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Article

Multidimensional Correlates of Childhood Stunting in India: A Spatial Machine Learning and Explainable AI Approach

by
Bhagyajyothi Rao
1,
Md Gulzarull Hasan
1,2,*,
Bandhavya Putturaya
1,
Asha Kamath
1,
Mohammad Aatif
3 and
Yousif M. Elmosaad
3,*
1
Department of Applied Statistics & Data Science, Prasanna School of Public Health, Manipal Academy of Higher Education, Manipal 576104, India
2
School of Public Health, Graduate School of Medicine, Kyoto University, Kyoto 606-8303, Japan
3
Department of Public Health, College of Applied Medical Sciences, King Faisal University, Al Ahsa 36362, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Stats 2026, 9(2), 34; https://doi.org/10.3390/stats9020034
Submission received: 18 January 2026 / Revised: 22 February 2026 / Accepted: 22 February 2026 / Published: 24 March 2026
(This article belongs to the Section Applied Statistics and Machine Learning Methods)
Browse Figures
Versions Notes

Abstract

Childhood stunting remains a major public health challenge in India and is influenced by multiple socioeconomic and environmental factors. This ecological study examined district-level correlates of childhood stunting, including Crimes Against Women (CAW), the Multidimensional Poverty Index (MPI), and drought severity, using data from NFHS-5, the National Crime Records Bureau, NITI Aayog’s MPI reports, and the Drought Atlas of India. Spatial autocorrelation and Spatial regression models were applied alongside machine learning approaches and SHAP-based Explainable AI (XAI) interpretation. Childhood stunting exhibited significant spatial clustering (Moran’s I = 0.520, p < 0.001), with hotspots in northern, central, and eastern India. Higher stunting was associated with higher birth order, low maternal BMI, child anaemia, and MPI, and negative associations with iodised salt usage, electricity access, and timely postnatal care. A significant spatial lag parameter (ρ = 0.348) indicated substantial spillover effects. Machine learning models consistently identified MPI, drought severity, and CAW as key predictors. The integrated spatial and machine learning framework identifies key correlates and spatial dependencies of childhood stunting, highlighting the need for region-specific, multisectoral interventions.

1. Introduction

The United Nations adopted the Sustainable Development Goals (SDG Target 2.2) in 2015, aiming to end all forms of malnutrition by 2030 [1]. Globally, during 2022, 148 million (22.3%) children under 5 years were estimated to be stunted (too short for age), 45 million (6.8%) were estimated to be wasted (too thin for height), and 37 million (5.7%) were overweight or living with obesity [2]. Despite sustained global efforts, the 2023 Joint Malnutrition Estimates indicate that progress toward achieving these nutrition targets remains insufficient and requires accelerated action [3].
According to the World Health Organisation (WHO), stunting among children under five in India declined from 41.6% in 2012 to 31.7% in 2022 [4]. To combat malnutrition, the Indian government has implemented programs like the Integrated Child Development Scheme (ICDS) [5], Reproductive and Child Health Program (RCH) [6], National Rural Health Mission (NRHM) [7], Pradhan Mantri Matru Vandana Yojana (PMMVY) [8], Anganwadi Services, targeted schemes for adolescent girls, and POSHAN Abhiyaan [9,10]. However, India still reports the second-highest child stunting in South Asia (38%), after Afghanistan (41%) [11]. With the population projected to increase by 17% from 2022 to 2030, addressing child stunting remains a critical public health priority [12,13,14].
The determinants of stunting are multidimensional, encompassing maternal nutritional status, birth order, household living conditions, access to health services, and exposure to infections [15,16,17,18,19,20,21,22,23]. Emerging evidence further underscores the role of broader structural factors such as climate vulnerability, poverty, and social instability, which often coexist with high levels of child undernutrition [24,25].
Climate-related stressors have been linked to declining food security and heightened nutritional risk across multiple settings [26,27,28,29]. According to UNICEF’s Children’s Climate Risk Index, a substantial proportion of child deaths attributable to climate change are expected to result from undernutrition [30].
The Multidimensional Poverty Index (MPI) captures deprivations in education, health, and living standards that often correspond with spatial patterns of child malnutrition [31,32,33]. Prior studies highlight the strong association between poverty and malnutrition, noting that income-based measures alone are insufficient, and emphasise the need to integrate nutrition indicators within the MPI to better capture the multidimensional nature of deprivation [34,35].
Studies have also documented associations between violence against women and adverse maternal and child outcomes, including compromised nutrition and low birthweight because of domestic violence against women during pregnancy [36,37,38,39].
Given India’s substantial geographic and socio-economic diversity, understanding how these multidimensional district-level characteristics relate to stunting and how they are spatially patterned is essential for designing regionally targeted strategies.
The existing literature indicates that only a limited number of studies have applied spatial analytical methods to examine childhood malnutrition in India, and most have focused primarily on mapping prevalence or identifying regional hotspots [15,16,40]. Few have incorporated spatial lag variables, as the conditions in neighbouring districts may be associated with stunting patterns due to shared socio-economic, environmental, or health-system contexts. The integration of spatial econometric methods with ML remains very limited in malnutrition research, despite their suitability for modelling complex and nonlinear associations. Spatial ML approaches offer enhanced predictive performance when analysing high-dimensional covariates but are often criticised for limited interpretability. Explainable Artificial Intelligence (XAI) techniques, such as SHapley Additive exPlanations (SHAP), provide a principled framework to decompose Machine Learning (ML) predictions and quantify the relative contribution and direction of individual predictors [41,42,43,44]. This study addresses this gap by integrating spatial econometric models, ML algorithms, and XAI to enable robust, interpretable, and spatially informed assessment of childhood stunting determinants.
To the best of our knowledge, no studies in India have simultaneously incorporated spatial lag effects and ML-based predictive interpretation to examine MPI, CAW, drought, and socio-economic determinants as correlates of childhood stunting.
Building on these gaps, the present study (i) investigates the spatial distribution of childhood stunting along with district-level MPI, CAW estimates, and drought severity across India (ii) evaluates the associations between stunting and other multidimensional covariates using spatial econometric models, and (iii) identifies how these variables along with the spatial lag variables, contribute to stunting prediction through spatial machine learning and explainable AI approaches, offering clearer insight into geographically clustered vulnerabilities and supporting more targeted policy responses.
The manuscript is organised as follows: Section 2 covers Materials and Methods; Section 3 presents the Results from spatial and ML analyses; Section 4 discusses key insights and the limitations of the study; and Section 5 concludes with future research directions.

