1 Introduction

Childhood stunting, characterized by low height-for-age, is more than a health issue-it is a developmental crisis that deprives children of normal interaction with peers, often leading to bullying and a significant loss of self-confidence. These early disadvantages can extend into adulthood, manifesting as considerable economic and human capital losses (Black et al. 2008; Akseer et al. 2022). As illustrated by Victora et al. (2008), malnutrition is linked to shorter adult height, reduced economic productivity, and-for women-a lower offspring birth weight, particularly in low- and middle-income countries. Given these profound impacts, policy intervention to prevent stunting is not just beneficial but imperative. This necessity underpins the need for reliable methods to monitor stunting trends, enabling consistent policy actions and evaluations.

Over the past two decades, Bangladesh has shown notable progress in tackling child malnutrition, as recent data from the Multiple Indicator Cluster Survey (MICS) by UNICEF highlights. The national stunting rate declined from 60% in 1997 to 28% in 2019 (NIPORT and ICF 2020; BBS and UNICEF 2019). This improvement aligns with the Sustainable Development Goals (SDGs), specifically target 2.2, which aims to reduce child malnutrition. The goal was to further reduce the stunting rate to 25% by the end of 2022 (MOHFW 2019). However, the onset of the COVID-19 pandemic has posed significant challenges, disrupting essential healthcare services and nutrition programs that are crucial for sustaining this progress. Despite these efforts, approximately one-third of children under five in Bangladesh still suffer from chronic malnutrition (NIPORT and ICF 2020), highlighting the ongoing urgency of this issue. According to the World Health Organization’s growth standards, stunting is when a child’s height-for-age is more than two standard deviations below the median (De Onis et al. 2019). The persistent high rate of stunting underscores the need for continued innovative and effective policy measures to combat this pressing public health issue.

Although Bangladesh has made significant progress in reducing child malnutrition, aggregate data often mask the stark regional disparities in stunting rates among children. From 1997 to 2018, while stunting rates decreased to about 25% in the socio-economically more affluent Dhaka and Khulna divisions (NIPORT and ICF 2020), they remained alarmingly high at 36% and 43% respectively in the less affluent Mymensingh and Sylhet divisions. These persistent inequalities, evident down to the district and sub-district levels (Haslett and Jones 2004; Haslett et al. 2014), underscore the need for a more granular analysis to understand and address the uneven distribution of child malnutrition. This study, therefore, aims to examine the trends in chronic malnutrition (stunting) among children under five years old in Bangladesh from 2000 to 2018, covering all 64 districts and 544 sub-districts. The central question our research addresses is: How do socio-economic and environmental factors influence the regional disparities in stunting rates across Bangladesh?

To address this question, we employ a multifaceted empirical approach, utilizing small area estimation techniques alongside remote-sensed data such as nighttime light intensity and vegetation indices to analyze stunting patterns. Our primary methodology is Bayesian multilevel time-series models, which integrate cross-sectional, temporal, and spatial data to estimate stunting rates for years not directly surveyed. This approach not only combines data from the intermittent Bangladesh Demographic and Health Surveys spanning 2000 to 2018 but also enhances it with continuous remote sensing data-ideal in settings where traditional data collection is sporadic and potentially biased. By incorporating these diverse data sources into a Bayesian framework and aggregating estimates from the sub-district level upwards, our methodology fills gaps between survey years and predicts trends at various administrative levels, aiding in the identification of targeted areas for policy intervention. Further details of our data and methods are provided in Section 2.

Our results can be briefly summarized as follows: We document a notable reduction in child stunting rates across Bangladesh, from approximately 50% in 2000 to just above 30% by 2018. Remarkably, the western divisions of Khulna, Rajshahi, and Rangpur demonstrated steady decreases in stunting post-2004, exhibiting stark differences compared to the more fluctuating trends observed in other regions. In particular, the northeastern Sylhet division continued to report persistently high stunting rates. On the other hand, only Dhaka and Khulna, in the central and southwestern regions respectively, succeeded in reducing stunting to below 25% by 2018.

Further results from a detailed district-level analysis reveal a clear positive correlation between increased nighttime light intensity–a proxy for socioeconomic development–and reductions in stunting rates, particularly in urbanized areas. Conversely, districts characterized by higher Normalized Difference Vegetation Index (NDVI) values, representative of the northeastern wetlands, consistently exhibited high stunting rates. The southwestern coastal districts such as Khulna, Bagerhat, and Satkhira also saw significant declines in stunting, despite environmental challenges reflected by lower nighttime light and volatile NDVI levels. However, at the sub-district level, although areas with higher nighttime light intensity generally reported lower stunting rates, the Khulna district was an exception where climate and access to natural resources played significant roles. This analysis highlights how a mix of geographic, economic, and environmental factors together influence nutritional outcomes among children.

We contribute to the broader literature on child malnutrition in a number of ways. First, our study introduces a robust spatio-temporal model designed specifically for Bangladesh’s third administrative level (i.e., subdistricts)—an area typically overlooked by conventional surveys. This spatio-temporal model effectively estimates stunting prevalence during non-survey periods by utilizing the relationship between remotely sensed data and stunting outcomes, accounting for inherent spatial and temporal dynamics. Additionally, our approach offers a comprehensive and consistent analysis of stunting across small areas. This understanding enables us to deliver actionable recommendations for policy development and monitoring. For instance, our findings underscore the significant impact of urbanization on reducing stunting, thus supporting public policy initiatives that promote urban development. Furthermore, the use of remote-sensed data, such as nighttime light intensity, adds reliability and verifiability to our data. This is particularly advantageous in developing economies where regular data collection is hindered by cost, time constraints, and susceptibility to bias. Our methodological framework not only fills critical gaps in the literature but also improves our capacity to monitor and address malnutrition effectively.

The rest of the paper is organized as follows: Section 2 describes the data and the econometric methods underpinning the empirical analysis. Section 3 develops a sub-district level time-series model for stunting using remote-sensed data and estimates stunting at higher administrative levels through aggregation. Section 4 presents the main empirical results, including a discussion of the findings. Section 5 concludes the paper. Additional materials supporting the main findings of this study are provided in an online supplement.

2 Materials and methods

2.1 Data sources

This study planned to utilize the seven rounds of the Bangladesh Demographic and Health Surveys (BDHS) conducted in 1996-97, 1999-2000, 2004, 2007, 2011, 2014, and 2017-18, where child anthropometric data were collected. However, the district and sub-district locations of the primary sampling units are not accessible in the 1996-97 survey, and so the data from the remaining six surveys are used in this study to develop multilevel time-series models at both district and sub-district levels. For consistency, child anthropometric indices have been calculated based on the World Health Organization (WHO) Child Growth Standards (World Health Organization 2006) for all the surveys using the R package anthro (Schumacher et al. 2020).

