When Schools Are Equal but Children Are Not: A Multilevel Analysis of Home-Driven Variance and Cumulative Disadvantage in Early Childhood

Abstract

Early childhood education and care (ECEC) systems in equitable welfare states are designed to provide comparatively standardised institutional inputs, yet substantial developmental gaps among children persist. This study examined this configuration—descriptively labelled the “Flemish Paradox”—using data from the OECD’s International Early Learning and Child Well-being Study (IELS 2025) for the Flemish Community of Belgium (2363 five year olds in 200 ECEC centres; parent-questionnaire data were available for a subset of the sample, and missing parent-report data were addressed through multiple imputation). Children’s cognitive and executive skills were measured with standardised direct tablet-based assessments, while home environments were reported by parents, separating measurement sources. Two-level hierarchical linear models with design-based weighting (child weight and 92 BRR replicate weights), pooled across five plausible values and 20 multiply imputed datasets, showed comparatively limited between-centre outcome variation (ICC ≈ 23% for foundational learning, ≈11% for executive function). Within centres, family socioeconomic status (B = 25.11, p < 0.001) and a print-focused home literacy index (PHLI; B = 16.60, p < 0.001) were positively associated with foundational learning, and centre-mean PHLI showed an independent contextual association (B = 24.11, p < 0.001). A positive within-centre indirect association through children’s executive function skills was estimated (3.60, 95% Monte Carlo CI [1.83, 5.40]); a secondary exploratory analysis indicated a parallel between-centre pattern (8.40, 95% CI [1.16, 15.65]). Centre socioeconomic composition was strongly associated with outcomes (B = 36.38, p < 0.001); the analysis did not provide evidence that it modified the within-centre PHLI–learning association (p = 0.219). The findings are consistent with cultural-capital perspectives and indicate that family resources, print-focused home literacy, and EFs are jointly associated with early learning within a multilevel ECEC context. However, the cross-sectional design does not establish temporal or causal mediation, and the results should not be interpreted as evidence regarding the effectiveness of particular family- or centre-based interventions.

1. Introduction

1.1. Background: Institutional Equalisation and the Limits of Structural Reform

Early childhood education and care (ECEC) centres play a foundational role in children’s cognitive, social, and emotional development (Balladares & Kankaraš, 2020; Duncan et al., 2022; OECD, 2017, 2026). A substantial body of international research frames improvements in institutional quality—refined curricula, upgraded infrastructure, and enhanced teacher professionalisation—as a primary policy mechanism for narrowing early developmental gaps between socioeconomically disadvantaged children and their peers (Burger, 2009; Dougherty & Morabito, 2023; Kulić et al., 2019; Nakato et al., 2025; Rad et al., 2022). In highly equitable welfare systems, school quality is additionally regulated by law and by central governance, with the explicit aim that children receive parallel institutional inputs regardless of neighbourhood or family background (Fukkink et al., 2017; Nusche et al., 2015; OECD, 2015). Standardised structural resources, centralised teacher salary scales, and universal pedagogical guidelines are intended to establish a common educational baseline (Badunenko et al., 2025; Santiago et al., 2016).

A recurring finding in large-scale assessment research, however, is that minimising institutional variation does not, by itself, eliminate the developmental differences children already display at ECEC entry and during the preschool years (Brunner et al., 2025; Cameron et al., 2012; Claes et al., 2026; Cornelißen et al., 2018; Scionti et al., 2020). Settings in which institutional arrangements are comparatively regulated, therefore, offer a theoretically informative vantage point, where between-centre outcome variation is comparatively limited, the processes that sustain the remaining child-level inequality become more clearly visible.

1.2. The “Flemish Paradox”: Definition and Evidence

The OECD’s International Early Learning and Child Well-being Study (IELS) provides a recent, well-documented instance of such a setting. In this study, we use the label “Flemish Paradox”—a descriptive term we introduce for the purposes of this analysis rather than an established construct in the literature—to denote the coexistence, within the Flemish Community of Belgium, of two empirically robust but seemingly contradictory observations (OECD, 2026).

First, between-centre variation in measured child outcomes is comparatively limited in the Flemish Community. In the official OECD estimates, approximately 27% of the variance in foundational learning and 16% of the variance in executive function lies among centres—both below the IELS 2025 international averages (36% and 22%, respectively) (OECD, 2026). Our own uniform-specification computations from the international microdata yielded a broadly similar comparative pattern (23.1% and 11.9%; see Section 3.2.1). At the same time, a cross-national comparison urges precision: the Flemish between-centre variance is low relative to most participating systems but is not the lowest observed—England shows a still smaller between-centre share in our uniform-specification comparison, and official OECD estimates additionally indicate lower values for the Netherlands, which was not included in our microdata comparison (OECD, 2026). The Flemish system is, thus, best characterised as comparatively—not uniquely—homogeneous.

Second, the dispersion of outcomes among Flemish children remains wide. The distance between the 10th and 90th percentiles of early learning achievement spans 191 score points (OECD, 2026). Because only a minority of the total variance lies among centres, the large majority—approximately three quarters or more, depending on the domain—is located within centres, that is, among children attending institutions within the same comparatively regulated system (OECD, 2026).

The “Flemish Paradox” refers here to the coexistence of comparatively limited between-centre variation in measured child outcomes and substantial within-centre heterogeneity. This descriptive label does not imply that centres are equivalent in structural resources, instructional processes, or pedagogical quality. The phenomenon raises a question that institutional-quality policy alone cannot answer: if a comparatively smaller share of total outcome variation lies among centres, which child- and family-level processes account for the rest, and what role might executive function play in these associations?

1.3. Limitations in the Extant Literature

Three features of the existing literature limit what it can currently say in answer to this question.