2. Materials and Methods

2.1. Data Sources

This ecological study integrates district-level data from four sources across 692 Indian districts. Data on stunting prevalence (dependent variable) and reliable estimates of key health and nutrition indicators (socioeconomic covariates) were obtained from the National Family Health Survey (NFHS-5), 2019–2021, a comprehensive multi-round survey designed to track health, nutrition, and family welfare metrics [45].
MPI scores (covariate) were sourced from the NITI Aayog Progress Review, based on the Alkire–Foster methodology, and capture deprivations in health, education, and living standards. It utilises 12 indicators, including nutrition, child mortality, maternal health, schooling, and access to basic services like clean water, electricity, and sanitation [46].
District-level relative risks of CAW (covariate) were derived by Pooja et al. [38] using the Besag–York–Mollié model, which accounts for spatial dependence and unstructured heterogeneity. In the study, National Crime Records Bureau (NCRB) data (2020–2022) [47] were analysed using small-area estimation methods and covered multiple CAW categories, including domestic violence, sexual violence against minors, dowry-related offences, rape, abduction, acid attacks, and human trafficking, with overall CAW relative risk computed across the Indian Penal Code and Special and Local Laws.
Drought severity (covariate) was measured using the Standardised Precipitation and Evapotranspiration Index from the Drought Atlas of India, categorising districts into normal, moderate, severe, and extreme drought conditions [48,49,50].
The analytical procedure and modelling approach are depicted in Figure 1.

2.2. Spatial Analysis

In the initial phase, the 707-district data were reduced to 692 districts to fit the India shapefile using NFHS-5 district-level data, along with information on CAW, drought, and the MPI [51]. Spatial exploratory data analysis was conducted using Moran’s I and Local Indicators of Spatial Association (LISA) to assess spatial autocorrelation and clustering patterns, implemented via QGIS (v3.38.3) and GeoDa (v1.22) [52,53,54]. An Ordinary Least Squares model was initially applied to identify determinants of childhood stunting, with multicollinearity checked using variance inflation factors (VIF), and residual diagnostics performed using the Jarque-Bera, Breusch-Pagan, and Lagrange Multiplier tests. Upon detecting spatial dependence, spatial econometric models, including the Spatial Durbin model (SDM), Spatial Durbin Error model (SDEM), Spatially Lagged X Model (SLX), Spatial Autoregressive Model (SAR), and Spatial Error Model (SEM), were employed, with model selection guided by the Likelihood Ratio Test (LRT) that simplify the model parameters [55,56,57]. Details provided in the Supplementary File S1.