In BDHS surveys, a two-stage stratified cluster sampling design is implemented, where clusters (primary sampling units in the survey and enumeration areas in the population census) are selected with a probability proportional to cluster size (number of households) from each of the strata in the first stage. Subsequently, households are selected from each cluster through systematic sampling in the second stage. The number of strata is usually defined according to the number of divisions at the survey time point along with their urban-rural characterization. Since the number of divisions has increased several times over the last 30 years, the number of strata, clusters, and households has consequently increased over the surveys. In the BDHS 2017-18, the number of divisions was eight, while it was seven in surveys conducted during 2004-16, and it was six in the earlier surveys. Details of the survey design are available in the respective survey reports NIPORT et al. (2001; 2005; 2009; 2016; 2013); NIPORT and ICF (2020). The number of sub-districts has also changed to reflect this over the time period. For consistency with the current administrative hierarchy in this study, we consider eight divisions, 64 districts (which remain the same), and 544 sub-districts for modelling over the entire 2000-2018 period and present the results accordingly. The three Housing Censuses of Bangladesh were conducted during the study period: in 1991, 2001, and 2011. In each of these surveys, the list of enumeration areas from the census available at the survey time point was used as a sampling frame of the primary sampling units for constructing the survey sampling design. Representative samples from these census data (10% of the 1991 Census, 10% of the 2001 Census, and 5% of the 2011 Census), which are publicly available from IPUMS-International (IPUMS 2020), are utilized to estimate the number of under-5 children (weighted) for districts and sub-districts. The number of domain-specific children is primarily used for aggregation purposes to estimate national, division, and district level trends to ensure numerical consistency from the top to the bottom of the administrative hierarchies.

2.2 Outcome variable

The target parameter of this study is the proportion of under-5 children who are stunted (short for their age) defined by those whose height-for-age Z-scores are less than -2.00 standard deviations. The proportions of stunted children at the sub-district level are calculated using the survey sampling weight, while the corresponding standard errors are estimated using both sampling weight and sampling design. However, the inclusion of survey design at the sub-district level results in zero standard errors for a substantial number of sub-districts, so only the sampling weights are used in estimating standard errors.

Since survey-weighted proportions tend to zeros and ones due to small sample sizes and the binary nature of the underlying response variable (either stunted or not stunted), developing a Fay-Herriot model (Fay and Herriot 1979) assuming the proportions follow a continuous (normal) distribution may be problematic when domain-specific sample sizes are very small and hence the sampling errors are too noisy. In addition, such a linear model-based approach can lead to negative predictions, and prediction intervals may include negative values. In such situations, generalized linear mixed models (GLMMs) are more suitable for modelling inherently discrete data arising from survey-weighted direct estimates (Malec et al. 1997; Ghosh et al. 1998; Rao and Molina 2015). Most of the considered surveys in this study covered all the districts, but the proportion of covered sub-districts per survey varies from 30 to 50%. Therefore, the direct estimates of stunting and the number of sampled children at the sub-district level are substantially sparse compared to those at the district level. This is a classic situation when small area estimation is required for reasonably consistent estimates of target parameters.

As the number of sub-district specific sample size is very small and a considerable number of domains are not sampled in the surveys, the number of stunted children is considered as the outcome variable for developing multilevel time-series models. We assume the outcome variable follows a binomial distribution with the mean as the true prevalence of stunting and the number of sampled children in a particular sub-district as the number of trials. Sub-district-specific counts of sampled children and the number of stunted children are calculated using the sampling weight to account for the survey design in developing the model (Chandra et al. 2019). Distributions of the number of sampled children and stunted children along with the stunting prevalence are shown in the Supplementary file with and without consideration of sampling weights.

2.3 Remote-sensed data

Satellite-detected nighttime light data have become a crucial tool for researchers measuring localized economic activity in regions lacking reliable traditional economic indicators like GDP or GNP. A foundational study by Sutton and Costanza (2002) revealed a strong correlation between the intensity of emitted light (per square km) and a nation’s GDP, marking the beginning of nighttime light data’s application across various fields. Subsequent research has expanded its use to explore health inequalities (Ebener et al. 2005), ethnic diversity (Alesina et al. 2016), well-being (Ghosh et al. 2013), natural disaster responses (Fabian et al. 2019), and the impacts of the COVID-19 pandemic (Elvidge et al. 2020).

Nighttime light intensity data serve as a dependable proxy for economic activity (Henderson et al. 2012), development, urbanization, and income disparities (Weidmann and Theunissen 2021), offering a consistent and repeatable method for data aggregation across different spatial and temporal scales (Levin and Duke 2012). One of the primary benefits of using nighttime light data is its free availability, automatic daily collection, and the ease with which aggregated values can be calculated, making it particularly useful for subnational analysis where economic data often lacks consistency (Chen and Nordhaus 2011; Elvidge et al. 2012; Basher et al. 2022).

Recently, the application of nighttime light data has extended beyond economic and urbanization analyses to include predicting child health outcomes, a novel area of research. Studies by Amare et al. (2020) and Ameye and De Weerdt (2020) have shown that nighttime light intensity can predict child nutrition outcomes in East Africa, suggesting a positive correlation between urbanization and child nutrition.

The correlation between urbanization, evidenced by nighttime light data, and child nutrition outcomes highlights the need for a broader set of environmental indicators. Accordingly, we incorporate measures such as the Normalized Difference Vegetation Index (NDVI), Land Surface Temperature (LST), aridity (calculated as average monthly precipitation divided by average monthly potential evapotranspiration), and rainfall. These indicators have been used to predict child malnutrition at country, regional, and grid cell levels (Du et al. 2013; Brown et al. 2014; Osgood-Zimmerman et al. 2018; Shaw et al. 2020; Seiler et al. 2021). Previous studies have explored the use of remotely sensed and modeled data to investigate their connections with human health and nutrition (Brown et al. 2014; Seiler et al. 2021). Johnson et al. (2013) utilized the Vegetation Continuous Fields (VCF) product (Hansen et al. 2003) to demonstrate the positive impact of forest cover on child health and nutrition in Malawi. Shaw et al. (2020) presented evidence linking child malnutrition to drought conditions by analyzing the negative spatial autocorrelation of these conditions with malnutrition in children under five across various districts in India. Chen et al. (2020) and Abiona and Ajefu (2023) explored the impact of temperature and drought respectively on birth outcomes. Groppo and Kraehnert (2017) used NDVI to study the impacts of extreme weather events on education. Helbling and Meierrieks (2023) used precipitation, cloud cover, ground frost frequency and potential evapotranspiration to study rural-to-urban migration on a global scale.

2.3.1 Nighttime light data

The nighttime light (NTL) data for the years 2000 to 2013 were derived from the Defense Meteorological Program (DMSP) Operational Line-Scan System (OLS), which detects visible and near infra-red light emission at night (Image and data processing by NOAA’s National Geophysical Data Center). The DMSP data are expressed as digital numbers in the range 0 to 63 and are available at a resolution of 1 km. Details of the construction of the DMSP NTL data used in this study are available in Basher et al. (2022). NTL data from 2014 to 2018 were derived from the Day/Night Band of the Visible Infrared Imaging Radiometer Suite (VIIRS) monthly composites, which has a spatial resolution of approximately 500m and values are expressed as average radiance in units of nanoWatts/cm2/sr. Google Earth Engine (GEE) was used to extract the data by importing the Bangladesh district level shape file and computing the mean monthly values for each district, and these were subsequently aggregated to mean annual values (Gorelick et al. 2017).