Separation of structure from process: Many studies model family background as a single composite predictor, which makes it difficult to distinguish the structural position of a family (socioeconomic status) from the processes through which resources are converted into developmental stimulation within the home, such as shared reading and access to literacy materials (Children’s Competencies Development in the Home Learning Environment, 2021; Duncan et al., 2022; Tóth et al., 2019). Although multilevel analyses of school composition effects are common in primary and secondary education research, studies that isolate within-centre home processes in comparatively standardised preschool systems remain relatively uncommon (Balladares & Kankaraš, 2020; Brunner et al., 2025; Santiago et al., 2016).

Integration of sociological and cognitive accounts: Sociological models of cultural reproduction and cognitive-developmental models of school readiness have largely proceeded in parallel (Brooker, 2015; Jackson, 2022; Jæger & Karlson, 2018). In particular, executive functions (EFs)—working memory, inhibitory control, and cognitive flexibility—are plausible candidate mechanisms through which home inputs may be associated with early learning, yet they have rarely been examined as intermediate variables within a multilevel framework (Cameron et al., 2012; Claes et al., 2026; Scionti et al., 2020). Without such integration, the internal pathway implied by the Flemish Paradox remains largely untested rather than theoretically contested.

Measurement and missing data: Much ECEC survey research measures both the home environment and child outcomes through the same informant, inviting common-method variance (Brunner et al., 2025). In addition, parental non-response is substantial in this literature—in IELS 2025, the Flemish parental participation rate was 72.4% (OECD, 2026)—and some derived background indices distributed with international databases are themselves imputed, which can attenuate their associations with outcomes; in the present data, the standard derived home literacy index correlated with foundational learning at only r = 0.037, far below what item-level analyses would suggest (OECD, 2026). Designs that separate measurement sources and handle missingness transparently are, therefore, needed before estimates for home-literacy resources and practices can be interpreted with confidence.

1.4. Theoretical Framework

1.4.1. Cultural Capital Theory in Early Childhood: A Critical Operationalisation

Bourdieu’s cultural capital theory holds that educational institutions are not culturally neutral: they tend to reward the linguistic codes, dispositions, and familiarity with scholastic culture that children from advantaged families acquire at home (Bourdieu, 1986; Bourdieu & Passeron, 1990; Brooker, 2015; Jæger & Karlson, 2018). Even where an educational system equalises the structural and material inputs of its centres, children’s capacity to engage with and profit from uniform instruction may still differ with the cultural resources transmitted in the domestic sphere (Brooker, 2015; Kulić et al., 2019).

Applying this framework to early childhood requires two adaptations, which we make explicit. First, Bourdieu’s original account was developed for class reproduction in secondary and higher education; at age five, children hold no institutionalised capital of their own, and transmission is overwhelmingly domestic and pre-institutional. At this stage, family resources are best understood as embodied and objectified cultural capital in formation, including daily practices, interaction styles, and material resources, rather than as institutionalised credentials (Lareau, 2011; Sénéchal & LeFevre, 2002). Second, the constructs must be mapped onto measurable quantities with care. In this study, the parental-report items indexing print-related home resources and practices (the frequency of shared book reading, library visits, and the number of children’s books at home) are treated as observable traces of this transmission process; they constitute the print-focused home literacy index. The database’s composite socioeconomic index (parental occupation, education, and home possessions) instead captures the family’s structural position. The distinction matters analytically: socioeconomic position indicates the resources a family has, whereas the print-focused home literacy index indicates what the family does with such resources in the child’s everyday environment (Duncan et al., 2022; Rodriguez & Tamis-LeMonda, 2011).

Two scope conditions accompany this operationalisation. On the one hand, our index is deliberately narrow: it covers print-related resources and practices but not play-based learning, numeracy interactions, or oral linguistic stimulation (Children’s Competencies Development in the Home Learning Environment, 2021; Tóth et al., 2019). Estimates in this study, therefore, pertain specifically to print-focused home literacy rather than to the broader home learning environment (see Limitations). On the other hand, cultural-capital applications in early childhood remain partial and contested (Jæger & Karlson, 2018); we treat the framework as an interpretive lens that generates testable expectations, not as a theory our design can confirm or refute as a whole.

The framework yields a specific expectation for the Flemish case: within a comparatively regulated ECEC system displaying relatively limited between-centre outcome variation, both within-centre family differences and between-centre compositional differences may be associated with foundational learning, while the larger share of total outcome variation remains located within centres.

1.4.2. Cumulative Disadvantage and the Matthew Effect

Cumulative-disadvantage accounts add a temporal dimension. Small early differences in stimulation and skill may not remain static: initial advantages can facilitate further learning, while initial disadvantages may constrain it, such that modest gaps widen over time (Duncan et al., 2022; Heckman, 2006; Kulić et al., 2019). In literacy research this dynamic is known as the Matthew Effect, in which early reading skill begets further growth (Merton, 1968; Stanovich, 1986). Within this perspective, home-driven differences observed at age five matter not only in themselves but as possible starting conditions for later trajectories. We stress the word possible: the present data are cross-sectional and speak to the size and structure of early gaps, not to their subsequent compounding, which requires longitudinal evidence.

1.4.3. Executive Functions as Candidate Cognitive Mechanisms

Executive functions, the family of top-down processes including working memory, inhibitory control, and cognitive flexibility, support goal-directed behaviour and are strongly implicated in school readiness (Cameron et al., 2012; Diamond, 2013; Miyake et al., 2000; Scionti et al., 2020). EF skills are highly malleable during preschool years and responsive to environmental stimulation (Blair & Razza, 2007; Kellens et al., 2023). Literacy-rich parent–child interactions such as shared and dialogic book reading place sustained demands on attention, memory, and self-regulation and are, therefore, a plausible conduit through which home practices are related to the development of EFs (Brunner et al., 2025; Bus et al., 1995; Sénéchal & LeFevre, 2002). This motivates examining EFs as a theoretically proposed intermediate correlate linking the PHLI to foundational learning, hereafter described cautiously as a candidate pathway rather than an established mechanism.

We use the term candidate deliberately. With cross-sectional data, a mediation analysis cannot establish that home inputs precede and produce EFs, which in turn precede and produce learning; alternative orderings and reciprocal influence are equally compatible with the same associations (see Section 4). Our mediation hypotheses are, thus, tests of whether the pattern of associations is consistent with the proposed pathway, not demonstrations of it.

