Spatiotemporal clustering and correlates of childhood stunting in Ghana: Analysis of the fixed and nonlinear associative effects of socio-demographic and socio-ecological factors

Childhood stunting remains a major public health issue in many low- and middle-income countries. In Ghana, the progress made is insufficient to reach the targets set by the 2025 World Health Assembly and the 2030 United Nations Sustainable Development Goals. Although studies have examined the socio-demographic determinants of childhood stunting, there has not been any systematic study to examine the spatial associative effects of the socio-demographic and socio-ecological factors at the district level, where health programmes are implemented and monitored. Bayesian geo-additive semiparametric regression technique was used to analyse five conservative rounds of Demographic and Health Surveys in Ghana, with socio-ecological covariates derived from the Demographic and Health Survey Program Geospatial Covariate datasets to examine the temporal trends in childhood stunting, the extent of geospatial clustering at the district level and their associative relationships with socio-demographic and socio-ecological factors. The findings show that childhood stunting in Ghana is not spatially randomly distributed but clustered. Clustering of high childhood stunting was observed amongst districts in the Upper West, Upper East, Northern, North East, Savannah, and Western North regions, whilst clustering of low childhood stunting was observed in districts in the Greater Accra, Volta, Bono and the Eastern regions. Whist socio-demographic factors were predominantly associated with clustering of districts with high childhood stunting, the socio-ecological factors were mainly associated with clustering of districts with low childhood stunting. The socio-ecological factors identified to have a nonlinear associative effect with childhood stunting were Insecticide Treated Net (ITN) coverage, nightlight composite, travel time to a main settlement and population density. The findings suggest that targeted interventions at the district level are essential to reducing childhood stunting in Ghana.

Introduction by Interval Eta [27]. The correlations were not high enough for potential multicollinearity. The district map used for this study covers the 216 districts created in June 2012 and adopted for the last (2014) GDHS considered for this analysis.

Statistical analysis
The percentage distribution of stunted children by the year of DHS survey and the fixed sociodemographic covariate were examined through cross-tabulation, using Chi-squared test to examine statistically significant differences by the levels of the covariates. Analysis of Variance (ANOVA) was used to examine the mean distributions of the continuous socio-demographic and socio-ecological covariates aggregated by the year of the survey and the stunting status of the children. Finally, the Bayesian Geoadditive Semiparametric (BGS) regression technique was used to examine the extent to which the socio-demographic and socio-ecological factors were associated with the observed spatial patterns of childhood stunting [28]. The advantage of the BGS technique is that it allows for simultaneous estimation of nonlinear effects of the continuous covariates as well as fixed effects of the categorical and continuous covariates in addition to the unobserved spatial effects, both spatially structured and unstructured [28].
The outcome variable of interest y ij was coded 1 if child i in district j is stunted and 0 otherwise. The outcome variable y ij follows a binomial distribution with the expected probability π ij  Place of residence 0 = Urban, 1 = Rural Categorical of being stunted. The logistic model linking the probability π ij of a child being stunted is of the form where η ij is the predictor of interest. If we have a vector x 0 ij ¼ ðx ij1 ; . . . ; x ijk Þ 0 of k continuous covariates and l 0 ij ¼ ðl ij1 ; . . . l ijd Þ 0 a vector of d categorical covariates, then the predictor η ij can be specified as Table 2. Socio-ecological covariate selected for the analysis.

Variable Definition
Built population An index ranging from 0 to 1, where 0 represents extremely rural and to 1 represents extremely urban.

Day land surface temperature
Mean annual daytime land surface temperature.

Enhanced vegetation index
Density and condition of the greenness of an area.
Global human footprint An index ranging between 0 (low) to 100 (high) covering human population pressure (population density), human land use and infrastructure (built-up areas, nighttime lights, land use/land cover), and human access (coastlines, roads, railroads, navigable rivers).

Irrigation
The average proportion of the area equipped for irrigation at the time.