2.3.2 Environmental data

In addition to the NTL data, we derived sub-district and district-level satellite-derived Normalized Difference Vegetation Index (NDVI), Land Surface Temperature (LST), and precipitation data. Similar to the NTL data, all data were extracted from GEE at the sub-district and district levels. For NDVI, we used the MODIS (or Moderate Resolution Imaging Spectroradiometer) Terra 16-Day, 1km NDVI product (MOD13A2.061) with values scaled to the range -1 to 1. LST (degrees Kelvin) was derived from the MODIS Terra Land Surface Temperature 8-Day, 1 km product (MOD11A2.061), and precipitation (in millimetres) from the Climate Hazards Group InfraRed Precipitation with Station Data (CHIRPS) Daily product. We trialled using these three datasets to develop indices of annual drought and flood conditions at the sub-district and district levels, i.e., Vegetation Condition Index (VCI), Temperature Condition Index (TCI), and Precipitation Condition Index (PCI). We followed the index definitions and source data in Du et al. (2013), with the exception of precipitation data, where we used an alternative data source to the authors. For PCI, we selected CHIRPS as an alternative to the Tropical Rainfall Measuring Mission (TRMM) dataset used in Du et al. (2013). Although TRMM has been shown to perform well over Bangladesh (Prodhan et al. 2020), CHIRPS is a higher-resolution product (daily, 0.05-degree resolution) and is routinely used as a spatial covariate in conjunction with DHS data (Mayala and Donohue 2022). Mean monthly sub-district and district-level data for all three indices were extracted using GEE, similar to the NTL data, and subsequently aggregated to annual data. Following Du et al. (2013), we also combine these three-dimensional climatic variables into one index through Principal Component Analysis, referred to as the Synthesized Drought Index (SDI), which is then utilized in the multilevel model.

Certainly, integrating remote-sensing data with traditional health indicators, such as the number of hospitals, maternal mortality, and child mortality, would enhance the prediction of children’s nutrition outcomes. However, the unavailability of these traditional health indicators at a sub-national level remains a significant challenge and will, therefore, be addressed in future research as they become available.

2.4 Small area estimation in measuring child malnutrition

In order to align with the SDGs and eliminate all types of malnutrition, it is essential to attain comparable decreases in malnutrition rates at more granular, disaggregated levels. However, acquiring precise data for these areas is challenging, as nationally representative surveys often lack the necessary detail in their design. In this regard, the Small Area Estimation (SAE) method, proposed by Rao and Molina (2015) and widely applied in various fields including poverty (Elbers et al. 2003; Molina and Rao 2010; Tzavidis et al. 2008), unemployment (Chambers et al. 2016), food security (Haslett et al. 2014; Hossain et al. 2020), and child malnutrition (Haslett and Jones 2004; Haslett et al. 2014, 2013), offers a solution.

The main idea behind SAE is to estimate trends for small domains (areas or groups) by leveraging information across space and time, especially when annual survey data are available (Rao and Yu 1994; Datta et al. 1999; You et al. 2003; You 2008; Pfeffermann and Burck 1990; Pfeffermann and Tiller 2006; Marhuenda et al. 2013; Boonstra and van den Brakel 2019). This approach is particularly relevant when direct estimates from surveys are not reliable due to small sample sizes or when data for specific areas or demographic groups are unavailable. It enables analysts to draw strength from existing data over time, producing more accurate estimates for small areas.

Two earlier studies that utilized the World Bank’s SAE method to assess child malnutrition levels in Bangladesh analyzed unit-level data from household surveys and censuses conducted simultaneously (Elbers et al. 2003; Haslett and Jones 2004; Haslett et al. 2014). However, aligning the timing of household surveys, conducted approximately every four to five years, with the census, which has been conducted every ten years since 1981, presents challenges for unit-level SAE applications. Moreover, since survey data are representative only at national and sub-national levels, deriving statistics for more granular levels from this data is not feasible.

In the context of Bangladesh, where household surveys are not conducted annually, standard time-series analysis for estimating population-based health indicators, such as child malnutrition, cannot be performed. To bridge this gap, this study applies a multilevel time-series modeling extension of small area estimation to provide a nuanced understanding of stunting trends across different regions. In so doing, this analysis utilizes six rounds of Demographic and Health Survey data and three Bangladesh Population and Housing Censuses conducted during 1997-2018. The multilevel time-series models in question leverage strength by accounting for cross-sectional, temporal, and spatial correlations (Boonstra and van den Brakel 2022, 2019; Boonstra et al. 2021). In the next subsection, we provide methodological details of multilevel time-series modelling.

2.5 Multilevel time-series modelling

Multilevel time-series (MTS) models are defined at the detailed level of 544 sub-districts for the period 2000-2018. Since the BDSH surveys are periodic with 3-4 years gap, the model is formed at annual frequency to account for the varying time-lags between the subsequent survey years. As a consequence, there are 10,336 sub-district level domains over this 19-year period. However, we have only 2008 sub-districts for which we observe under-5-year-old children in the survey data. In the model, survey years are referred to as 2000, 2004, 2007, 2011, 2014, and 2018, and the remaining (non-survey) years are considered as missing to correctly specify period-to-period change in the trend. This method helps to predict the target parameters for the non-survey years’ domains based on the developed MTS models. We calculated the stunting prevalence as well as the number of stunted children (weighted) for the observed domains from the micro-data as the direct estimates of the target parameter and the outcome variables for developing the MTS model, respectively.

To define the MTS model for the count outcome values, let \(\hat{{y}}_{dt}\) denote the number of stunted children for domain d and year t. The index d runs over 1 to \(M_d = 544\) for sub-district level model, and t over 1 to \(T = 19\) years. Direct estimates \(\hat{y}_{dt}\) are combined in a large vector of dimension \(M = M_d{T}\) as \(\hat{\varvec{y}} = (\hat{y}_{11}, \ldots \hat{y}_{M_{d 1}}, \dots \hat{y}_{1 T}, \dots \hat{y}_{M_{d T}})'\) to define a hierarchical Bayesian MTS model for \(\hat{\varvec{y}}\) as general linear additive form following Boonstra et al. (2021)

$$\begin{aligned} \hat{\varvec{y}} \sim f(\varvec{\mu },\varvec{\phi }) \quad ; \quad g(\varvec{\mu }) = \varvec{\eta } = \varvec{X}\varvec{\beta } + \sum _\alpha \varvec{Z}^{(\alpha )} \varvec{v}^{(\alpha )}\,, \end{aligned}$$
(1)

where f(.) is a probability distribution depending on the vector of \(\hat{\varvec{y}}\) with an optional scale or dispersion parameter \(\phi \) and g(.) is a link function that links the mean vector to the linear predictor \(\varvec{\eta }\), \(\varvec{X}\) is a \(M\times p\) design matrix for a p-vector of fixed effects \(\varvec{\beta }\), and the \(\varvec{Z}^{(\alpha )}\) are \(M \times q^{(\alpha )}\) design matrices for \(q^{(\alpha )}\)-dimensional random effect vectors \(\varvec{v}^{ (\alpha )}\). We assume f(.) is a binomial distribution with mean vector \(\varvec{\mu }\) and logistic link function as \(g(\varvec{\mu })=\log \frac{\varvec{\mu }}{(1-\varvec{\mu })}\). A Gaussian distribution with identity link function can be considered if stunting level is modeled as proportion. The summation term indicates the possibility of adding several random effects terms at different levels (e.g., temporal, spatial and non-spatial random effects at district and sub-district levels). More detail on these random effects terms can be found in Boonstra et al. (2021); Das et al. (2022).

