Spatial Stochastic Modeling of Adolescent and Under-Five Children Nutritional Status: A Case Study fromAceh, Sumatera Island, Indonesia

Purpose – The purpose of this study is to explore the concept of spatial modeling in adolescent and underfive children’s nutritional status. Design/Methodology/Approach – The indicator used to identify spatial autocorrelation is the Local Indicator of Spatial Association (LISA). LISA is a method of exploratory analysis of spatial data capable of detecting spatial relationships at the local level and its effects globally. Aplication of stochastic modeling in spatial nutrition identification mapping can be categorized into two cases based on spatial autocorrelation and non-spatial autocorrelation. Findings – This results of this study indicate that there is no spatial autocorrelation in the adolescent nutritional dataset. The thematic map for anemia showed that that the highest number of anemia in adolescents was in KutaAlam sub-districts (48 people). Sub-districts that were second most common were Meuraxa, Jaya Baru, and Baiturrahman sub-districts. The fewest cases were found in Lueng Bata sub-district (12 people). There were no sub-districts affected by neighboring areas, in the case of adolescents’ anemia in Banda Aceh. For the under-five nutritional data set, it shows that there are four factors that significantly affect spatial influence, which are malnutrition, chronic energy deficiency, woman of child-bearing age, proportion of family planning, percentage of households with PHBS and coverage of access to clean water. Research Limitations/Implications – Anemia data were obtained with a school-based survey. Household survey would be better to implement in spatial analysis. © Siti Rusdiana, Zurnila Marli Kesuma, Latifah Rahayu, Edy Fradinata. Published in the Emerald Reach Proceedings Series. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode Spatial Stochastic Modeling


Introduction
Practical decision problems for which optimal solutions are sought are subject to uncertainty in the problem data especially with spatial data.As transition, opportunities are arranged in a matrix called the transition probability matrix or transitinstochastics matrix.In general, stochastic analysis can describe the cause and effect relationship between one dependent variable with one or several independent variables called linear regression analysis (Draper & Smith, 2014).It ignores the spatial dependence so that data analysis for spatial data is a spatial regression analysis.The fundamental component of the spatial model is the matrix of the spatial weights as well as the transitional stochastic matrix, reflecting the relationship between one region and another.This aspect is important for study because inter-region certainly has different characteristics (Anselin, 1995).
Nutritional status is one of the measures indicating development in healthcare, and this is of special concern when it is focused on the nutritional condition of under-five children, which is seen from the parameter of body weight and height only (Gaetan & Guyon, 2010).Unfulfilled nutritional needs during this time can result in delayed sexual maturation and growth restriction.At this time, important nutrients should be given to prevent the occurrence of chronic diseases associated with nutrition in later adulthood.These diseases include cardiovascular disease, diabetes, cancer, and osteoporosis.

Spatial and geostatistical data analysis
Spatial method is a method to get observational information that is influenced by the effect of space or location.Spatial data type consists of point data (point pattern analysis), which shows the location of a point, for example, latitude and longitude (longitude and latitude) and x and y axis.Data line (geostatistical data) and data area (polygons or lattice data) indicate the location of an area, such as a country, district, city, and so forth.Geostatistical techniques rely on stochastic models based on the theory of random functions (or random variables) to model the uncertainties associated with spatial estimation and simulation.
For example, Z (s) random variable is measured at n location point, with S 1 , S 2 , . . ., S n and area D & Rd.The random process is shown in n measurements: And there is a random process  (Fradinata, 2012).

Index Moran's global and local indicator of spatial autocorrelation (LISA)
The Moran I Index can be used to identify local auto-correlation coefficients (local autocorrelation) or spatial correlations in each area studied.Methods of analysis through the stages of exploration of data are thematic maps followed by spatial auto-correlation analysis, namely Moran's Global Index and LISA.The weights used are binary code and sideways (Rook contiguity) calculated using the Z test count statistics (Kesuma & Rahayu, 2017).
Moran's Global Index is based on the following equation: I is the value of the Moran index, n is the number of observations, y is the mean value of yi from n location, yi is the value at the ith location, yj is the value at the jth location, and wij is the spatial weighted matrix element (Dolores Ugarte, 2011).

Results and discussion
Application of stochastic modeling in spatial nutrition identification mapping can be categorized into two cases based on spatial autocorrelation and non-spatial autocorrelation.
In this case, it is important to note whether there is inter-regional spatial dependence.This spatial auto-correlation is one of the assumption tests that is used to know whether a spatial linear regression model between regions were correlated with the existence of dependence of one region with the surrounding area.