ITN coverage
The proportion of people who slept under an insecticide-treated net the night before they were surveyed.
Land surface temperature The average annual land surface temperature.

Malaria prevalence
The average parasite rate of plasmodium falciparum (PfPR) in children between the ages of 2 and 10 years old.

Nightlights composite
The average nighttime luminosity of the area shows the differentiation of regions based on the density of population and the degree of electrification of dwellings, commercial and industrial premises, and infrastructure. The indicator is a proxy measure of urbanisation and development, with higher intensity of nightlight reflecting higher degree of urbanisation and development.
Night land surface temperature The average nighttime land surface temperature.

Proximity to national borders
The geodesic distance to the nearest international borders.

Proximity to protected areas
The geodesic distance to the nearest protected area (e.g., national parks, national forests, and national seashores) is defined by the United Nations Environment World Conservation Monitoring Centre.
Proximity to water The geodesic distance to either a lake or the coastline.

Rainfall
The average annual rainfall.

Slope
Roughness the terrain.

Travel times
The average time (minutes) required to reach a settlement of 50,000 or more people. where α is a vector of unknown regression coefficients for the categorical covariates, l 0 ij , β is a vector of unknown regression coefficients for the continuous covariates x 0 ij . To account for nonlinear effects of the continuous covariate and the spatial correlation of the proportion of children stunted, the BGS framework, which replaces the strictly linear predictors with flexible semiparametric predictors, was adopted. The model is thus specified as where f k (x) are nonlinear smoothing function (an approximating function that reduces randomness and allows patterns of associations to be identified) of the continuous variable x ijk and f spatðS i Þ accounts for unobserved spatial heterogeneity at district j (j = 1,. . .,S), some of which may be spatially structured (correlated) and others unstructured (uncorrelated). The spatially structured effects show the effect of location by assuming that geographically close areas are more similar than distant areas, whilst the unstructured spatial effect accounts for spatial randomness in the model. Eq 5 is thus specified as where f str is the structured spatial effects and f unstr is the unstructured spatial effects and f spatðS i Þ ¼ f str þ f unstr . The spatially structured effects depict the extent of childhood clustering and the associative effects of unaccounted predictor covariates, which may be spatially clustered or random. The smooth effects of continuous factors are modelled with P-spline priors, whilst the spatial effects are modelled using Markov random field priors (correlated random effect for the spatial location of observation). P-splines are efficient for modelling nonlinear smooth effects of continuous covariates for varying coefficient models [29]. The approach uses a piecewise continuous function composed of many polynomials to establish the relationships of continuous covariates with the outcome variable instead of fitting one polynomial for all the data. The posterior mode (the expected value of the parameter estimate) of the structured spatial effects and their corresponding probabilities at a 95% nominal level were used to examine spatial correlations of the outcome variable at the district level. The posterior probabilities at the 95% nominal level show districts where childhood stunting was statistically significantly high (high positive estimates of the posterior mode), significantly low (high negative estimates of the posterior mode), and where the effects were not significant (estimated posterior mode not significantly different from zero). The estimated posterior mode of the spatial effects characterises unexplained spatially correlated covariate information. Thus, districts, where the sociodemographic and the socio-ecological factors were spatially correlated with childhood stunting were identified using a sequential modelling approach.
To examine if significant geospatial clustering exists in childhood stunting at the district level, a null model (constant model) was initially fitted (Model 0). Model 1 accounted for only the spatial effects. Model 2 included the year of the survey, whilst Model 3 added the sociodemographic factors. The socio-ecological factors were then included in Model 4. Only covariates significant at p < 0.05 were retained in the model.