2.3. Spatial Machine Learning Models and XAI

We then incorporated spatial lag features to capture the influence of neighbouring districts using an ML approach. Random Forest and XGBoost models were then applied using both spatial and spatial lag predictors, following feature selection through the Least Absolute Shrinkage and Selection Operator (LASSO) method [42,43,58,59]. Model interpretability was enhanced using SHAP, which provided transparent insights into how socio-economic characteristics, MPI, drought severity, and CAW indicators contributed to the model’s predictions of childhood stunting [60].

3. Results

3.1. Descriptive Analysis

Descriptive statistics are summarised in Table 1. Descriptive analysis showed that 33.56% of children under five are stunted, with prevalence ranging from a high of 60.6% in Pashchimi Singhbhum (Jharkhand) to a low of 13.2% in Jagatsinghpur (Odisha). Among predictors, the Population living in households with electricity has the highest mean value of 97%, with the minimum at Sitapur (68.35%) in Uttar Pradesh, and nearly 18 districts have the maximum (100%) electric facilities. The average for Households using iodised salt was 95.1%, ranging from Koppal (47.93%) in Karnataka to Khowai (100%) in Tripura. The Population living in households with an improved drinking water source accounted for 93.8%, and 31 of 692 districts had such sources. Nearly 79.2% of Children are receiving postnatal care from a doctor/nurse/LHV/ANM/midwife/other health personnel, whereas the lowest percentage is in Mon (22.6%), Nagaland. The average percentage of Children aged 9–35 months who received a vitamin A dose was 72.5%, with the highest at Mysore (98.1%) in Karnataka and the lowest at Tuensang (27.46%) in Nagaland. Nearly 71.8% of the population lives in households with improved sanitation facilities, with the highest percentage in Malappuram (99.8%) in Kerala and the lowest in Purulia (29.2%) in West Bengal. Children aged 6–59 months who were anaemic accounted for 65.8%, with the highest rate recorded at Leh (95.5%) in Ladakh and the lowest at East Garo Hills (28%) in Meghalaya.

3.2. Exploratory Data Analysis

3.2.1. Moran’s Statistic

Spatial autocorrelation was assessed using Global Univariate Moran’s I statistic (Table 1). The value for childhood stunting (Moran’s I = 0.525, p < 0.001) indicates a moderate and statistically significant spatial dependency across India. Among the predictors, the highest univariate Moran’s I was observed for drought (0.843), followed by women with BMI below normal (0.729), mothers who consumed iron-folic acid for 180+ days during pregnancy (0.716), and children who received postnatal care (0.709). All these values indicate significant (p < 0.001) strong positive spatial autocorrelation.
Figure 2 presents the Univariate Moran’s Scatterplot: quadrant I groups districts with high values, quadrant III with low values, while quadrants II and IV represent spatial outliers where high and low values are grouped together.
Bivariate Moran’s I was used to examine spatial correlations between childhood stunting and drought, CAW, and MPI. Moran’s I for stunting and drought was −0.061 (p < 0.05), showing very weak but statistically significant spatial autocorrelation. Stunting and CAW showed a similarly weak negative spatial autocorrelation (Moran’s I = −0.084, p < 0.05). For stunting and MPI, Moran’s I was 0.426 (p < 0.05), reflecting a moderate and significant positive spatial autocorrelation.