1.4.4. Synthesis: An Integrated Model for the Flemish Paradox

Combining the two frameworks with the EF literature yields the model that organises this study. At the individual level, structural position (SES) and domestic cultural-capital practices (PHLI) are expected to be independently associated with foundational learning (direct associations). Part of the PHLI association is expected to run through children’s EF skills (indirect association). At the centre level, the average SES and average PHLI of a centre’s intake capture the compositional climate in which a child is embedded—the collective home ecology of the peer group—which may carry its own contextual associations. Finally, the framework raises the question of whether the within-centre PHLI–learning association varies with centres’ socioeconomic composition; we treat this as an exploratory research question rather than a null-effect hypothesis (Section 1.6).

1.5. The Present Study

This study examines the Flemish Paradox using the most recent IELS cycle. Its intended contribution is one of synthesis and setting rather than of a new analytic technique: it brings together, within a single multilevel framework and in a comparatively regulated ECEC context with relatively limited between-centre outcome variation, (i) the separation of structural (SES) and process (PHLI) family influences, (ii) a cognitive candidate pathway (EF) examined as a proposed intermediate variable at both the individual and the centre level, and (iii) a boundary-condition test of whether centre composition conditions the home–learning association. Methodologically, the design separates measurement sources (direct tablet assessments of children; parent reports of the home), uses design-based weighting with replicate weights appropriate to the IELS complex sample, and handles substantial parental non-response with multiple imputation alongside complete-case sensitivity analyses so that the robustness of every substantive conclusion to missing-data handling can be reported transparently (OECD, 2026).

The study addresses one guiding question: within a comparatively regulated ECEC system displaying relatively limited between-centre outcome variation, which family-level processes are associated with child-level differences among five year olds, and what role does executive function play in those associations?

1.6. Research Hypotheses

Based on this theoretical synthesis, we examine two hypotheses and one exploratory research question within a multilevel framework, as follows:

Hypothesis 1 (Direct Associations). 

Within ECEC centres, family socioeconomic status and print-focused home-literacy resources and practices are each positively associated with children’s foundational learning (emergent literacy and numeracy).

Hypothesis 2 (Indirect Association via EFs). 

The within-centre association between the individual print-focused home literacy index and foundational learning is partly accounted for by children’s executive function capacities (working memory, inhibition, and mental flexibility); we additionally explore whether a parallel indirect structure exists at the centre level.

Research Question 1 (Boundary Condition). 

Does centre socioeconomic composition modify the within-centre association between print-focused home literacy and foundational learning? Because a non-significant interaction cannot by itself establish the absence of moderation, this question is framed as exploratory rather than as a null-effect hypothesis.

Because IELS 2025 is cross-sectional, all hypotheses are formulated and tested as statements about associations; Hypothesis 2 in particular evaluates whether the observed pattern is consistent with the theoretically proposed PHLI → EF → learning sequence and cannot by itself establish that sequence (see Section 2 and Section 4).

2. Method

2.1. Research Design

This study utilised a multivariate, two-level hierarchical linear modelling design based on large-scale international survey data (Balladares & Kankaraš, 2020; Brunner et al., 2025; Claes et al., 2026; OECD, 2026). The hierarchical data structure nested individual children within their respective early childhood education and care centres (Brunner et al., 2025; OECD, 2026). This design allowed for the simultaneous estimation of individual-level (within-centre) relationships and centre-level (between-centre) contextual associations (Balladares & Kankaraš, 2020; Brunner et al., 2025).

2.2. Sample and Participants

Analyses were conducted using secondary data from the IELS 2025 Flemish Community sample (Claes et al., 2026; OECD, 2026). The original Flemish sample contained 2363 five-year-old children attending 200 ECEC centres, together with child-linked parent and teacher questionnaire data where available (Claes et al., 2026; OECD, 2026).

Because parent-report variables (socioeconomic status and home learning activities) carry substantial missingness, all primary analyses were conducted on the full sample (N = 2363 children in 200 ECEC centres) using multiple imputation (see Section 2.5); the parental participation rate was 72.4% (OECD, 2026). Complete-case analyses on the subsample of 1550 children nested in 195 centres (65.6% of the full sample) are reported as sensitivity analyses (Pepinsky, 2018).

To assess selection into the respondent sample, we compared children with and without matched parent questionnaires on variables observed for (nearly) all children. Children whose parents did not respond scored, on average, 29.46 points lower on foundational learning (463.46 vs. 492.92; t = −9.17, p < 0.001, Cohen’s d = 0.43) and 13.34 points lower on executive function (488.64 vs. 501.99; t = −4.35, p < 0.001, d = 0.20). The two groups did not differ statistically in age (p = 0.127) or sex composition (χ² = 3.71, p = 0.054); the average socioeconomic composition of their centres was slightly lower among non-respondents (p = 0.030, d = 0.11). Parental non-response is, thus, associated with observed disadvantage, so missingness cannot be treated as completely random; the observed pattern is consistent with—but cannot by itself prove—a missing-at-random mechanism conditional on observed covariates (Engzell & Jönsson, 2015). This motivated reporting multiple-imputation estimates as primary and quantifying the sensitivity of every key coefficient to the missing-data handling (Section 3.4).

The sample included 200 centres, with an average of 11.81 children per centre (median = 12.00, range = 5 to 16) (Brunner et al., 2025; Nusche et al., 2015; OECD, 2015, 2026).

2.3. Measures and Variable Construction

2.3.1. Dependent Variable: Foundational Learning Composite Score

Children’s performance in emergent literacy and emergent numeracy was directly assessed using standardised, play-based tablet tasks administered by trained assessors (Claes et al., 2026; OECD, 2026). Emergent literacy captured vocabulary, phonological awareness, and narrative comprehension (Claes et al., 2026; OECD, 2026). Emergent numeracy assessed number recognition, counting, shape identification, and simple addition/subtraction (Claes et al., 2026; OECD, 2026). To account for measurement error, the OECD provides five plausible values per domain. For each plausible-value index m = 1, …, 5, the corresponding literacy and numeracy plausible values were averaged to form FOUND_m; the five resulting FOUND plausible-value variables were analysed separately and pooled—they were not averaged into a single observed score (Brunner et al., 2025; OECD, 2026).