The linear predictor \(\varvec{\eta }\) has one part for fixed effects and another part for random effects. The vector of fixed effects parameters (\(\varvec{\beta }\)) is assigned a very weakly informative normal prior \(p(\varvec{\beta }) = \mathcal{N}(0, 100 I)\). The vectors of random effects \(\varvec{v}^{(\alpha )}\) for different \(\alpha \) are assumed to be independent, but the components within a particular vector \(\varvec{v}^{(\alpha )}\) can be assumed correlated to accommodate temporal, spatio-temporal, or cross-sectional correlation.

To detail more on the random effects, we suppress the superscript \(\alpha \) for notational convenience. We assume that each random effects vector is distributed as \(\varvec{v} \sim \mathcal{N}(0, A \otimes V)\), where V and A are respectively \(d \times d\) and \(l \times l\) covariance matrices, and the Kronecker product of A with V (\(A \otimes V\)) which indicates the total length of v is \(q = d l\). To illustrate, assuming division level effects (\(d=8\)) varying over time (\(l=19\)) consists of \(q = 8 \times 19 = 152\) random effects. The covariance matrix A describes the covariance structure among the levels of the factor variable, and is assumed to be known. Instead of covariance matrices, precision matrices \(Q_A = A^{-1}\) are actually used, because of computational efficiency (Rue and Held 2005).

The covariance matrix V for the d varying effects can be parameterized in three different forms: (i) an unstructured, i.e. fully parameterized covariance matrix, (ii) a diagonal matrix with unequal diagonal elements, and (iii) a diagonal matrix with equal diagonal elements.

Models of the form Eq. 1 have been fitted to the data using Markov Chain Monte Carlo (MCMC) sampling, specifically the Gibbs sampler (Geman and Geman 1984; Gelfand and Smith 1990). The models were developed using the R package mcmcsae (Boonstra 2021), following the procedures detailed in Boonstra and van den Brakel (2022), Boonstra et al. (2021), and Das et al. (2022). For the comparison of models using the same input data, the Widely Applicable Information Criterion, or Watanabe-Akaike information criterion (WAIC) (Watanabe 2010, 2013), the deviance information criterion (DIC) (Spiegelhalter et al. 2002), leave-one-out (LOO) information criteria (LOOIC), and expected log predictive density (ELPD) are calculated for model comparison, following Vehtari et al. (2017) and using the R package LOO (Vehtari et al. 2022). In addition to the information criteria, competitive MTS models are compared in terms of graphical comparison of trend predictions at various aggregation levels to select the best model. Finally, these MTS models are developed using 1000 burn-in and 5000 iterations, of which the draws of every fifth iteration are stored. Consequently, \(3\times 1000 = 3000\) draws are used to compute estimates and standard errors. Longer simulations of the selected model provide a Gelman-Rubin potential scale reduction factor (Gelman and Rubin 1992) below 1.05 and sufficient effective numbers of independent draws for all model parameters and model predictions for valid inference.

3 Model development and assessment

The main objective of this study is to develop a suitable area-level time-series model of stunting at the sub-district level using remote-sensed data, and then estimate the stunting level at higher administrative levels– district, division, and country– through aggregation. The aggregated model-based estimates, particularly at the national and division levels, are compared with the survey-weighted direct estimates to examine how the model developed at the sub-district level provides numerically consistent estimates at both detailed and higher aggregation levels. In the following subsections, we discuss model development, model assessment, and finally model selection for estimating the trend of stunting at all four administrative levels, denoted as admin-0 (country), admin-1 (division), admin-2 (district), and admin-3 (sub-district).

The model development and selection in this context involves several steps aimed at identifying the most appropriate model which describes the data. Furthermore, in small area modelling, we need to ensure that the derived estimates are consistent at hierarchical levels of geography (i.e., the sub-districts, districts, division, and country level estimates of stunting), as this underpins the reliability and validity of the model-based statistical inference (Boonstra et al. 2021). In the next sections, we describe in detail the steps involved in model building, assessment, and performance of the final model. However, this can be summarised as follows: (1) Specify the optimal number of fixed effects required; (2) Reduce the risk of overfitting the model by specifying the remaining parameters as random effects; (3) Identify the appropriate type of random effects (e.g., structured with spatial terms which capture the association between neighbouring areas, or unstructured to account for unobserved heterogeneity) at the appropriate level (sub-district, district, or division); (4) Extend the model by incorporating remote-sensed data (e.g., nighttime light intensity to capture socio-economic differences and environmental variables, such as vegetation cover and aridity to explore the impact of factors affecting agricultural productivity and food availability); (5) Compare the direct and model-based estimates and trend predictions at different levels of geography, to ensure that the final model selected provides consistent and reliable results. We follow Bayesian model fitting and selection criteria due to the ability of this approach to incorporate model uncertainty and its flexibility in dealing with missing data (Vehtari et al. 2017; Gabry et al. 2019).

3.1 Model development

The model of the form Eq. 1 has two basic types of components: fixed effects and random effects. As fixed effect components, we used the Division factor variable with eight levels (Barisal, Chittagong, Dhaka, Khulna, Mymensingh, Rajshahi, Rangpur, and Sylhet), the standardized version of the year variable denoted as year.std to account for a linear time trend, and the remote-sensed variables– nighttime light intensity (NTL), mean NDVI (NDVI), mean LST (LST), and total annual precipitation (Precipitation)– at both the district and sub-district levels. As for random effects components, we considered domain-specific unstructured (non-spatial), structured (spatial), and temporal random effects to account respectively for unobserved heterogeneity, spatial correlation, and temporal correlation at different administrative units (division, district, and sub-district). The unstructured random effects are essentially random intercepts at a particular level, say sub-district (denoted as \(RI\_SUBDIST\)). Spatial random effects at the sub-district level are assumed to follow an intrinsic conditional auto-regressive (ICAR) model (Besag and Kooperberg 1995). Spatial components are considered only at the sub-district level to avoid over-smoothing at the higher aggregation levels. To harness temporal strength, we model the underlying time-series structure through a random walk (RW) which imposes a certain level of smoothness in the data over time. The random walk model of order 1 (RW1) assumes that the current value depends on its immediate past value, while the random walk model of order 2 (RW2) assumes the current value depends on its two immediate past values. The local level trends at a particular administrative unit are accounted for by the RW1 and smooth trends by the RW2. We examined both types of trends at division, district, and sub-district levels in the model development stage.

At first, an MTS model was fitted by incorporating (i) division and year.s as fixed effects components; (ii) either sub-district level unstructured random effects denoted as \(RI\_SUBDIST\) or structured random effects denoted as \(SP\_SUBDIST\); (iii) local level trend components at the division and district levels, denoted as \(RW1\_DIV\) and \(RW1\_DIST\) respectively. As both \(RI\_SUBDIST\) and \(SP\_SUBDIST\) components cannot be included simultaneously due to model complexity (as the model is not possible to fit), we initially developed models using only the unstructured random effects. The incorporation of the linear time trend component year.s provided biased estimates in the survey years 2004 and 2011, thus another model was fitted without the linear time-trend component. In fact, the linear trend term can not capture the slow improvement at the two time points. This is depicted in Fig. 1. These two models are denoted as MTS-1 and MTS-2 respectively. It is worth noting that the MTS model with a linear time trend provides better accuracy (indicated by the narrower confidence band) even in the non-survey years compared to the MTS model without a linear time-trend component. The difference between these two types of models becomes less significant at the detailed level compared to the aggregated level. However, the detailed (district and sub-district) level model-based estimates are not comparable with the corresponding direct estimates - which are noisy and inconsistent due to based on very small sample size (even none). So model-based estimates are aggregated at the higher administrative levels (such as country and division) and then compare with the direct estimates - which are design unbiased and consistent. In addition, for the sake of numerical consistency from the sub-district to the national level, we chose the model without a linear time trend component. Figures in the Supplementary Files confirm this comparison.