3.2.2. Spatial Distribution

The spatial variation of childhood stunting and its correlates was analysed using spatial maps. Figure 3 presents district-level prevalence, clusters, and their significance.
Stunting: Figure 3a shows the district-level prevalence of childhood stunting across 692 districts, with 78 districts exhibiting the highest stunting rates. Figure 3b,c show that high stunting rates are mainly concentrated in Uttar Pradesh, Bihar, Madhya Pradesh, Gujarat, and Jharkhand, with some parts of Karnataka, Chhattisgarh, Maharashtra, Meghalaya, and Odisha. In contrast, low stunting prevalence is predominantly observed in northern states like Himachal Pradesh and Punjab, and in southern states such as Kerala, Tamil Nadu, and Telangana, reflecting better-performing regions in terms of child stunting
Drought: The district-level prevalence map Figure 3d, shows that 109 of 692 districts experienced the most severe drought conditions. Figure 3e,f illustrate High-High clusters of districts with severe drought surrounded by similarly affected neighbours, primarily concentrated in Northeast India, particularly in Assam and neighbouring states. Additional High-High clusters appear in North India, including parts of Punjab, Haryana, and Uttar Pradesh, and in Central India, particularly in Odisha, Madhya Pradesh, and Chhattisgarh. In contrast, Low-Low clusters of districts with low drought surrounded by similarly less-affected neighbours are mainly located in Southern India, including Tamil Nadu, Karnataka, and Kerala. Some districts in Central India, such as Maharashtra, also exhibit Low-Low clustering.
CAW: The prevalence map for CAW (Figure 3g) identifies 68 districts with the highest CAW rates, predominantly in Northern and Central India. Figure 3h,i highlight hotspots in Uttar Pradesh, Haryana, Rajasthan, and Madhya Pradesh, showing the most significant concentrations of high CAW. Additional elevated CAW levels are observed in parts of Bihar, Gujarat, Chhattisgarh, Maharashtra, and Telangana. Conversely, districts with low CAW rates are concentrated in the Northeast and the South. In the Northeast, Mizoram, Sikkim, and Arunachal Pradesh stand out, while in the South, Kerala, Tamil Nadu, and Andhra Pradesh show the highest concentrations of low-CAW districts. Northern states like Himachal Pradesh and Uttarakhand also exhibit low CAW levels.
MPI: The district-level MPI prevalence map Figure 3j, identifies 88 districts with the highest levels of multidimensional poverty, largely concentrated in North and Western India. These areas are marked by severe deprivations in education, healthcare, and sanitation. Figure 3k,l display High-High clusters prominently found in parts of Uttar Pradesh, Bihar, Meghalaya, Madhya Pradesh, Jharkhand, Odisha, and Chhattisgarh, indicating persistent poverty. In contrast, 43 districts form Low-Low clusters, indicating low MPI surrounded by similarly low-poverty areas.

3.3. Ordinary Least Squares Regression Model

An Ordinary Least Squares regression model was applied to identify key predictors of childhood stunting, using variables with variance inflation factors (VIFs) below 5. Model diagnostics validated the regression assumptions. The Jarque-Bera test confirmed that the residuals were normally distributed (p-value > 0.05), while the Breusch-Pagan test indicated homoskedasticity in the error terms (p-value > 0.05). The Lagrange Multiplier and Robust Lagrange Multiplier tests were both highly significant (p-value < 0.001), indicating spatial dependency in the data.

3.4. Spatial Regression Models

To account for spatial dependency, spatial regression models were applied to identify significant factors associated with childhood stunting. SDM addressed global spatial dependencies, while SDEM focused on local spatial effects. This dual approach allowed a comprehensive analysis of spatial interactions.
Among SDM and SDEM models, the SDM performed better with a lower AIC and higher R2 (AIC = 4344, R2 = 0.6268) compared to the SDEM (AIC = 4348, R2 = 0.6242). Then, to identify the best-fitting spatial model, the SDM was simplified to SLX, SAR, and SEM. LRT showed that the SAR model was the best fit. In the SAR model, 7 of 26 predictors were significantly associated with childhood stunting prevalence. Model details and results are provided in Supplementary File S2. Table 2 presents the estimates for the SDEM, SDM, and SAR models.
Significant negative associations in the SAR model were observed for electricity (β = −0.19, SE = 0.09, 95% CI: −0.37 to −0.01), iodised salt (β = −0.14, SE = 0.06, 95% CI: −0.26 to −0.02), and postnatal care (β = −0.08, SE = 0.04, 95% CI: −0.16 to −0.002). On average, a 1% increase in these variables may decrease the prevalence of childhood stunting by 0.19%, 0.14%, and 0.08%, respectively. Conversely, significant positive associations were observed for third or higher-order births (β = 0.92, SE = 0.27,95% CI: 0.39 to 1.45), low maternal BMI (β = 0.26, SE = 0.06, 95% CI: 0.14 to 0.38), child anaemia (β = 0.11, SE = 0.04, 95% CI: 0.03 to 0.19), and MPI (β = 12.26, SE = 7.29, 95% CI: −2.03 to 26.55). On average, a 1% increase in these variables may increase stunting prevalence by 0.92%, 0.26%, 0.11%, and 12.26%, respectively.
The significant lag coefficients (ρ = 0.3132 in SDM; ρ = 0.348 in SAR) indicate strong spatial spillover, suggesting that stunting prevalence in a district is statistically associated with stunting levels in neighbouring districts.

3.5. Machine Learning Models

3.5.1. Feature Selection

Spatial lag variables were derived from the SLX model to capture neighbourhood dependencies. The most relevant lagged features are selected using LASSO regression, as shown in Figure 4.