FOUND_m = (LITERACY_PV_m + NUMERACY_PV_m)/2

for m = 1, …, 5. The scale scores are standardised with a global mean of 500 and a standard deviation of 100 (Claes et al., 2026; OECD, 2026).

2.3.2. Independent Variables (Level 1 Predictors)

Family Socioeconomic Status: We utilised the pre-computed SES index from the database, which combines parental occupation, parental educational level (expressed in ISCED levels), and home possessions (Jæger & Karlson, 2018; Kulić et al., 2019; OECD, 2026; Radulović & Krstić, 2017). The variable was converted to standard numeric vectors (OECD, 2026).

2.3.3. Print-Focused Home Literacy Index (PHLI)

The standard derived home literacy index showed only a weak correlation with foundational learning in the present data (r = 0.037) (Claes et al., 2026; OECD, 2026). We therefore constructed a transparent three-item print-focused index from the underlying parent-report indicators, as follows: reading frequency to the child from a book (PA2_C_Q15_01), frequency of visiting a library (PA2_C_Q15_12), and the number of children’s books in the home (PA2_C_Q16) (Attig & Weinert, 2020; Children’s Competencies Development in the Home Learning Environment, 2021; OECD, 2026; Rodriguez & Tamis-LeMonda, 2011; Tóth et al., 2019). Each item was standardised across the Flemish sample, and the average was computed, as follows:

PHLI = (Read_z + Library_z + Books_z)/3

A valid composite was computed whenever at least one of the three items was observed (the mean of the available standardised items); 28.7% of the full sample have no valid PHLI score because all three items are missing, and these cases are handled by multiple imputation in the primary analyses. In the primary MI analyses, however, missing item responses were imputed and the PHLI was reconstructed from all three completed standardised indicators within each imputed dataset; the available-item mean was used only for descriptive purposes prior to imputation.

The 3-item PHLI scale yielded a Cronbach’s alpha of 0.55. Internal consistency was modest (α = 0.55, ω_t = 0.57); given the small number and heterogeneous behavioural content of the indicators, the measure is interpreted as a brief composite index rather than as a highly reliable unidimensional latent scale (Brunner et al., 2025; OECD, 2026). The mean inter-item correlation was 0.29, within the recommended range of 0.15 to 0.50 for homogeneous short scales and consistent with adequate item coherence (Brunner et al., 2025). The corrected item-total correlations were all positive and exceeded the standard 0.20 threshold, with r_it = 0.474 for reading frequency, r_it = 0.453 for books in the home, and r_it = 0.233 for library visits; all three items, therefore, contribute positively to the composite index (Brunner et al., 2025; OECD, 2026). To relax the tau-equivalence assumption of Alpha (equal factor loadings), we also computed McDonald’s omega total, which gave a higher reliability estimate of ω_t = 0.5704 (Brunner et al., 2025). For convergent validity, we examined the correlation between our custom 3-item index and the original pre-computed home literacy index in the database (Claes et al., 2026; OECD, 2026). Despite its weak association with foundational learning, the original index correlated significantly with the custom PHLI index (r = 0.353, p < 0.001, N = 1550) (OECD, 2026). The custom PHLI index also correlated positively with foundational learning (r = 0.355) (Attig & Weinert, 2020; Rodriguez & Tamis-LeMonda, 2011). Finally, the low correlation between the custom PHLI index and family SES (r = 0.0814) indicates limited empirical overlap between the two indices in the analytical sample, although it should not by itself be treated as a formal test of discriminant validity (Children’s Competencies Development in the Home Learning Environment, 2021; Duncan et al., 2022; Tóth et al., 2019).

2.3.4. Proposed Intermediate Variable: Executive Function

Executive Function Composite Score: Children’s executive functions were directly assessed via tablet tasks across three cognitive domains: working memory (dimensional change card sort tasks), inhibition (standardised go/no-go tasks), and mental flexibility (Cameron et al., 2012; Kellens et al., 2023; OECD, 2026; Scionti et al., 2020). For each plausible-value index, the corresponding inhibition, working-memory, and mental-flexibility plausible values were averaged; the five resulting EF plausible-value variables were analysed separately and pooled (Brunner et al., 2025; OECD, 2026), as follows:

EF_m = (INHIBITION_PV_m + WORKINGMEM_PV_m + MENTALFLEX_PV_m)/3

for m = 1, …, 5.

2.3.5. Contextual Variables (Level 2 Predictors)

To separate within-centre and between-centre effects (computational variable labels in parentheses), we calculated centre-level aggregated averages of SES (center_SES_c) and the PHLI (center_HLE_c) (Balladares & Kankaraš, 2020; Brunner et al., 2025; OECD, 2026). For the mediation model, centre-level average executive function (center_EF_c) was also computed (Brunner et al., 2025; Kellens et al., 2023). These Level 2 predictors were grand-mean centred (Brunner et al., 2025).

2.3.6. Control Variables

We controlled for children’s biological age (converted to months: ITAGE × 12) and sex (dummy coded: 1 = Female, 0 = Male), both grand-mean centred (Brunner et al., 2025; Claes et al., 2026; OECD, 2026).

2.4. Methodological Justification of the Multi-Method Approach

A key strength of this study’s design was its multi-method assessment structure (Brunner et al., 2025; Claes et al., 2026; Kellens et al., 2023; OECD, 2026). While children’s cognitive and executive functions were measured via standardised direct tablet-based assessments (direct assessment), the home environment and parental indicators were gathered through independent parent questionnaires (indirect assessment) (Claes et al., 2026; OECD, 2026). This design reduces the risk of common-method variance, which can inflate relationships in ECEC research when the same informant (usually the parent or teacher) reports on both the child’s academic competence and the home characteristics (Brunner et al., 2025; Kellens et al., 2023; OECD, 2026).