The smooth trend at the sub-district level was examined to incorporate temporal strength at the detailed level. Incorporating such a smoothed trend improves model prediction in terms of information criteria, but the model fails to benchmark the estimates at the district level, where better time-series observations are available. Since direct estimates of stunting prevalence are not available for many sub-districts over time, we place more importance on the district-level trend and spatial location of the sub-districts in the model development. The random effects components used in these models are shown in Table 1.

Fig. 1
figure 1

National level trends in stunting among under-5 children in Bangladesh during 2000-2018 estimated by DIR estimator (black error-bar line), MTS-1 (blue line), MTS-2 (green line), and MTS-3 (red line) model-based estimators with 95% credible interval

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Table 1 Summary of the random effect components for the selected multilevel time-series model for stunting at the sub-district levels
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Table 2 Fitted multilevel time-series models– MTS-1: with linear time trend (year.sd); MTS-2: without linear time trend and MTS-3: MTS-2 with NTL and NDVI
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Table 3 Mean and t values for the regression coefficients and the variance parameters for the fitted multilevel time-series models MTS-1, MTS-2 and MTS-3 with structured and unstructured random effects at the detailed sub-district level separately
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Model MTS-2 was extended by including remote-sensed variables. To account for period-to-period change by space in the model development, we first examined the time-series of NTL data available at the district and sub-district levels. The time-series of NTL at the district level shows more consistency compared to that at the sub-district level, and so the district-level NTL variable has been included in the model as a fixed effect component. Incorporating the NTL variable slightly improved the model in terms of information criteria but substantially in terms of the accuracy of the estimates. The other remote-sensed variables were added separately to MTS-2 to examine their contributions. Since the annual trends of NDVI and LST by space do not change considerably over time, their contributions were found to be negligible at the sub-district level. However, the district-level NDVI values are negatively correlated (\(r=-0.16\), p-value \(< 0.01\)) and were also found to be significant in the MTS model. While NDVI and LST variables have less variability over time, the Precipitation variable fluctuates considerably over time at both district and sub-district levels. The trends of precipitation amount are found to have a positive relationship but they provide highly volatile trends over the whole period and so are not considered. Thus, the model with NTL and NDVI values at the district level has been considered as the final model, denoted as MTS-3.

All these three models were redeveloped by replacing the \(RI\_SUBDIST\) component with \(SP\_SUBDIST\). A comparison of the information criteria statistics shown in Table 2 indicates that the models with structured random effects at the sub-district level perform better than the models with unstructured random effects according to the WAIC2, LOOIC, and ELPD values, while DIC and WAIC1 values are comparatively smaller for the MTS-2 model. The estimated regression coefficients and variance parameters under the multilevel models are shown in Table 3, which shows that the NTL and NDVI variables have a significant contribution to the models and all the variance parameters are statistically significant.

From this point onward, we compare models that include sub-district level spatial random effects. In the next sub-section, we compare the performances of these three models to examine whether MTS-3 can be considered as the best model for estimating trends at the sub-district level.

The effect of including remotely-sensed variables at the sub-district scale in model development was tested, however, the size of sub-districts is insufficiently large compared to the spatial resolution of the remotely-sensed data. For example, some sub-districts within urban centers are \(< 1km^2\), while the spatial resolution of rainfall data is \(5 km^2\). Meanwhile, the minimum district area is \(> 700 km^2\) and was therefore deemed an appropriate scale for utilizing the remotely-sensed variables in model development.

3.2 Model assessment

In this study, models developed with the same input estimates are compared based on the values of several information criteria (WAIC1, WAIC2, DIC, LOOIC, and ELPD), as well as graphical comparisons of the trend predictions at various aggregation levels. The trend estimates of child stunting at higher aggregation levels are computed based on the MCMC simulation results at the detailed level. The simulation vectors of linear predictions based on the fitted model are formed as follows:

$$\begin{aligned} \eta ^{(r)} = X \beta ^{(r)} + \sum _\alpha Z^{(\alpha )} v^{(\alpha , r)}\,, \end{aligned}$$
(2)

where superscript (r) indexes the retained MCMC draws for the detailed level domains for all years. Therefore, each \(\eta ^{(r)}\) has a dimension of M. The means and standard deviations over the MCMC draws are used as trend estimates and standard error estimates, respectively, at the most detailed level. The trends at the most detailed level are then aggregated to obtain trends at the division, district, and country levels. Aggregations at higher levels are the weighted average of the estimated detailed level proportions, using the total number of under-five children for the target domains obtained from the three census datasets mentioned in Section 2.1.

Fig. 2
figure 2

Division level trends in stunting among under-5 children in Bangladesh during 2000-2018 estimated by DIR estimator (black error-bar line), MTS-1 (blue line), MTS-2 (green line), and MTS-3 (red line) model-based estimators with 95% credible interval

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Fig. 3
figure 3

District level trends in stunting among under-5 children in Bangladesh during 2000-2018 estimated by DIR estimator (black error-bar line), MTS-1 (blue line), MTS-2 (green line), and MTS-3 (red line) model-based estimators with 95% credible interval for the districts in north-eastern region having wetland areas

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Fig. 4
figure 4

District level trends in stunting among under-5 children in Bangladesh during 2000-2018 estimated by DIR estimator (black error-bar line), MTS-1 (blue line), MTS-2 (green line), and MTS-3 (red line) model-based estimators with 95% credible interval for the districts with higher NTL intensity over time

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Fig. 5
figure 5

District level trends in stunting among under-5 children in Bangladesh during 2000-2018 estimated by DIR estimator (black error-bar line), MTS-1 (blue line), MTS-2 (green line), and MTS-3 (red line) model-based estimators with 95% credible interval for the districts in south-western coastal region having lower NTL intensity

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In addition to the graphical comparison, three discrepancy measures are used as model diagnostics to evaluate and compare the MTS models. These are (i) relative bias (RB), (ii) absolute relative bias (ARB), and (iii) relative reduction of the standard errors (RRSE). For a particular MTS model, these three measures are defined as follows:

$$\begin{aligned} \begin{gathered} RB_{dt} = \frac{ (\hat{\theta }_{dt} - \hat{Y}_{dt})}{ \hat{Y}_{dt}} \times 100\%\,\\ ARB_{dt} = \frac{ |\hat{\theta }_{dt} - \hat{Y}_{dt}|}{ \hat{Y}_{dt}} \times 100\%\,\\ RRSE_{dt} = 100\% \times (se(\hat{Y}_{dt}) - se(\hat{\theta }_{dt})) / se(\hat{Y}_{dt})\, \end{gathered} \end{aligned}$$
(3)

where \(\hat{\theta }_{dt}\) and \(\hat{Y}_{dt}\) are the model-based and direct estimates respectively for domain d in year t. The RB and ARB indicate how much \(\hat{\theta }_{dt}\) deviates from \(\hat{Y}_{dt}\) relative to the latter, with and without taking direction into account respectively. These discrepancies are expected to be as small as possible since the average of the direct estimates is expected to equal the true average. The third measure, \(RRSE_{dt}\), quantifies the percentage reduction in the standard error of \(\hat{\theta }_{dt}\) compared to the standard error of \(\hat{Y}_{dt}\). Higher values of RRSE indicate that the MTS model provides more accuracy than the direct estimates. In addition, the coverage rate (CR) of the model-based estimators is also calculated by determining whether the direct estimates lie within the 95% credible interval of the model-based estimates, as detailed in Das et al. (2022).