3.5.2. ML Models

After selecting the spatially lagged features, an integrated modelling framework was implemented by combining the original covariates with the selected spatial lag variables in Random Forest and XGBoost models. The dataset was partitioned into training (70%) and independent test (30%) sets, with 10-fold cross-validation applied exclusively to the training data to assess model stability and reduce overfitting.
The Random Forest model was implemented using 500 trees to ensure stable estimation, while other hyperparameters were retained at their default settings to maintain model interpretability in an ecological analysis context in both algorithms. Final model performance was evaluated on the independent test set, and feature importance measures from both models were examined to identify key predictors of childhood stunting.

3.5.3. Variable Importance

While identifying the important features, both the models consistently highlighted MPI, low BMI, CAW, child anaemia and the infrastructure-related variables, such as access to sanitation, electricity, and clean cooking fuel, as the most significant correlates of stunting prevalence in children. The severe drought variable was an important predictor in the XGBoost model. The important features identified by both algorithms are shown in Figure 5a,b.

3.5.4. Model Evaluation

The Random Forest model could explain approximately 54.8% (R2) of the variance in the target variable. The XGBoost model achieved an R2 score of 0.520, explaining 52.0% of the variance. Akaike Information Criterion (AIC) for the Random Forest model (AIC: 2333.98) was lower compared to the XGBoost model (AIC: 2346.73), indicating a better balance of model complexity and goodness-of-fit for the Random Forest model.

3.6. Explainable Artificial Intelligence

The SHAP analysis decomposed the Random Forest model’s prediction into a baseline and feature-specific contributions. The baseline prediction across districts was 33.592%, while the selected observation had a final predicted stunting level of 40.831%, reflecting a cumulative contribution of +7.239%. Features that increased the predicted value included MPI (+5.45), spatially lagged iodised salt (+0.68), spatially lagged MPI (+0.46), access to electricity (+0.30), women with a below-normal BMI (+0.28), and higher-order birth (+0.28). Smaller contributions from the remaining variables collectively shaped the final model prediction (Figure 6).

4. Discussion

The findings demonstrate pronounced spatial clustering of childhood stunting, with high-prevalence districts concentrated in northern, central, and eastern India [15,17,18,40]. The significant spatial lag coefficients estimated in the SAR and SDM models further indicate substantive spatial spillover effects, implying that stunting levels within a district are statistically associated with those in neighbouring districts. This pattern highlights geographic interdependence and suggests that contextual socio-economic and environmental conditions extend beyond administrative boundaries. These results reinforce the importance of explicitly incorporating spatial structure in nutrition research to ensure valid inference and context-sensitive policy planning [61,62].
Spatial regression models identified several district-level factors significantly associated with childhood stunting. Higher multidimensional poverty, higher birth order, low maternal BMI, and child anaemia were positively associated with increased stunting prevalence [15,16,17,18,19,20,21,22,23,24,25,31,32,33,34,35]. In contrast, improved sanitation, access to electricity, and iodised salt utilisation were associated with lower stunting levels, underscoring the importance of household living conditions and hygiene environments in shaping nutritional outcomes.
Indicators such as drought severity and CAW showed associations in ML models, underscoring the limitations of conventional approaches for capturing complex, nonlinear interactions and for linking environmental and social vulnerability to child nutrition disparities. The role of drought as a significantly associated covariate highlights the need for climate-resilient agricultural and food security policies to mitigate the long-term nutritional consequences of climate variability. Policies aimed at women’s safety, economic empowerment, and access to justice could improve maternal and child health outcomes [26,27,28,29,30,31,32,33,34,35,36,37,38,39,50].
Additionally, the strong association between MPI and stunting, observed in both spatial and ML models, underscores the urgent need for integrated poverty alleviation strategies. Policies should focus on improving access to healthcare, maternal nutrition, education, and sanitation, as these factors directly contribute to reducing childhood malnutrition [62].
The ML models complement spatial regressions by capturing nonlinear relationships and higher-order interactions between spatial and non-spatial variables that are not identifiable within conventional spatial econometric frameworks. Although predictive performance gains between non-spatial and spatial ML models were modest, incorporating spatial lags remains statistically justified, as significant Moran’s I statistics and spatial lag (ρ) coefficients confirm residual spatial dependence in childhood stunting [38,39,40,62]. The presence of spatial autocorrelation violates the independence assumption underlying non-spatial models and indicates potential spatial bias. The spatial model results also demonstrate substantive spillover effects, suggesting that district-level stunting is systematically associated with neighbouring districts, even after controlling locally observed covariates. Thus, incorporating spatial effects strengthens the validity of the estimates and better accounts for geographic dependence, even when improvements in predictive performance are limited [41,42,43]. MPI, drought severity, and CAW emerged as influential contributors to prediction performance, reflecting broader socio-economic and environmental vulnerabilities associated with district-level stunting prevalence [22,27,33,38,39,40,62].
The SHAP analysis enhanced interpretability by decomposing predictions into feature-specific contributions; however, these contributions represent model behaviour rather than causal effects, consistent with recommendations for interpreting explainable AI outputs [41,42,43,44].
Limitations: Despite its strengths, this study has certain limitations. First, the use of district-level aggregated data may bound the importance of within-district heterogeneity in childhood stunting, limiting the ability to identify localised disparities. Second, the spatial weight matrix relies on predefined geographic contiguity, which may not fully reflect social, economic, or environmental interactions across districts. Third, the study doesn’t assess temporal changes or the directionality of observed associations.