2.5. Data Analysis Pipeline

Weighting: Final student weights were applied to all descriptive and inferential statistics to maintain population representativeness (Brunner et al., 2025; Claes et al., 2026; OECD, 2026).

Replication Method: To compute unbiased standard errors and account for the complex stratified cluster sampling design, 92 Fay-adjusted balanced repeated replication (BRR) weights (SRWGT1 to SRWGT92) were incorporated with a Fay factor of k = 0.5, translating to a variance multiplier of fayfac = 4/92 ≈ 0.04348 (Brunner et al., 2025; OECD, 2026).

Variance Decomposition: Unconditional null models were estimated to calculate the Intraclass Correlation Coefficient for both Foundational Learning and Executive Function, establishing the proportion of variance residing among centres (Balladares & Kankaraš, 2020; Brunner et al., 2025; Claes et al., 2026; OECD, 2026).

Centring: Level 1 predictors were group-mean centred (centred around the ECEC centre mean) to isolate pure within-centre individual effects (Brunner et al., 2025; OECD, 2026). Level 2 contextual variables (centre averages) and control variables were grand-mean centred (Brunner et al., 2025; Claes et al., 2026).

Plausible Values, Multiple Imputation, and Pooling: Analyses were conducted within the R statistical environment (v4.4.2) using the BIFIEsurvey (v3.8.0) package (OECD, 2026). Missing values on parent-report variables were imputed with multiple imputation by chained equations (MICE; M = 20 imputed datasets) (v3.19.0). In the substantive models, plausible values served as both dependent variables and predictors; each multilevel model was, therefore, estimated separately for every combination of imputed dataset and plausible-value set (20 × 5 = 100 fits per model), and the resulting coefficients, standard errors, and variance components were pooled using Rubin’s Rules (Brunner et al., 2025; Claes et al., 2026; OECD, 2026). Multiple-imputation estimates are reported as primary throughout; complete-case estimates (n = 1550) are reported alongside as sensitivity analyses.

Imputation specification: The imputation model included all substantive analysis variables—the three PHLI items, SES, child sex, child age, the centre identifier, the child sampling weight, and all 15 plausible-value variables—as predictors of the missing parent-report variables. The three PHLI items and SES were imputed with predictive mean matching and sex with logistic regression; plausible values, identifiers, and design variables were not imputed. M = 20 imputations were generated after 20 iterations (seed = 2026), and within each completed dataset, the PHLI was reconstructed as the mean of the three completed standardised indicators, and centre-level aggregates were recomputed. Density and trace diagnostics were inspected to assess the plausibility and stability of the imputations.

Mediation and Interaction: The within-centre indirect association (ab_w = a_w × b_w) and between-centre indirect association (ab_b = a_b × b_b) were estimated from the pooled path coefficients (Brunner et al., 2025; Kellens et al., 2023). Because the product of two regression coefficients is not normally distributed, 95% confidence intervals for the indirect associations were computed with the Monte Carlo method: 100,000 draws were taken from the joint sampling distribution of the pooled a and b paths, the product was formed for each draw, and the 2.5th and 97.5th percentiles of the resulting distribution were taken as the interval limits. This procedure makes no normality assumption about the a × b term.

3. Results

3.1. Descriptive Statistics and Pre-Diagnostics

The weighted descriptive statistics for the full sample (N = 2363) are presented in Table 1.

Table 1. Weighted descriptive statistics of the study variables (full sample, N = 2363).

Variable	Mean (M)	Standard Deviation (SD)	Min	Max	Missing (%)
Foundational Learning Composite (FOUND)	492.92	73.46	132.41	684.82	0.00
Executive Function Composite (EF)	501.99	72.93	237.63	731.68	0.00
Family Socioeconomic Status (SES)	0.008	1.003	−2.717	1.774	31.02
Print-Focused Home Literacy Index (PHLI)	0.021	0.714	−1.899	1.749	28.73
Female	0.508	0.500	0.000	1.000	0.51
Age (in months)	66.30	3.32	59.67	72.69	0.00

Marginal missingness rates are shown for each variable on the full sample (N = 2363); the joint complete-case rate across all parent-report predictors is 65.6% (n = 1550). Standard deviations for FOUND and EFs are pooled across the five plausible values using Rubin’s total-variance formula (within-plus between-plausible-value variance) and, therefore, exceed simple averages of per-PV standard deviations. SES and the PHLI indicators were standardised across the Flemish sample. The provisional descriptive PHLI was computed when at least one component was observed; in the primary MI analyses, the PHLI was reconstructed from all three completed indicators. Primary analyses use multiple imputation (M = 20); complete-case analyses (n = 1550) are reported as sensitivity (Section 3.4).

The weighted correlation matrix (accounting for plausible values and replication weights) is presented in Table 2.

Table 2. Weighted correlation matrix.

Variable	1. FOUND	2. EF	3. SES	4. PHLI	5. Female	6. Age
1. FOUND	1.0000
2. EF	0.6318 *	1.0000
3. SES	0.4896 *	0.2982 *	1.0000
4. PHLI	0.3555 *	0.2895 *	0.0814 *	1.0000
5. Female	−0.0188	0.0227	0.0271	0.0903 *	1.0000
6. Age	0.2364 *	0.2320 *	0.0371	−0.0627 *	0.0088	1.0000

* p < 0.05. Correlations involving PVs (FOUND and EF) are averaged across the five plausible values. Correlations are computed on the complete-case sample (n = 1550) with child weights.

3.2. Multilevel Modelling Estimations

3.2.1. Null Models and International Variance Decomposition

To justify the multilevel design, we estimated fully unconditional null models. For foundational learning, the intraclass correlation was 23.14% (design-weighted full sample; 21.39% in the complete-case sample). For executive function, the between-centre share was lower: 11.91% (design-weighted full sample; 10.89%, complete-case) and 11.90% under the uniform unweighted full-sample specification used for cross-national comparison (Table 3). Both domains, thus, place the large majority of variance within centres, while the between-centre share remains large enough to warrant two-level modelling.