Graphical comparison of trend prediction at the national level, as shown in Fig. 1, indicates that the model MTS-1 provides comparatively biased estimates in the initial time period of 2000-2007 compared to the models without a linear time trend (year.std in the fixed effects component). The model MTS-2, which lacks any remote-sensed variables, shows a trend very similar to that of the direct estimates, while the MTS-3 model provides a slightly different trend in the non-survey years, due to the influence of the remote-sensed variables NTL and NDVI.

Division-level trends of stunting estimated by the direct and model-based estimators are shown in Fig. 2. Time-series plots indicate that model MTS-2 demonstrates better performance in terms of unbiasedness, particularly for the Barisal, Mymensingh, and Sylhet divisions. On the other hand, the MTS-3 model aligns with the MTS-2 model in the survey years, but diverges from other models in the non-survey years. The differences between MTS-2 and MTS-3 are most pronounced in the Mymensingh and Sylhet divisions, where large wetland areas are usually submerged and may vary over time.

Table 4 Mean relative bias (MRB, %) and mean absolute relative bias (MARB, %) of MTS-1, MTS-2 and MTS-3 model-based estimators at administrative levels 0 (national), 1 (division), 2 (district) and 3 (sub-district) based on the structured (spatial) and unstructured random effects at sub-district level
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At the district level, the differences among the three models are more pronounced in the north-eastern region where child malnutrition has a significant negative correlation with the nighttime light intensity (Fig. 3). The values of NTL and NDVI also vary in this north-eastern region due to frequent flash floods during the monsoon period. On the other hand, the differences are not pronounced in districts with very high nighttime light intensity, such as Dhaka and Chittagong (as shown in Fig. 4), and are also minimal in the south-western coastal region (Fig. 5). This coastal region has experienced rapid changes in its social-ecological systems over the last few decades due to environmental and climate change (Dearing and Hossain 2018).

Table 4 displays the mean relative bias (MRB) and mean absolute relative bias (MARB) for the model-based estimators at the first four administrative levels– nation (admin-0), division (admin-1), district (admin-2), and sub-district (admin-3). The MRB and MARB statistics for the models developed at the sub-district level show that models MTS-2 and MTS-3 have a slightly lower bias than model MTS-1, which incorporates a linear time trend. The difference is more visible at the national and division levels in the case of mean ARB values than those of RB. Comparison of models based on either structured or unstructured random effects at the sub-district (admin-3) level indicates that the former performs better at higher aggregation levels (admin-0 to admin-2), where the direct estimates are significantly better in terms of the number of sampled observations.

Table 5 Mean relative reduction of standard error (MRRSE, %) and coverage rate (CR, %) of MTS-1, MTS-2 and MTS-3 model-based estimators at administrative levels 0 (national), 1 (division), 2 (district) and 3 (sub-district) based on the structured (spatial) and unstructured random effects at sub-district level
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Table 5 presents the mean relative reduction in standard error (MRRSE, %) and coverage rate (CR, %) for the model-based estimators at the four administrative levels under consideration, providing insight into the uncertainty of the model-based estimates. The performance of the developed models also varies by administrative level. At the national and division levels, model MTS-1 provides lower standard errors, consequently resulting in a higher mean value of RRSE and a lower coverage rate. At the district and sub-district levels, model MTS-3 performs better than MTS-1 and MTS-2 in terms of coverage rate, although the differences are small. Comparisons based on structured and unstructured random effects indicate minimal differences at the top three administrative levels, while at the sub-district level the former provides a slightly higher gain in accuracy and thus a slightly lower coverage rate. The overall comparison of these MTS models confirms that the models without a linear time trend (MTS-2 and MTS-3) provide lower bias but with a higher confidence band at the national and division levels compared to the model with a linear time trend (MTS-1). However, the differences in the considered discrepancy measures are minimal at the district and sub-district levels. The inclusion of remote-sensed variables in the MTS-3 model slightly but consistently improves all the measures.

As a standard diagnostic of a Bayesian model, a posterior predictive check has been shown in Fig. 6 following Gabry et al. (2019). The comparison of simulated draws (thin lines) with the kernel density of direct estimates (thick lines) shows how the considered time-series model provides reasonably smoothed trends at the detailed sub-district level by avoiding the noisy direct estimates (tends to either zero or one) and follows the trends of direct estimates at the higher aggregation (division and national) level at which the surveys are representative.

In the following sub-sections the estimated trends at different administrative levels are discussed based on the MTS-3 model with structured random effects at the sub-district level.

Fig. 6
figure 6

Posterior predictive check of the model-based trend estimates at the sub-district, district, division and national levels. The thin lines present kernel densities of simulated draws from the posterior distributions based on model M3 with sub-district level structured random effects, while the thick lines show the kernel density of direct estimates (empirical data) obtained from the survey data

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4 Results and discussion

Based on the model-based estimator that incorporates remote-sensed data of nighttime light and the vegetation index in the MTS-3 model, we estimated the trends of stunting prevalence at four administrative units for the period 2000-2018. The trend estimates are discussed in the following subsections according to the administrative units. In these subsections, we highlight some key findings based on the model-based estimates, with more detailed results available in the Supplementary File.

4.1 Trends at national and division level

The national-level trend demonstrates a steep decline in stunting levels throughout the entire period, from about 50% in 2000 to just above 30% in 2018, according to both the design-based and model-based estimates (see Fig. 1). The direct estimates show no significant decline for the periods 2000-2004 and 2007-2014. This pattern is captured in the MTS-2 and MTS-3 models, except that the MTS-3 model provides slightly different estimates in the non-survey years based on the relationship of stunting levels with the NTL and NDVI during the survey periods. The trends in the 95% credible intervals display a decreased width during survey years compared to non-survey years, resulting in a wave pattern in the confidence band. This pattern indicates that the MTS models provide more accuracy when sample information is available and less accuracy when there is no sample information, as expected.

The division-level trends shown in Fig. 2 indicate that stunting levels steadily declined over the entire period after 2004 in all the western divisions - Khulna, Rajshahi, and Rangpur - while other divisions exhibit a flat trend during the 2007-2011 period. For the Sylhet division, the stunting level plateaued around 45-50% for a long period from 2007 to 2014 (resembling an S-shape). Only Dhaka and Khulna divisions have stunting levels below 25%, while the prevalence was still above 40% in the Sylhet division and above 30% in the Barisal, Mymensingh, and Chittagong divisions. Therefore, these divisions are still above the threshold of “very high prevalence” (\(\ge 30\%\)). The MTS-3 model-based trend estimates reflect the difference by accounting for socioeconomic and environmental changes over the time period.