5. Conclusions

In summary, the study demonstrated that childhood stunting in India follows distinct spatial patterns shaped by multidimensional socio-economic, social, maternal, environmental, and regional-level characteristics. By integrating spatial econometric models with ML and explainable AI, the analysis reveals important spatial spillover effects and highlights key correlates of district-level stunting patterns. These findings underscore the value of geographically targeted, multisectoral strategies that address shared vulnerabilities across neighbouring districts.
Further exploration using spatial–temporal models or causal inference frameworks may help explain the mechanisms underlying these observed patterns. Additionally, qualitative or mixed-methods research could provide deeper insights into how multidimensional poverty, CAW, and environmental stressors relate to child nutrition at the household and community levels. Strengthening local and regional efforts that consider spatial dependencies may support progress toward reducing undernutrition and advancing national goals aligned with Sustainable Development Goals 2 and 3.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/stats9020034/s1.

Author Contributions

Design and concept: B.R. and M.G.H.; Data acquisition: B.R.; Data analysis: B.R. and M.G.H.; Data Interpretation: B.R. and M.G.H.; Drafting of the first version of the manuscript: B.R. Conceptualization, B.R. and M.G.H.; methodology, B.R. and M.G.H.; software, B.R.; validation, B.R.; formal analysis, B.R. and B.P.; resources, B.R. and A.K.; writing—original draft preparation, B.R.; writing—review and editing, B.R., M.G.H., A.K., M.A. and Y.M.E.; visualization, B.R.; supervision, M.G.H., A.K., M.A. and Y.M.E. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Deanship of Scientific Research Vice Presidency for Graduate studies and Scientific Research, King Faisal University, Saudi Arabia [Grant No. KFU261092].

Informed Consent Statement

This study utilises publicly available datasets, including the National Family Health Survey-5, National Crime Records Bureau data, and Drought Index data. Since these datasets are open source and publicly accessible, no separate ethical approval or consent for publication was required.

Data Availability Statement

The original contributions presented in this study are included in the article/Supplementary Materials. Raw data sets are publicly available and can be accessed via the provided weblinks. NFHS 5 District-level Data: https://www.data.gov.in/resource/india-districts-factsheets-national-family-health-survey-nfhs-5-2019-2021-provisional (accessed on 16 July 2025). Drought status: https://zenodo.org/records/8280551 (accessed on 16 July 2025). Multidimensional Poverty Index: https://niti.gov.in/publications/division-reports (accessed on 16 July 2025). District-level relative risks of crime against women: https://doi.org/10.3389/fpubh.2024.1362406. Further inquiries can be directed at the corresponding author(s).

Acknowledgments

The authors are grateful to the reviewers and the journal editor for their valuable comments and suggestions, which have significantly improved the manuscript.

Conflicts of Interest

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Abbreviations

The following abbreviations are used in this manuscript:
CAWCrimes Against Women
MPIMultidimensional Poverty Index
MLMachine Learning
XAIExplainable AI
SHAPSHapley Additive exPlanations
NFHSNational Family Health Survey
NCRBNational Crime Records Bureau
LISALocal Indicators of Spatial Association
SDMSpatial Durbin Model
SDEMSpatial Durbin Error model
SLXSpatially Lagged X Model
SARSpatial Autoregressive Model
SEMSpatial Error Model
LRTLikelihood Ratio Test
LASSOLeast Absolute Shrinkage and Selection Operator