The Akaike weight w r is used as the model selection criteria since it accounts for the spatial correlation of the variables [30,31]. The Akaike weight w r is formulated as where Δ j (AIC) is the difference between the AIC for each model and the model with the lowest AIC, and r is the number of fitted models. The Akaike weight ranges between 0 and 1, with the sum of all candidate models equal to 1, and analogous to the probability that model R r is the best model given the available data and all candidate models [32]. Interpretation of the final results was based on the best-fitted model. The statistical software R was used for the analysis [33]. Table 3 shows the weighted percentage of stunted children aggregated by year of survey and the selected categorical socio-demographic covariates. Chi-squared test was used to examine   For all the surveys, twin children were significantly more likely to be stunted when compared to singletons. Where the results show statistically significant differences, children who were born by Cesarean section were less likely to be stunted. Generally, recent illnesses such as diarrhoea, fever, and cough had no significant association with childhood stunting. Consistently, maternal education had a statistically significant association with childhood stunting, with a decline in the percentage of children stunted as maternal education increases. Across all the surveys, children whose mothers had no access to media information were significantly more likely to be stunted. With regards to religious affiliation, statistically, significant differences were found in the 1998 (protestants less likely to be stunted, traditionalist/spiritualist more likely to be stunted), 2003 (no religion and traditionalist/spiritualist more likely to be stunted) and 2014 (traditionalist/spiritualist more likely to be stunted) GDHS. Other than the 2008 GDHS, there was a significant difference in childhood stunting by ethnicity. The results further show that the higher the number of births in the last five years, the higher the likelihood of the child being stunted, and the effects were statistically significant for the 1998, 2003, 2008, and 2014 GDHS. Consistently across all the surveys, the higher the number of antenatal visits, the lower the likelihood of a child being stunted. Similarly, children born in public and private health facilities were significantly less likely to be stunted when compared to those born at home, and the effects were statistically significant for all the surveys. Save for the 1993 GDHS; children were significantly more likely to be stunted in households where the number of children under five years was high. Paternal education was significantly associated with childhood stunting for all the surveys. Those whose fathers had secondary or higher education were less likely to be stunted compared to their counterparts. Also, household wealth status and place of residence were consistently associated with childhood stunting, with those belonging to the wealthier households and urban areas being less likely to be stunted. The bivariate analyses of the continuous socio-demographic factors are shown in Table 4. The table shows that stunted children's mean age was lower than non-stunted children, and the effects were statistically significant across all the surveys. The results further show that maternal age was significantly lower for mothers whose children were stunted when compared to those whose children were not stunted, with statistically significant effects in the 1993, 2008, and 2014 GDHS. The age of household heads was significantly associated with childhood stunting for the 2003 GDHS. Other than the 2003 GDHS, age at first birth was significantly associated with childhood stunting, with mothers of stunted children having a lower mean age at first birth compared to those who were not stunted. The results from the 1998, 2008, and 2014 GDHS show that age at first marriage was significantly associated with childhood stunting, revealing that the mean at first marriage for mothers of stunted was lower compared to those who were not stunted. Likewise, the 1993, 2008, and 2014 GDHS show that the mean age at first sex was statistically significantly lower for mothers of stunted children. Furthermore, the results further show that the mean number of household members and the number of living children were significantly associated with childhood stunting. The mean number of household members and the number of living children in a household was higher for stunted children than children who were not stunted.

Bivariate analysis
The bivariate analyses of the continuous socio-ecological factors are shown in Table 5. The analyses revealed that the built population, global human footprint, irrigation, malaria prevalence, nightlights composite, proximity to protected areas, and travel times were statistically significantly associated with childhood stunting across all the selected surveys. In addition, the results show that the mean estimate for built population, global human footprint, irrigation, and nightlights composite were significantly lower for stunted children when compared to non-stunted children. However, the mean malaria prevalence, proximity to protected areas, and travel times were significantly higher for stunted children when compared to non-stunted children.

Geospatial analysis
The estimated posterior odds ratios of childhood stunting and their corresponding 95% credible intervals for the fixed covariates are shown in Table 6, along with their model summary statistics. A sequential model building technique was used to analyse the associative effects of the socio-demographic and socio-ecological factors on childhood stunting. Interpretation of the model coefficients was based on the final model (Model 4).

