Model-based recursive pratitioning. J Comput Graph Stat 17 (2): 492–514. https://doi.org/10.1198/106186008X319331 . 32

    doi

  18. [2010]

    J Clin Epidmiol 63: 1195–1204

    Relative to the general US population, chronic diseases are associated with poorer health-related quality of life as measured by the Patient-Reported Outcomes Mea- surement Information System (PROMIS). J Clin Epidmiol 63: 1195–1204. https: //doi.org/10.1016/j.jclinepi.2010.04....

    doi

  19. [2011]

    Comput Stat 26: 355–69

    Classification of repeated measurements data using tree-based ensemble methods. Comput Stat 26: 355–69. https://doi.org/ 10.1007/s00180-011-0249-1 . Bell, A., M. Fairbrother, and J. Jones

    doi

  20. [2012]

    J Comput Simul 84: 1313–28

    Mixed-effects random forest for clustered data. J Comput Simul 84: 1313–28. https://doi.org/10.1080/00949655. 2012.741599 . Heagerty, P. and B. Kurland

    2012

  21. [2013]

    Int J Epidemiol

    Data Resource Profile: The Survey of Health, Ageing and Retirement in Europe (SHARE). Int J Epidemiol . https: //doi.org/10.1093/ije/dyt088 . Bowling, A. and P. Stenner

    doi

  22. [2014]

    Adv Data Anal Classif 8: 403–425

    A comparison of five recursive partitioning methods to find person subgroups involved in meaningful treatment – subgroup interactions. Adv Data Anal Classif 8: 403–425. https://doi. org/10.1007/s11634-013-0159-x . European Commission and Eurostat

    doi

  23. [2015]

    FORS Working Papers

    An evaluation of the CASP-12 scale used in the Survey of Health, Ageing and Retirement in Europe (SHARE) to measure Quality of Life among people aged 50+. FORS Working Papers . https: //doi.org/10.24440/FWP-2015-00004 . B¨ orsch-Supan, A., M. Brandt, C. Hunkler, T. Kneip, J. K...

    2015 doi

  24. [2018]

    J Comput Graph Stat 27: 380–392

    Tree-structured clustering in fixed effects models. J Comput Graph Stat 27: 380–392. https://doi.org/10.1080/10618600.2017.1371030 . Berger, M., G. Tutz, and M. Schmid

    2017

  25. [2019]

    Stat Comput 29: 217–229

    Tree-structured modelling of varying coefficients. Stat Comput 29: 217–229. https://doi.org/10.1007/s11222-018-9804-8 . Bergmann, M., M. Wagner, and A. B¨ orsch-Supan

    doi

  26. [2020]

    https: //doi.org/10.1371/journal.pone.0240024

    Role of clinical, functional and 30 social factors in the association between multimorbidity and quality of life: Findings from the Survey of Health, Ageing and Retirement in Europe (SHARE). https: //doi.org/10.1371/journal.pone.0240024 . Makovski, T.T., S. Schmitz, M.P. Zeege...

    doi

  27. [2024]

    Publications Office of the European Union

    Demography of Europe: 2024 edition . Publications Office of the European Union. Fisher, W.D

    2024

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