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Figure 1. Schematic workflow of the study illustrating the analytical framework.
Figure 1. Schematic workflow of the study illustrating the analytical framework.
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Figure 2. Univariate Moran’s scatterplots of childhood stunting, drought severity, crime, and MPI.
Figure 2. Univariate Moran’s scatterplots of childhood stunting, drought severity, crime, and MPI.
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Figure 3. Spatial distribution and local spatial autocorrelation of selected factors across 707 districts in India. (a) District level childhood stunting prevalence; (b) LISA cluster map of childhood stunting; (c) LISA significance for childhood stunting; (d) Prevalence of drought severity; (e) LISA cluster map of drought severity; (f) LISA significance for drought severity; (g) Prevalence of crimes against women; (h) LISA cluster map of crimes against women; (i) LISA significance for crimes against women; (j) Prevalence of MPI; (k) LISA cluster map of MPI; (l) LISA significance for MPI.
Figure 3. Spatial distribution and local spatial autocorrelation of selected factors across 707 districts in India. (a) District level childhood stunting prevalence; (b) LISA cluster map of childhood stunting; (c) LISA significance for childhood stunting; (d) Prevalence of drought severity; (e) LISA cluster map of drought severity; (f) LISA significance for drought severity; (g) Prevalence of crimes against women; (h) LISA cluster map of crimes against women; (i) LISA significance for crimes against women; (j) Prevalence of MPI; (k) LISA cluster map of MPI; (l) LISA significance for MPI.
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Figure 4. Top 15 spatially lagged variables selected using LASSO regression.
Figure 4. Top 15 spatially lagged variables selected using LASSO regression.
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Figure 5. (a) Feature importance from the Random Forest model. (b) Feature importance from the XGBoost model.
Figure 5. (a) Feature importance from the Random Forest model. (b) Feature importance from the XGBoost model.
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Figure 6. SHAP waterfall plot illustrating feature contributions to model prediction.
Figure 6. SHAP waterfall plot illustrating feature contributions to model prediction.
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Table 1. Descriptive statistics and univariate spatial autocorrelation of district-level variables.
Table 1. Descriptive statistics and univariate spatial autocorrelation of district-level variables.
Variables (%)Mean ± SDRange
(Min–Max)		Univariate Moran’s I
Response Variable
Children under 5 years who are stunted (Stunting)33.5 ± 8.4513.2–60.60.525
Predictors
Population living in households with electricity (electric)97 ± 4.3368.3–1000.291
Population living in households with an improved drinking water source (d-water)93.8 ± 8.5641.2–1000.484
Population living in households that use an improved sanitation facility (sanit)71.8 ± 14.329.2–99.80.653
Households using clean fuel for cooking (clean-fuel)54.2 ± 24.18.61–99.80.677
Households using iodized salt (iod-salt)95.1 ± 5.5147.9–1000.391
Women (15–49) with 10 or more years of schooling (w-school)40.4 ± 14.213.6–88.20.691
Births in the 5 years preceding the survey that are third or higher order (high-birth)2.06 ± 1.600–7.980.574
Women age 15–19 years who were already mothers or pregnant at the time of the survey (teen-mothers)6.13 ± 4.980–27.30.658
Mothers who had at least 4 antenatal care visits (4anc-visits)60.6 ± 20.34.36–98.70.681
Mothers who consumed iron folic acid for 180 days or more when they were pregnant (ifa-180)27.4 ± 17.90.78–84.60.716
Children who received postnatal care from a doctor/nurse/LHV/ANM/midwife/other health personnel within 2 days of delivery (c-pnc)79.2 ± 14.722.4–99.60.709
