*3.3. Small Area Estimates of Malnutrition*

Some of the second administrative level in the country (zones) were not represented at all in the EMDHS 2019. These include the Oromiya Zone in Amhara, Yem Special, Sheka, Konta Special, Mirab Omo, Basketo, Alle, Derashe, Amaro and Burji in SNNP, Borena, East Bale in Oromia, and Daawa in Somali. Meanwhile, no woredas, the third adminstrative level in the country, in the unrepresented zones nor some more woredas from represented zones were represented at all, and a few of them had small sample sizes. Accordingly, the application of small area estimation is of paramount importance at the zonal level and woreda level. Aside from that, to comply with the assumption of the model, we considered the zone as secondary small area (SA2) and woreda as primary small area (SA1). The 2 resolutions with 72 knot points were considered for dimension reduction.

A total of 20,000 MCMC samples were generated from the posterior distribution. Considering a burnin period of 6000 and thinning for every third, 4667 samples were retained for the final process. The convergence and independence of the samples were confirmed from the trace plots (Figure 4), density plots (Figure 5), autocorrelation plots (Figure 6), and Geweke's test of convergence (Table 3). All these show that there is no evidence of assumption violations; that is, the samples were a realisation of stationary distribution.

**Figure 4.** *Cont*.

**Figure 5.** Kernel density plots of MCMC samples.

**Table 3.** Geweke's test of convergence for application.


The PMSE plots were generated, showing the variability of the benchmarked HB estimates at the zonal level in Ethiopia (Figure 7).

(**a**) Stunting.

**Figure 7.** *Cont*.

(**c**) Underweight.

**Figure 7.** PMSE for benchmarked HB small area estimates.

The predictive posterior variance of prevalence of undernutrition and correction bias due to benchmarking are given in Figure 8.

**Figure 8.** *Cont*.

**Figure 8.** Posterior variance of HB SAE and benchmarking correction bias for undernutrition.

The estimates of malnutrition and its corresponding 95% credible interval using the proportion of literate persons and proportion of individuals from improved sources of drinking water as auxiliary variables are given. Accordingly, the plot for stunting generated from small area estimation is given in Figure 9. From the figure, we can understand the distribution of the burden of stunting among children under five at the zonal level in the country. The highest small area estimated prevalence of stunting was observed in the southwestern part of the country of Ethiopia. The corresponding measures of precision using the 95% credible interval is given in Figure 9, which shows the SAE-provided precise estimate.

**Figure 9.** Prevalence of undernutrition from benchmarked HB small area estimation at zonal level in Ethiopia.

#### **4. Discussion**

The national level estimates of stunting (38.9%), wasting (22.5%), and being underweight (6.9%) indicate that stunting is still a severe public problem in the country, followed by wasting. This is in line with the related studies.

In addition to the national estimates, the local-level prevalence of malnutrition in Ethiopia was estimated. The design-based estimates were not adequate for estimation in the lower-level administrative areas, as the survey was not representative for lower-level administrative areas. There was a significant overall spatial autocorrelation, as well as hotspot areas with a high prevalence of undernutrition among children under five in Ethiopia. It was determined that including a spatial random effect in the estimation process was crucial in Ethiopia.

Accordingly, the hierarchical Bayesian spatial small area model was applied to estimate the prevalence of stunting, wasting, and being underweight. The estimate showed the existence of spatial variation of undernutrition at the zonal level.

In the midst of significant advancements in global economic growth, issues connected to child malnutrition have consistently posed a major challenge in low- and middle-income nations [2,31,32]. Globally, hunger and malnutrition diminish a country's gross domestic product (GDP) by USD 1.4–2.1 trillion every year. Malnutrition costs the 54 African countries between 3 and 16 percent of their annual GDPs, with Ethiopia accounting for 16.5 percent, Malawi accounting for 10.3 percent, Rwanda accounting for 11.5 percent, and Burkina Faso accounting for 7.7 percent [3,31,33].

Increased agricultural productivity, girls' education promotion, immunisation, integrated management of neonatal and childhood illnesses, improved access to water and sanitation, and skilled birth delivery could all help to reduce the burden of undernutrition among Ethiopian children under the age of five [34].

The spatial variation of undernutrition at the zonal level could be related with economical variation, drought, food insecurity, and variation in cultivation [35]. This might suggest the need for the design and implementation of effective public health interventions at the zonal level to reduce undernutrition among children under five in Ethiopia.

This study is not without limitations. It is probable that there are other auxiliary variables that impact children's nutritional conditions, but the current study did not evaluate those variables due to a lack of information in the census data. Furthermore, the census data used were 15 years old, which may have influenced the results. Hence, readers are advised to take these limitations into account.

#### **5. Conclusions**

The prevalence of undernutrition among children under five in Ethiopia was estimated at the zone level using small area estimation techniques. The small area estimation concept was sought out by linking the most recent possible survey data and census data in Ethiopia. In Ethiopia, undernutrition had significant spatial variations across the country. The results specifically show that there is spatial variation in stunting, wasting, and being underweight across the zone level, showing that different locations faced different challenges and to different extents of undernutrition. Therefore, public health interventions that reduce undernutrition among children and enhance women's awareness toward undernutrition in zones with a high prevalence of undernutrition are crucial, and the Ethiopian Federal Ministry of Health (FMOH) should design tailored nutritional intervention for children under five who are living in zones with a high prevalence of undernutrition.

**Author Contributions:** Conceptualisation, K.F.M., A.K.W. and S.M.M.; methodology, K.F.M., A.K.W. and S.M.M.; software, K.F.M.; validation, K.F.M., A.K.W. and S.M.M.; formal analysis, K.F.M.; investigation, K.F.M.; resources, K.F.M.; data curation, K.F.M.; writing—original draft preparation, K.F.M.; writing—review and editing, K.F.M., A.K.W. and S.M.M.; visualisation, K.F.M.; supervision, A.K.W. and S.M.M.; project administration, K.F.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** The analysis presented in this study was based on the EMDHS 2019 and Census 2007, which are publicly available data sets with no identifiable information on the participants in the survey. Standard survey and census procedures for all ethical issues, like informed consent, were followed strictly in the EMDHS 2019 and Ethiopian Census 2007, respectively. Accordingly, for this study, no separate informed consent or ethical approval was required. However, we have received a grant of permission from Major DHS (http://dhsprogram.com, accessed on 5 February 2021) and IPUMS (https://international.ipums.org, accessed on 12 May 2021) to use survey data and census data, respectively.

**Data Availability Statement:** Minimal data that support the findings of this study can be accessed from the correspondence upon reasonable request. The data are not publicly available due to privacy or ethical restrictions.

**Acknowledgments:** We would like to express our appreciation to the Pan African University Institute of Basic Sciences, Technology and Innovation for the support. We also extend our appreciation to Major DHS and IPUMS for granting us permission to use the data. The authors wish to acknowledge the statistical office that provided the underlying data making this research possible: Central Statistical Agency, Ethiopia. We also would like to acknowledge four anonymous reviewers for their insightful comments which helped us to improve the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