Fig. 7
figure 7

District level trends in stunting among under-5 children in Bangladesh during 2000-2018 estimated by MTS-3 model-based estimators, NTL intensity and NDVI for some districts: (i) densely populated along with higher NTL intensity (upper panel); (ii) north-eastern region with wetland areas; and (iii) south-western coastal region. The trends are smoothed and the corresponding shaded confidence bands indicate how the time-series are volatile for NDVI compared to the time-series of NTL and estimated stunting prevalence

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4.2 Spatio-temporal distribution of stunting at district level

In the MTS-3 model-estimated trends of stunting at the district level, as shown in Figs. 4, 3 and 5, the trends of NTL intensity and those for the NDVI are plotted in Fig. 7 for some districts representing three categories of districts in Bangladesh. The trends are smoothed using the locally estimated scatterplot smoothing (LOESS) method to understand how the trends of stunting levels are associated with the trends of NTL and NDVI. The wider confidence band indicates how volatile the trends of NDVI and NTL are. The upper-panel plots in Fig. 7 indicate that the steady increase of NTL intensity in the densely populated districts is associated with a decline in stunting prevalence. Interestingly, Dhaka and Narayanganj districts, which have the highest levels of NTL intensity, have the lowest levels of NDVI values over the entire time period. The middle-panel plots represent districts in the northeastern region containing a substantial amount of wetland areas (known as Haor). Both the NDVI and NTL levels are found to be comparatively lower in Sunamganj and Natrakona districts, which are expected to be associated with the highest level of stunting over the entire period. All the districts under the Sylhet division show very similar trends of decreasing stunting level from the period of 2011-2014, from when the NTL intensity started to increase rapidly. While the districts in the southwestern coastal region show steady declining trends of stunting over the entire period, NTL intensities were very poor over most of the time period and NDVI is too volatile due to frequent natural calamities such as cyclones, storm surges, and saline soil due to its geographical location and low-lying topography (Ashrafuzzaman 2022). The association of NTL and NDVI seems lower compared to other regions. The lower level stunting prevalence in these districts is associated with demographic and population dynamics such as lower female fertility and higher female education.

Fig. 8
figure 8

Model-based stunting prevalence and district level nighttime light (NTL) intensity in survey years. District level interactive maps for 2018 can be found in the given links: District Stunting 2018 and District NTL 2018

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To understand the spatio-temporal distribution of stunting levels at the district level, alongside the change in NTL intensity, maps of stunting prevalence and NTL intensities are provided for the survey years in Fig. 8. These maps indicate that NTL levels have consistently increased in the central region surrounding Dhaka district and the stunting levels have steadily declined over time. In the northeastern region, the stunting levels have always been higher with slow progress, and the change in NTL intensity was very slow. The hilly districts in the southeastern region (except Chittagong and Cox’s Bazar) and the coastal districts in the southwestern region had lower NTL intensity until 2011. However, the pattern of declining stunting levels was opposite: very steady in the latter region compared to very slow in the former region.

Historically, regions within the Sylhet division have had the highest incidence of stunting in Bangladesh. Despite rising income (as proxied by nighttime lights), it can take many generations for a previously malnourished population to reach the national average height, as argued by Deaton and Drèze (2009). Hence, even if the population or sub-population of the Sylhet division is well-nourished today, they may still be shorter for a considerable period. Several empirical studies also indicate the limited impact of rising GDP per capita on stunting. For instance, across six studies, McGovern et al. (2017) found that a 10% increase in GDP per capita is associated with a reduction in stunting of only 0-2%. Moreover, the fact that children in Sub-Saharan Africa are taller than Indian children, despite Sub-Saharan Africa being poorer than India, suggests that intermediary factors such as disease and the implementation of nutrition programs play a crucial role in determining the extent of stunting (Coffey et al. 2013; McGovern et al. 2017).

Fig. 9
figure 9

Sub-district level (model-based) stunting prevalence and nighttime light (NTL) intensity at the DHS survey years in Bangladesh during 2000-2018. Interactive maps for 2018 can be found in the given links: Sub-district Stunting 2018 and Sub-district NTL 2018

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The nutrition of children can be said to depend on a number of factors: the income of the parents, which allows them to purchase adequate nutritious food; the knowledge of the parents regarding the nutritional needs of their children; and finally, the appealing nature of the foods actually offered to the children. The first factor is not normally amenable to policy interventions at the micro-level, unless substantial nutrition subsidies are provided to parents; however, this is often unaffordable in developing economies. The second factor is also tied to economic growth, and while general education may not be easily targeted, nutritional education for parents can certainly help. The third factor, making the available food appealing to children, is a challenge that parents and nutritionists will have to solve in local circumstances. The challenge for policymakers is to focus on those areas which require targeted support. The rapid growth of the Bangladesh economy suggests that neither income support nor education enhancement policies are the primary need. The correlation between nighttime light and urbanization indicates that the urbanization occurring will, by itself, create forces that reduce malnutrition. Nighttime light data can be most useful where they suggest areas for intervention, specifically in areas where light intensity is low; these are the areas not affected by the forces driving urbanization and are therefore most likely to need help with child nutrition.

Fig. 10
figure 10

Model-based stunting prevalence and nighttime light (NTL) intensity at sub-district level in survey years for Dhaka district. The eastern part of Dhaka district (mainly the metropolitan part) has higher NTL intensity and lower stunting prevalence compared to the north-eastern and south-eastern parts (Rural parts)

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4.3 Spatio-temporal distribution of stunting at sub-district level

The spatio-temporal distribution of stunting and NTL intensity at the sub-district level is visualized through geospatial maps for the survey years in Fig. 9. Although the geospatial distribution of stunting is easy to interpret due to substantial variation, the distribution of NTL intensity is difficult to discern due to a very homogeneous pattern in the NTL intensity. This uniformity primarily occurs because NTL intensity steadily increases in sub-districts that are either administrative centers of a particular district (known as Sadar Upzila with large municipalities) or are located in business areas, particularly adjacent sub-districts of densely populated cities (Dhaka, Gazipur, Narayanganj, and Chittagong) (Rahman et al. 2019). This trend is mainly attributed to the boom in ready-made garment industries in Bangladesh since the 1990s (Swazan and Das 2022).

To illustrate how the NTL intensity of a Sadar Upzila significantly differs from its neighboring sub-districts, sub-district level NTL intensity and stunting levels have been mapped for three districts-Dhaka, Sylhet, and Khulna-which represent three types of districts. Dhaka represents districts with very high population density, where urbanization has boomed over the last two decades. Sylhet represents districts where stunting levels have been high for a long time in the north-eastern region. In contrast, Khulna represents districts in the south-west coastal region where stunting levels have consistently been the lowest. Figure 10 reveals that sub-districts in the eastern parts of Dhaka district, covering the capital city, have higher NTL levels and lower stunting levels. The NTL intensity increased and stunting level decreased consistently over the considered period from 2000 to 2008. The north-western and south-eastern sub-districts, which are relatively remote from the capital city, had consistently higher stunting levels, although the stunting level steadily declined.