Children age 9–35 months who received a vitamin A dose in the last 6 months (vitA-dose)72.5 ± 13.327.5–98.10.529
Prevalence of diarrhoea in the 2 weeks preceding the survey (diarrhoea)6.48 ± 4.100–39.30.415
Children Prevalence of symptoms of acute respiratory infection (ARI) in the 2 weeks preceding the survey (ari)2.55 ± 2.060–11.20.281
Children under age 3 years breastfed within one hour of birth15 (bf-1hr)44.7 ± 16.37.77–88.50.557
Breastfeeding children aged 6–23 months receiving an adequate diet16, 17 (adeq-diet)11.8 ± 7.670–54.10.397
Women (age 15–49 years) whose Body Mass Index (BMI) is below normal (BMI < 18.5 kg/m2) (low-bmi)17.9 ± 7.441.17–43.60.729
Children age 6–59 months who are anaemic (c-anaemia)65.8 ± 12.128–95.50.525
All women age 15–49 years who are anaemic (w-anaemia)56.0 ± 11.914.9–93.50.622
Drought0.445 ± 1.25−2.84–3.430.843
Crime0.958 ± 0.680.02–6.090.459
MPI0.066 ± 0.0690–1.120.481
Table 2. Results from spatial econometric models of childhood stunting.
Table 2. Results from spatial econometric models of childhood stunting.
VariablesSDEM (β, SE)SDM (β, SE)SAR (β, SE)
Negative Association
iod-salt−0.13 (0.09) *−0.12 (0.10) *−0.14 (0.06) *
c-pnc−0.05 (0.06) *−0.05 (0.07) *−0.08 (0.04) *
Electric−0.15 (0.13)−0.14 (0.14)−0.19 (0.09) *
w-anemia−0.12 (0.05)−0.13 (0.06)−0.06 (0.04)
Sanit−0.04 (0.05)−0.05 (0.05)−0.02 (0.03)
Clean-fuel−0.02 (0.03)−0.02 (0.03)−0.002 (0.02)
w-school−0.05 (0.05)−0.06 (0.06)−0.01 (0.04)
Ifa-180−0.004 (0.04)−0.002 (0.04)−0.009 (0.03)
Diarrhea−0.12 (0.14)−0.13 (0.16)−0.12 (0.09)
Drought (Moderate Drought)−0.55 (2.56)−0.69 (3.12)−0.28 (1.52)
Drought (Severe Drought)−1.24 (3.44)−1.37 (4.05)−1.20 (2.03)
Crime−0.33 (0.65)−0.36 (0.77)−0.42 (0.533)
vitA-dose−0.003 (0.04)−0.01 (0.05)0.02 (0.03)
bf-1hr−0.007 (0.03)−0.008 (0.04)0.003 (0.03)
Drought (Abnormal Drought)−0.45 (2.58)−0.78 (3.17)0.08 (1.36)
Positive Association
MPI11.96 (13.77) *10.95 (17.11) *12.26 (7.29) *
low-bmi0.26 (0.09) *0.24 (0.11) *0.26 (0.06) *
c-anemia0.13 (0.06) *0.13 (0.07) *0.11 (0.04) *
high-birth0.90 (0.42) *0.89 (0.45) *0.92 (0.27) *
4anc-visits0.05 (0.04)0.06 (0.05)0.05 (0.03)
d-water0.01 (0.06)0.01 (0.06)0.01 (0.04)
teen-mothers0.02 (0.11)0.0003 (0.12)0.08 (0.08)
Ari0.15 (0.27)0.17 (0.33)0.13 (0.18)
adeq-diet0.05 (0.08)0.05 (0.09)0.05 (0.05)
Drought (Exceptional Drought)2.80 (2.19)3.11 (2.55)0.94 (1.80)
Drought (Extreme Drought)2.20 (3.30)2.21 (4.06)2.32 (2.13)
Lambda value (Lag coefficient)0.3105--
Rho value (Lag coefficient)-0.31320.3480
AIC 434843444300
R20.62420.62680.6050
* Indicates significance at 5% level of confidence. The values in the table are given as a coefficient (standard error).
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Rao, B.; Hasan, M.G.; Putturaya, B.; Kamath, A.; Aatif, M.; Elmosaad, Y.M. Multidimensional Correlates of Childhood Stunting in India: A Spatial Machine Learning and Explainable AI Approach. Stats 2026, 9, 34. https://doi.org/10.3390/stats9020034

AMA Style

Rao B, Hasan MG, Putturaya B, Kamath A, Aatif M, Elmosaad YM. Multidimensional Correlates of Childhood Stunting in India: A Spatial Machine Learning and Explainable AI Approach. Stats. 2026; 9(2):34. https://doi.org/10.3390/stats9020034

Chicago/Turabian Style

Rao, Bhagyajyothi, Md Gulzarull Hasan, Bandhavya Putturaya, Asha Kamath, Mohammad Aatif, and Yousif M. Elmosaad. 2026. "Multidimensional Correlates of Childhood Stunting in India: A Spatial Machine Learning and Explainable AI Approach" Stats 9, no. 2: 34. https://doi.org/10.3390/stats9020034

APA Style

Rao, B., Hasan, M. G., Putturaya, B., Kamath, A., Aatif, M., & Elmosaad, Y. M. (2026). Multidimensional Correlates of Childhood Stunting in India: A Spatial Machine Learning and Explainable AI Approach. Stats, 9(2), 34. https://doi.org/10.3390/stats9020034

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