Table 3. Share of variance occurring among ECEC centres/schools, by IELS 2025 jurisdiction: own computations from the international microdata (%).

Jurisdiction	Child N	Centre N	Foundational Learning (%)	Executive Function (%)
Flemish Community (Belgium)	2363	200	23.12	11.90
England (United Kingdom)	2523	191	13.80	5.94
Korea	2894	222	25.49	12.84
Malta	1644	101	30.85	21.15
United Arab Emirates	4122	299	40.85	21.65
Baku and Sumgait (Azerbaijan)	2731	208	58.24	29.17
Ceará, Pará and São Paulo (Brazil)	2598	210	43.67	20.91

Own computations: unconditional (empty) two-level models fitted to the IELS 2025 international microdata, unweighted, pooled across the five plausible values per domain. The Netherlands is excluded from this analysis by scope. Brazil estimates correspond to averages across the three participating states. For orientation, the official OECD estimate for the IELS 2025 international average is approximately 36% for foundational learning and 22% for executive function, and approximately 27% and 16% for the Flemish Community (OECD, 2026); the official values derive from a different estimation convention (maximum-likelihood two-level models on composite domain scores) and are, therefore, not directly comparable cell by cell.

The between-centre variance shares published for the Flemish Community in the official OECD IELS 2025 materials (approximately 27% for foundational learning and 16% for executive function) derive from a two-step decomposition of the full Flemish sample using maximum-likelihood two-level models on composite domain scores (OECD, 2026). Our estimates differ in analytical sample, weighting, and pooling conventions: we fit two-level hierarchical linear models to each plausible-value set with design-based replicate weights and pool using Rubin’s Rules. For direct comparability with other jurisdictions, we additionally computed unconditional ICCs from the international microdata under a uniform, unweighted specification for the participating systems included in our microdata comparison (Table 3); these uniform-specification estimates yielded a broadly similar comparative pattern to the official OECD figures: Flemish between-centre variation is below the IELS 2025 average but above that of England, while official OECD estimates additionally indicate lower values for the Netherlands, which was not included in our microdata comparison (OECD, 2026). Remaining numerical differences between our estimates and official OECD values reflect these conventions rather than discrepancies in the underlying data.

3.2.2. Direct Associations with Foundational Learning

The direct-effects model regressed foundational learning on the individual-level predictors (individual SES and individual PHLI, centred within ECEC centres) and centre-level contextual predictors (centre-mean SES and centre-mean PHLI, grand-mean centred), controlling for child sex and age. Primary estimates pool 100 fits (20 imputations × 5 plausible values) under design-based weighting; results are presented in Table 4.

Table 4. Direct associations with foundational learning (primary estimates, multiple imputation, N = 2363).

Parameter	Estimate (B)	Standard Error (SE)	t	p
Null-Model Intercept	483.79	1.09	443.31	<0.001
Intraclass Correlation, FOUND (null model)	23.14%	—	—	—
Individual SES	25.11	0.92	27.22	<0.001
Individual PHLI	16.60	1.63	10.19	<0.001
Child Age in Months [control]	4.37	0.19	22.97	<0.001
Child Sex (Female) [control]	−1.50	1.58	−0.95	0.342
Centre-Mean SES	36.38	2.78	13.10	<0.001
Centre-Mean PHLI	24.11	5.80	4.16	<0.001
Between-Centre Variance (τ00)	563.83	—	—	—
Within-Child Variance (σ2)	3271.30	—	—	—
R2 Level 1/Level 2/Total	27.9%/55.9%/34.0%	—	—	—

Unstandardised raw-score estimates pooled across 100 fits (20 multiply imputed datasets × 5 plausible values) with design-based weighting (child weight and 92 BRR replicate weights, Fay k = 0.5; centres equally weighted at Level 2). The null-model intercept reflects the centre-equal-weighted between-centre mean and, therefore, differs from the child-weighted grand mean in Table 1. The sex coefficient varies modestly across weighting specifications (B between −0.91 and −2.63) and is retained as a control without substantive interpretation. Complete-case estimates (n = 1550) are reported in Section 3.4. Computational variable labels SES_c, PHLI_c, EF_c, center_SES_c, center_HLE_c, and center_EF_c correspond to individual SES, individual PHLI, individual EF, centre-mean SES, centre-mean PHLI, and centre-mean EF, respectively. Level-specific R² values were calculated as proportional reductions in the corresponding residual variance components relative to the unconditional model; total R² was calculated from the proportional reduction in total residual variance.

Individual SES (B = 25.11, p < 0.001) and individual PHLI (B = 16.60, p < 0.001) were positively associated with foundational learning, consistent with Hypothesis 1. Centre-mean SES showed a strong contextual association (B = 36.38, p < 0.001), and the centre-mean PHLI showed an independent positive association (B = 24.11, p < 0.001). The model accounted for 27.9% of within-centre, 55.9% of between-centre, and 34.0% of the total variance.

3.3. Two-Level Direct and Indirect Associations and the Boundary-Condition Question

To test Hypothesis 2, we estimated the within- and between-centre indirect associations of print-focused home literacy with foundational learning via executive function, with 95% Monte Carlo confidence intervals (100,000 draws; Section 2.5). The results are presented in Table 5.

Table 5. Two-level direct and indirect associations (PHLI → EF → FOUND; primary estimates, multiple imputation).