Geospatial dependence in childhood stunting
The estimated AIC for Model 0 (null model) was 13933.0 (Table 3). When the spatial effects were included in the model (Model 1), the AIC reduced by 369.7. The high reduction in the AIC after the spatial effects were included in the model, indicates that childhood stunting in Ghana is not spatially randomly distributed but clustered. Fig 1A shows districts where the posterior mode of the structured spatial effects were positive and significantly high (clusters of high childhood stunting) and negative and significantly low (clusters of low childhood stunting) at the 95% nominal level. The figure shows clustering of high childhood stunting within districts in the Upper West, Upper East, Northern, and Western North regions. Clustering of low childhood stunting was observed in districts in the Greater Accra, Volta, Bono, and those in the Eastern region bordering the Greater Accra and Volta regions.

Temporal trends in childhood stunting
When the survey years were included in the model (Model 2), the AIC reduced by 239.0, indicating that the year of the survey has an important association with childhood stunting.   structured spatial effects became statistically insignificant (p>0.05) in the Hohoe Municipal (low childhood stunting) and the Daffiama Bussie district (high childhood stunting) (Fig 1B).

Associative effects of the socio-demographic factors with the observed spatial clustering of childhood stunting
The socio-demographic covariates were included in Model 3, leading to a reduction of 1,276.0 in the AIC. The fixed effects of the socio-demographic covariates that were statistically significant at p<0.05 were the sex of the child, type of birth, birth interval, maternal educational attainment, religious affiliation, ethnicity, antenatal visits for pregnancy, household wealth status, sex of household head, and place of residence ( Table 6). The important nonlinear covariates were the child's age, maternal age, and birth order number ( Table 6). The posterior odds Regarding the maternal factors, the results show that children whose mothers had secondary or higher education were 33% less likely to be stunted when compared to those whose mothers had no formal education. Concerning religion, the results show that children whose mothers were Catholics, Protestants, and Other Christians had reduced odds of 20%, 22%, and 20%, respectively, of being stunted compared to those whose mothers had no religious affiliation. Children whose mothers were of the Ewe-Guan and Mole-Dagbane ethnicity had lower odds of 21% and 20%, respectively, of being stunted compared to those whose mothers were Akan. High antenatal uptake was also associated with reduced odds of childhood stunting. Children whose mothers had four to six antenatal visits and those who had more than six visits had reduced odds of 18% and 29%, respectively, of being stunted compared to those who had no antenatal care. Considering the household factors, children who belong to rich households and households headed by men had lower odds of being stunted. Children who belong to the rich and richest households were 0.74 times and 0.48 times less likely to be stunted when compared to those from the poorest households. Children in households headed by females were 1.18 times more likely to be stunted when compared to those from households headed by males. On the place of residence, children from rural areas were 1.27 times more likely to be stunted when compared to their counterparts in urban areas. The posterior mode of the structured spatial effects and their corresponding probabilities at 95% nominal level for Model 3, shows that, the socio-demographic covariates were spatially correlated with high childhood stunting in the Sefwi Akontombra, Sefwi-Wiawso, Sefwi Bibiani-Anhwiaso Bekwai, Juabeso, Suaman, and Bodi districts in the Western North Region, Nkwanta South district in the Oti region, Kpandai district in the Northern region, Garu Tempane in the Upper East region, and Wa East in the Upper West region (Fig 1B). In addition, the socio-demographic covariates are also spatially correlated with low childhood stunting in the Awutu Senya district in the Central region, Ga South, Ga West and Ga Central Municipal in the Greater Accra region, Ho Municipal, Ho West, Afadzato South, and North Dayi in the Volta region and Nsawam Adoagyiri, Akwapem North and Akwapem South district in the Eastern region.