Fig. 11
figure 11

Model-based stunting prevalence and nighttime light (NTL) intensity at sub-district level in survey years for Sylhet district. The mostly urbanized part (Sylhet Sadar Upzila, brightest area in NTL plot) of Sylhet district (again the metropolitan part) has higher NTL intensity and lower stunting prevalence compared to the other sub-districts (mostly rural areas)

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When we examine Fig. 11 for Sylhet district, the corresponding Sadar Upzila (yellowish area in NTL panel) shows the highest level of NTL intensity among the sub-districts, as expected, and a comparatively lower stunting level. Also, the neighboring sub-districts of Sadar Upzila in south-western areas show smaller stunting levels than the northern sub-districts, which are close to the Indian border. The relationship between NTL intensity and stunting level is not explicit in Khulna district (Fig. 12) as in Dhaka and Sylhet districts. The NTL intensity level is consistently lower in the south-west coastal part, particularly in the Sundarban mangrove forest region, and the stunting level is also comparatively higher within Khulna district. Stunting levels improved over time, but the NTL intensity did not change at that level. However, the sub-districts in the north-eastern part with comparatively higher NTL intensity show comparatively lower stunting prevalence compared to the southern sub-districts.

Overall, there appears to be a minimal association between NTL intensity and the reduction of stunting levels in Khulna district. Climatic factors such as soil salinity, dense vegetation, the resilience of the coastal mangrove forest, access to natural resource-based foods (like fruits and honey), and the significant potential for ecosystem-specific climate change mitigation and adaptation within the coastal zone (Hoque and Datta 2005; Duncan et al. 2018) could be some of the inherent reasons for the consistently lower stunting prevalence in Khulna districts and throughout the Khulna division over the entire time period.

Fig. 12
figure 12

Model-based stunting prevalence and nighttime light (NTL) intensity at sub-district level in survey years for Khulna district. The variation in NTL intensity is minimal, however, there is substantial variation in stunting level. The north-eastern sub-districts with comparatively lower stunting have slightly higher levels of NTL intensity over the whole time period

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5 Conclusion

The main objectives of this study were twofold. Firstly, we aimed to provide model-based estimates of stunting at the second (64 districts) and third (544 sub-districts) administrative hierarchy levels in Bangladesh for the period of 2000-2018. Secondly, we examined how remote-sensed data, reflecting changes in socio-economic conditions and climate change at local levels over the last two decades, can aid in estimating trends of stunting prevalence when information on the target variable is too sparse over time and space.

We achieved this through developing multilevel time-series models at the sub-district level for estimating trends in child chronic malnutrition (stunting) across Bangladesh’s divisions, districts, and sub-districts from 2000 to 2018, using geo-coded data from the Bangladesh Demographic and Health Surveys. These models fill gaps between survey years by estimating stunting levels, incorporating survey data and remote-sensed variables (e.g., nighttime light intensity, vegetation index) within a hierarchical Bayesian framework. Our methodology facilitates the prediction of stunting trends at various administrative levels by aggregating sub-district-level estimates, with Markov Chain Monte Carlo (MCMC) simulations enhancing model consistency. Although machine learning was considered for its robustness in small area estimation, we ultimately employed Bayesian methods, recognizing their qualitative similarities in model assessment.

Our findings reveal a significant decline in child stunting throughout Bangladesh, with national levels dropping from roughly 50% in 2000 to just over 30% in 2018, as indicated by both design-based and model-based estimates. Particularly after 2004, the western divisions of Khulna, Rajshahi, and Rangpur saw consistent reductions in stunting rates, unlike other divisions where trends varied. Specifically, the northeastern Sylhet division exhibited high stunting rates persistently, while only the central Dhaka and southwestern Khulna divisions achieved stunting levels below 25% by 2018. District-level analysis reveals a strong positive relationship between increased nighttime light (NTL) intensity-a marker of socioeconomic growth-and a decrease in stunting rates, particularly in densely populated areas. However, districts with elevated Normalized Difference Vegetation Index (NDVI) values, representing the northeastern wetlands, persistently reported high stunting rates. The southwestern coastal region encompassing the districts of Khulna, Bagerhat, and Satkhira also experienced significant declines in stunting, despite the challenges posed by low NTL intensity and NDVI volatility due to environmental factors. In contrast, sub-district level analyses indicates that areas with heightened NTL intensity, typically administrative and commercial hubs, had significantly lower stunting rates than their surrounding areas, illustrating the impact of urbanization and economic activities on child nutrition. Yet, in the Khulna district, this correlation was less evident, as other factors such as climate and natural resource access played a substantial role in maintaining lower stunting levels.

However, our research is not without limitations. The imprecision of geospatial locations in the Demographic and Health Surveys, the underutilization of sub-district-specific contextual variables, and the exclusion of seasonally variable weather-related data due to data unavailability or volatility, particularly impact the modeling accuracy. Additionally, the inconsistent trends of remote-sensed variables across sub-districts, especially in urban areas with small boundaries and specific climatic conditions, limited our ability to incorporate these data at the sub-district level, necessitating reliance on district-level trends for some variables.

Despite these challenges, our study makes a compelling case for the incorporation of remote-sensed climatic and economic data in the spatio-temporal modeling of stunting. The predictive capabilities of such data, particularly nighttime light, present a new approach for monitoring health indicators and identifying regions where child nutrition status improvement is delayed. This is particularly valuable for policymakers focused on targeted interventions to enhance child nutrition and achieve sustainable development goals. Furthermore, while machine learning methods have been suggested for small area estimation due to their robustness and accuracy, as noted by Kriegler and Berk (2010) and Kontokosta et al. (2018), our study opted for Bayesian techniques. These methods align closely in model assessment with machine learning approaches, including the application of ensemble methods or bootstrapping techniques, as discussed by Viljanen et al. (2022). Our choice of methodology was thus influenced by the specific challenges and objectives of our study, emphasizing the nuanced comparison between Bayesian methods and machine learning approaches in the context of our research.

Our research contributes to the broader narrative of Bangladesh’s development surpriseFootnote 1 by offering a more nuanced understanding of the socio-economic and environmental determinants of child nutrition. Despite the country’s challenging initial conditions, our findings on the significant decline in child stunting rates from 2000 to 2018 reflect the remarkable progress observed in health, education, and demographic outcomes across Bangladesh. Incorporating remote-sensed data to model stunting prevalence, our study supports the view of Bangladesh’s development not just as a surprise but as evidence of the wide-ranging progress possible even under challenging conditions.

Our study’s results have a direct and significant link to the current policies and plans regarding nutrition and health in Bangladesh – see MGFW (2021). For instance, the persistent high stunting rates in the northeastern Sylhet division, as opposed to the improvements in the Khulna, Rajshahi, and Rangpur divisions, underscore the need for region-specific strategies. These could be incorporated into the operational plans for Lifestyle & Health Education and Promotion (L&HEP) and Information Education and Communication (IEC) under HPNSDP and the 4th Sector Plan of the Government of Bangladesh. Furthermore, the strong positive relationship between increased nighttime light intensity and reduced stunting rates, as well as the correlation between high NDVI values and high stunting rates, can guide the refinement of the Bangladesh Country Investment Plan (CIP 2) and the Second National Plan of Action for Nutrition (NPAN2). These plans should consider socio-economic growth and environmental factors more closely to effectively reduce child stunting.

5.1 Supplemental online material

A supplementary file has been submitted for review purposes and also for online publication. The supplementary file provides detailed information on the preparation of data inputs, model development, and trend estimates at various disaggregated levels.