Model Level/Parameter	Estimate (SE) or [95% Monte Carlo CI]	p
Within-Centre (Level 1)
Path a_w: Individual PHLI → Individual EF	7.37 (1.84)	<0.001
Path b_w: Individual EF → Foundational Learning	0.488 (0.017)	<0.001
Direct Association c′: Individual PHLI → Foundational Learning	12.99 (1.48)	<0.001
Within-Centre Indirect Association (ab_w)	3.60 [1.83, 5.40]	—
Between-Centre (Level 2)
Path a_b: Centre-Mean PHLI → Centre-Mean EF	12.08 (5.30)	0.023
Path b_b: Centre-Mean EF → Foundational Learning	0.695 (0.023)	<0.001
Between-Centre Conditional Direct Association c′_b: Centre-Mean PHLI → Foundational Learning	15.65 (4.34)	<0.001
Between-Centre Indirect Association (ab_b)	8.40 [1.16, 15.65]	—

Pooled across 100 fits (20 imputations × 5 plausible values) with design-based weighting. Indirect-association intervals are 95% Monte Carlo confidence intervals (100,000 draws) and make no normality assumption about the a × b product. The conditional direct association c′_b is taken from the full Path B model; the decomposition is internally consistent (24.11 − 15.65 = 8.46 ≈ ab_b = 8.40). p-Values are not reported for the indirect associations; inference is based on the Monte Carlo intervals.

A positive within-centre indirect association was estimated between print-focused home literacy and foundational learning through executive function (ab_w = 3.60, 95% CI [1.83, 5.40]), consistent with Hypothesis 2. A secondary exploratory analysis indicated a parallel indirect association at the centre level (ab_b = 8.40, 95% CI [1.16, 15.65]): centres whose intake averages higher print-focused home literacy also average higher executive-function skills, which in turn is associated with higher centre-level learning.

Regarding Research Question 1, the analysis did not provide evidence that centre SES modified the within-centre association: the cross-level interaction between individual print-focused home literacy and centre-mean SES was small and non-significant in the primary model (B = 2.92, SE = 2.38, p = 0.219) and in the complete-case sensitivity model (B = 0.97, SE = 1.88, p = 0.610). This non-significant result does not establish equivalence or invariance across centres; smaller moderating associations cannot be ruled out.

3.4. Sensitivity to Missing-Data Handling

Table 6 compares the primary multiple-imputation estimates with the complete-case (listwise) estimates for the key parameters.

Table 6. Primary (MI, N = 2363) vs. complete-case (n = 1550) estimates (design-based).

Parameter	Complete Case	MI (Primary)	Δ
ICC, Foundational Learning (%)	21.39	23.14	+1.75 pp
Individual SES (Level 1)	25.21	25.11	−0.41%
Individual PHLI (Level 1)	17.19	16.60	−3.40%
Centre-Mean SES (Level 2)	40.63	36.38	−10.47%
Within-Centre Indirect Association (ab_w)	3.86	3.60	−6.64%
Cross-Level Interaction p-Value	.610	.219	—

Substantive conclusions are unchanged across the two missing-data handlings: all primary direct and indirect associations retained their direction and statistical interpretation, remaining within 0.4–10.5% of their complete-case counterparts, while the cross-level interaction remained non-significant for both.

4. Discussion & Conclusions

4.1. Theoretical Interpretation of the Findings

The findings of this study are consistent with the two theoretical lenses outlined in Section 1.4 and sharpen the descriptive configuration we labelled the “Flemish Paradox” (Brooker, 2015; Jæger & Karlson, 2018; Kulić et al., 2019; OECD, 2026; Radulović & Krstić, 2017).

First, comparatively limited between-centre outcome variation coexisted with substantial within-centre differences associated with family SES and print-focused home literacy (Balladares & Kankaraš, 2020; Brunner et al., 2025; Claes et al., 2026; OECD, 2026). Between-centre variance in foundational learning is comparatively low in the Flemish Community (ICC = 23.14% in the primary sample), sitting below the IELS 2025 average but above the lowest observed values (Table 3) (Nusche et al., 2015; OECD, 2015, 2026). Yet within centres, children remain markedly unequal, and that inequality is systematically associated with family SES (B = 25.11) and with print-related home learning practices (B = 16.60) (Attig & Weinert, 2020; Duncan et al., 2022; Kulić et al., 2019; OECD, 2026; Rodriguez & Tamis-LeMonda, 2011). This pattern is what cultural-capital accounts lead one to expect: where common governance arrangements are in place, children’s engagement with and benefit from provision may still vary with the cultural resources transmitted at home (Brooker, 2015; Jackson, 2022; Jæger & Karlson, 2018; Radulović & Krstić, 2017). The contextual associations point in the same direction: centre-mean SES (B = 36.38) and centre-mean PHLI (B = 24.11) indicate that the collective home ecology of a centre’s intake is independently associated with its average outcomes.

Second, the pattern of associations is consistent with executive function as a candidate pathway (Brunner et al., 2025; Cameron et al., 2012; Kellens et al., 2023; Scionti et al., 2020). At the individual level, part of the PHLI association is accounted for by children’s EF skills (ab_w = 3.60, 95% CI [1.83, 5.40]). In a secondary exploratory analysis, a parallel compositional pattern was observed among centres (ab_b = 8.40, 95% CI [1.16, 15.65]): centres averaging richer print-focused home literacy also average higher EF skills, which in turn are associated with higher average learning. This between-centre pattern reflects associations among centre aggregates and should not be interpreted as an individual-level developmental pathway. Print-rich parent–child interactions (shared reading, library visits, and books at home) place sustained demands on attention, memory, and self-regulation and are, therefore, a plausible conduit through which home practices relate to the development of EFs (Attig & Weinert, 2020; Children’s Competencies Development in the Home Learning Environment, 2021; Kellens et al., 2023; OECD, 2026; Rodriguez & Tamis-LeMonda, 2011; Tóth et al., 2019). We stress that cross-sectional mediation cannot establish this sequence (see Section 4.2); the result is consistent with the proposed pathway but does not establish the underlying mechanism.