Associative effects of the socio-ecological factors with the observed spatial clustering of childhood stunting
When the socio-ecological covariates were added (Model 4), the AIC reduced by 19.90 (Table 6). All the significant socio-ecological covariates showed nonlinear associative effects, except for distance to the nearest national border. Distance to the nearest national border was included in the model as a categorical variable. The socio-ecological factors which exhibited nonlinear associative effects with childhood stunting were ITN coverage, nightlights composite, travel times, and population density ( Table 6). The results show that children who reside more than 1 km away from a national border had reduced odds of being stunted. However, the effects were only significant for those between 1.00 to 4.99 km away from a national border (Table 6). Fig 2B shows a rise in the posterior log odds of a child being stunted where the proportion of people with an insecticidetreated net was between 0 and 0.1 (0-10%) and starts to decline with increasing coverage. The figure also shows a decline in the posterior log odds of a child being stunted with increasing nightlight composite. With regards to the average time (minutes) required to reach a settlement of 50,000 or more people (main settlement), the findings show that the posterior log odds of childhood stunting increases for those resident more than 220 minutes (4 hours) away from a main settlement. Regarding population density, the results show that the posterior log odds of childhood stunting decreased with population densities between 0 and 2000 persons per square kilometre but increased where the population density was between 2000 and 5000 persons per square kilometre and began to decline thereafter.
From Model 4, the posterior mode of the structured spatial effects and their corresponding probabilities at 95% nominal level show that the socio-ecological covariates were spatially correlated with high childhood stunting in the Nkwanta North district in the Oti region, the East Gonja, West Mamprusi, North Gonja, Mamprugu Moagduri districts in the Savannah region and Bawku West district in the Upper East region. The socio-ecological covariates were also spatially correlated with low childhood stunting in the Ga East, Accra Metropolis, Adenta, Ledzokuku/Krowor, Ashaiman, Tema Metropolis, Shai Osu Doku, Ada East, La Dade Kotopon, La Nkwantanang Madina, Kpone Katamanso, Ningo Prampram and Ada West districts in the Greater Accra region, the South Tongu, Keta Municipal, Ketu South, Ketu North, Akatsi South, Central Tongu, Agotime Ziope, South Dayi, North Tongu, Akatsi North and Adaklu districts in the Volta region and the Lower Manya and Asuogyaman districts in the Eastern region, the Sunyani West, Tain, and Wenchi districts in the Bono region.

Observed spatial clustering of childhood stunting not explained by the socio-demographic and socio-ecological factors
The posterior mean of the structured spatial effects shows high childhood stunting in districts of Ghana's Northern and North East regions, even after adjusting for the socio-demographic and socioeconomic covariates (Fig 1A and 1B). The districts in the Northern region with significantly high childhood stunting and not correlated with the covariates accounted for in the model were the Nanumba South, Nanumba North, Zabzugu, Yendi Municipal, Tamale North Sub Metro, Tolon, Savelugu Nanton, Karaga, Gushiegu, Saboba, Kumbumgu, Sagnerigu, Mion and Tatale districts. The Bunkpurugu Yonyo, Chereponi, and Mamprusi East districts in the North East region with significantly high childhood stunting and the Berekum district in the Bono region with significantly low childhood stunting were also not explained by the covariates accounted for in the model.

Discussion
Previous studies have examined the socio-demographic factors associated with childhood stunting at the national level. However, in many low-and middle-income countries where health planning, implementation, and monitoring are decentralised [5,6], there is the need to identify geographical clusters where childhood stunting is high and their associated factors. Also, socio-ecological factors are location-specific and potentially affect health outcomes at the local level, yet their associations with childhood stunting have not been systematically studied. Therefore, using five rounds of GDHS and DHS Program Geospatial Covariate datasets, this study has examined the spatiotemporal clustering of childhood stunting and the socio-demographic and socio-ecological factors associated with the observed spatial clustering.
The findings of the study show that childhood stunting in Ghana is not spatially randomly distributed but geographically clustered. Thirty-four districts were identified as clusters of high childhood stunting, whilst 46 were clusters of low childhood stunting. High childhood stunting was identified in districts in the northern part of Ghana (Upper West, Upper East, Northern, North East and the Savannah regions) and also the Western North region, whilst low childhood stunting was observed in districts in the Greater Accra, Volta, Bono, and the Eastern regions. The northern part of Ghana is characterised by high fertility, low access to health services, high infant, child and maternal mortality, high poverty levels, and low educational attainments, in contrast to the more developed southern part of the country [22,34,35]. In this regard, the clustering of high childhood stunting observed amongst districts in the northern part of the country concur with the demographic and socioeconomic characteristics of the region.
With regards to the temporal effects, the results show a declining trend in childhood stunting. Nonetheless, research suggests that the country remains off track to achieving national and international targets [36]. Evidence from this analysis indicates that the socio-demographic factors (sex of the child, type of birth, birth interval, maternal education, religious affiliation, ethnicity, antenatal visits for pregnancy, household wealth status, sex of household head, and place of residence) are associated with high childhood stunting in 10 of the 34 districts identified as clusters of high childhood stunting. In these districts, children of mothers with no formal education or primary education, no religious affiliation, no antenatal visits, or less than four antenatal visits, those from poor households and rural communities, are significantly more likely to be stunted. On the other hand, the socio-demographic factors are also associated with clustering low childhood stunting in 13 of the 46 districts with low childhood stunting. These findings concur with previous evidence that childhood malnutrition is predominantly associated with socioeconomic inequalities, particularly poverty and the lack of and use of health care services [13,16,[36][37][38].
Regarding the socio-ecological factors, they were observed to be associated with childhood stunting in six of the 34 districts identified as clusters of high childhood stunting, and 29 of the clusters identified as clusters of low childhood stunting. The statistically significant socio-ecological factors (distance to nearest border, ITN coverage, nightlights composite, travel times, and population density) associated with childhood stunting mainly reflect urban development, industrialisation, and access to amenities [39]. [39] concluded that rapid urbanisation in Africa is not only changing its demographics but also its nutritional landscapes. For example, in Nigeria, using nightlight intensity (referred to in this study as nightlight composite), [39] reported a decline in childhood stunting with increasing light intensity, up to an intermediate level, but rising levels of childhood stunting at higher levels of light intensity. This indicates that, as cities grow much bigger, the benefits of urbanisation in reducing child stunting become less important. Contrary to the findings of [39], the findings of this study show that in Ghana, the benefit of urbanisation in reducing childhood stunting remains important as cities grow larger. The findings also show that the impact of ITN coverage on childhood stunting is less effective where less than 10% of the population use insecticide-treated nets. The results further show an increased odd of childhood stunting with increased distance to main settlements, indicating a lack of access to essential services and facilities [13,38].
The findings from this study assert the need for targeted interventions to reduce child stunting in Ghana. This study, having identified districts where childhood stunting is strongly clustered and further revealed the socio-demographic and socio-ecological factors spatially associated with the observed clustering, will aid efforts to reduce childhood stunting, particularly targeting at-risk populations.

Conclusions
This study systematically examined the temporal trends in childhood stunting, spatial clustering, and the spatial associative effects of the socio-demographic and socio-ecological factors at the district level, where health policies are implemented and monitored, using the Bayesian Geo-additive Semiparametric regression technique. The study shows that childhood stunting in Ghana is not spatially randomly distributed but clustered. The socio-demographic factors associated with the observed spatial patterns were predominantly associated with clustering of high childhood stunting, whist the socio-ecological factors were mainly associated with clustering of low childhood stunting. Targeted interventions to strengthen childhood nutrition programmes are essential, particularly amongst districts in the northern part of the country, where there is an observed strong clustering of districts with high childhood stunting. These districts should be targeted with both direct (nutritional education and provision of supplementary food) and indirect (malaria prevention, hygiene promotion and good quality water and sanitation) nutrition strategies. In addition, given the observed association between childhood stunting and low uptake of antenatal care, community outreach programmes targeting the poor and less educated women in rural communities may be essential.