Third, the boundary-condition question yielded a non-significant interaction (p = 0.219, primary; p = 0.610, complete case): we found no statistically significant evidence that centre SES modified the within-centre PHLI association (Balladares & Kankaraš, 2020; Brunner et al., 2025; OECD, 2026). The confidence surrounding the interaction estimate does not establish equivalence, and smaller moderating associations cannot be ruled out. More broadly, the family-level gaps observed at school entry may represent starting conditions relevant to cumulative-disadvantage accounts (Burger, 2009; Duncan et al., 2022; Kulić et al., 2019; Rad et al., 2022), but the present cross-sectional study cannot determine whether these differences widen, persist, or narrow over time; tracing their compounding requires longitudinal data (Section 4.4).

4.2. Reverse Causality and the Limits of Causal Interpretation

Several features of the design limit causal interpretation. With cross-sectional data, the PHLI → EFs → learning ordering implied by the estimated indirect associations cannot be distinguished from at least three alternatives: (i) reverse influence, whereby children with stronger early skills elicit more literacy-rich interaction from their parents; (ii) reciprocal influence, in which home practices and child skills reinforce one another over time; and (iii) unmeasured common causes—parental education, income, or cognitive ability—that shape both the home environment and child outcomes and could generate the same pattern of coefficients (Engzell & Jönsson, 2015; Grant et al., 2023). The use of separate measurement sources (direct assessment of children; parent reports of the home) reduces shared-informant concerns but does not address temporal ordering, measurement error, or unobserved confounding. We, therefore, interpret the indirect associations as evidence that the observed pattern of associations is consistent with the proposed pathway, not as demonstrations of it (see Section 1.4.3). Longitudinal designs that measure home practices, executive function, and learning at multiple waves are required to adjudicate between these orderings and to trace how early gaps compound over time (Ferraro et al., 2015; Masten & Cicchetti, 2010).

4.3. Educational and Policy Implications

The estimated associations are of modest but practically relevant size (Duncan et al., 2022; Kulić et al., 2019; OECD, 2017, 2026; Richter et al., 2021). A one-standard-deviation difference in the print-focused home literacy index, whose observed weighted standard deviation was 0.714, corresponded to an estimated total within-centre difference of approximately 11.85 foundational-learning score points (about 0.16 of an outcome standard deviation). This total comprised an estimated conditional direct component of approximately 9.28 points and an indirect component of approximately 2.57 points through EFs (Attig & Weinert, 2020; OECD, 2026; Rodriguez & Tamis-LeMonda, 2011). These values are descriptive model-based associations and should not be interpreted as intervention effects or developmental gains.

The findings identify print-focused home literacy as a potentially relevant complement to centre-level provision (Attig & Weinert, 2020; Children’s Competencies Development in the Home Learning Environment, 2021; Duncan et al., 2022; OECD, 2026; Rodriguez & Tamis-LeMonda, 2011; Tóth et al., 2019). Family-facing initiatives may, therefore, warrant consideration alongside, rather than instead of, investments in ECEC quality (Duncan et al., 2022; OECD, 2017; Rad et al., 2022; Richter et al., 2021). Examples aligned with the measured construct include access to age-appropriate books, shared-reading guidance, and library engagement. However, the present observational analyses did not evaluate any intervention and cannot establish the effectiveness, optimal design, or cost-effectiveness of such programmes (see Section 4.4).

4.4. Methodological Limitations and Future Directions

Several limitations qualify these findings. First, IELS 2025 is cross-sectional: all models are associational, and the indirect associations, in particular, are pattern-consistency tests rather than demonstrations of a causal sequence (Section 4.2) (Grant et al., 2023). Cumulative-disadvantage accounts are inherently temporal; longitudinal data are needed to observe compounding directly (Ferraro et al., 2015; Masten & Cicchetti, 2010).

Second, the parental non-response is substantial (27.6% of the full sample) and selective: Children without matched parent questionnaires scored significantly lower on directly assessed foundational learning and executive function (Section 2.2). To avoid confusion among distinct concepts, the parental questionnaire nonparticipation rate was 27.6%; variable-level missingness was somewhat higher for SES (31.0%) and the PHLI (28.7%), and joint missingness across the required parent-report predictors reduced the complete-case sample to 65.6% of the original sample. Multiple imputation addresses this under a missing-at-random assumption conditional on observed covariates, but that assumption cannot be verified, and a missing-not-at-random mechanism—whereby the most vulnerable families are least likely to respond—remains plausible (Engzell & Jönsson, 2015; Lingwood et al., 2019; Pepinsky, 2018). Under-representation of the lower SES tail may restrict variance and attenuate family-side associations (Falk et al., 2021); reassuringly, the PHLI coefficient differs by only 3.4% between the complete-case and imputed analyses, and all substantive conclusions are stable across the two handlings (Table 6).

Third, the index is a deliberately narrow, print-focused window: it covers shared reading, library visits, and books at home but not play-based learning, numeracy interactions, or oral linguistic stimulation (Children’s Competencies Development in the Home Learning Environment, 2021; Tóth et al., 2019). The estimates should, therefore, be interpreted as pertaining specifically to print-focused home literacy rather than to the broader home learning environment, and the policy implications above are correspondingly scoped. The index’s modest reliability (α = 0.55; ω_t = 0.57) introduces measurement error that may affect the magnitude of the estimated associations, often through attenuation under classical measurement-error assumptions.

Fourth, home-environment measures rely on parent reports and may be affected by social-desirability bias (Grolig, 2020). Although the use of separate measurement sources reduces shared-informant concerns, it does not address temporal ordering, other forms of measurement error, or unobserved confounding (Bennetts et al., 2016). Direct observational measures of the home environment would strengthen future work.

5. Conclusions

Using design-based multilevel models with multiply imputed parent-report data, this study found positive within-centre associations of family SES and print-focused home literacy with foundational learning in the Flemish Community. A positive indirect association through EFs was observed at the child level, while a secondary parallel pattern emerged among centres. The analysis did not provide evidence that centre SES modified the within-centre PHLI association. Flemish between-centre outcome variation was comparatively limited relative to most, but not all, participating jurisdictions. These findings clarify the multilevel structure of associations among family resources, print-focused home literacy, EFs, and foundational learning, but they do not establish causal mediation, institutional equality, or cumulative change over time.