Case of adolescent nutrition in banda aceh city (non-spatial autocorrelation)
The phenomenon of growth in adolescence demands high nutritional needs.The high demand for energy and nutrients for adolescents are due to several factors such as changes and the increase of various dimensions of the body (weight and height), body mass and body composition, nutrient intake, etc.The case of anemia in adolescents is a nutritional problem in Kota Banda Aceh consisting of nine districts, which to date have not received special attention.Based on the number of respondents and cases of anemia in Banda Aceh city from a survey of adolescent nutritional status, data were recorded and presented in Table 1.
The descriptive analysis conducted in this study aims to see the spread of anemia and its relationship with the independent variables depicted in the thematic map of Banda Aceh city through GeoDa software.The thematic map is used descriptively to test the spatial Spatial Stochastic Modeling autocorrelation locally and globally among sub-districts for cases of anemia in adolescents in Banda Aceh city, which is shown in Figure 1 as follows: Based on Figure 1, it appears that the highest number of cases of anemia in adolescents was in KutaAlam sub-districts (48 people).Sub-districts with the second most common occurrence were Meuraxa, Jaya Baru, and Baiturrahman sub-districts.The fewest cases were found in Lueng Bata sub-district (12 people).

Spatial-weighted matrix for anemia in banda aceh
The spatial weighting matrix used for anemia cases in Banda Aceh can be determined based on the neighboring relationships among sub-districts in Kota Banda Aceh by drawing adjacent neighboring maps of software R.
Figure 2 shows the relationship between sub-districts in Kota Banda Aceh based on the border between sub-districts.Among them are Banda Raya Sub-district (1) adjacent to Jaya Baru sub-district (2), Lueng Bata sub-district, (3) and Baiturrahman sub-district (4).The results of the data from the above map were presented in Table 2.The spatial weighted matrix is formed according to Figure 2. The neighboring districts are assigned a value of 1, and the non-neighboring districts are given a value of 0.

Global spatial auto-correlation
Global spatial auto-correlation is done to find out whether there is a spatial relationship between the sub-districts for adolescent anemia cases in Banda Aceh city.This test is

Proceedings of MICoMS 2017
performed by Moran's I test on equation ( 9).Based on testing using software R (Appendix 3, part 2), Moran's I score for adolescent anemia is -1.2163 ( p-value 5 0.2239 means p-value> a 5 0.05).This figure indicates that there is no spatial relationship between sub-districts in Kota Banda Aceh for anemia cases in adolescents.This means that each adjacent subdistrict in Kota Banda Aceh has no similarity to cases of anemia in adolescents.
Based on Table 3, there is no single sub-district in Banda Aceh city that has spatial autocorrelation.This is indicated by the value of p-value > a 5 0.05.That is, no sub-districts are actually affected by neighboring areas in the case of anemia in adolescents in Banda Aceh city (Table 4).The prevalence of malnutrition and under-nutrition in infants on the island of Sumatra is still quite alarming.There are still some districts/cities with prevalence rates above the national prevalence rate (19.6%) and above the WHO standard rate (30%).That is, nutritional problems of children under five in Sumatra are quite serious (Draper & Smith, 2014).The spread of malnutrition and malnutrition prevalence in under-fives in eight provinces of Sumatra Island can be seen in Figure 3.
3.3.2.Spatial weighted matrix.Based on the distribution of malnutrition prevalence, Figure 4 shows a spatial weighted (W ) matrix of 125 Â 125.The method is used to determine the nearest neighbor k.In this study using the k-nearest neighbor's method, that is the method with the distance approach in equation ( 6).Given the wide coverage of the island of Sumatra, the nearest k number of k selected is k 5 4 using trial and error, for k 5 4 means   5.
The independent variables are divided into three categories, namely health under-five children, maternal health, and environmental health.The health of children under one of the sample distribution profiles can be seen in Figure 5.As representative, underweight infants and early breastfeeding treatment (IMD) are still approximately 40% located in the regency/ municipality of Sumatra Island.Similarly, the maternal health profile shows that the constipation visits of complete pregnant women (K4) is still low (<30.9%)(Kesuma & Chongsuvivatwong, 2015).Furthermore, the family planning program is still uneven in North Sumatra Island.This is indicated by the number of districts with a low percentage of family planning (<5%), and even the highest percentage is only 36.21% (<50%) (Kesuma & Chongsuvivatwong, 2016).With regard to the health of the environment, access to clean  The spatial regression model consists of three models, namely the spatial autoregressive model (SAR), the spatial error model (SEM), and SARMA.However, other models can be used, such as the Lagrange multiplier test and the result of the Lagrange multiplier test.The SAR model for malnutrition and malnutrition cases in infants on the island of Sumatra can be written according to the following equation: j¼1;j6 ¼i w ij y j þ 0; 139X 9 À 0; 370X 10 À 0; 136X 11 À 0; 254X 12 (3) where y i 5 prevalence of malnutrition and under-nutrition in under-fives in the 1st district/ city for i 5 1, 2, ..., 125.Yj is the prevalence of malnutrition and under-five nutrition in the junior districts / cities that are neighboring region i where j 5 1, 2, ..., 125 and j = i.X9 is a prevalence of chronic energy deficiency in women of child-bearing age.X10 is the proportion of KB users, X11 is the percentage of households with PHBS, X12 is the coverage of access to clean water, wij is a 125 Â 125 spatial weighted matrix and value r 5 0.24355.

Conclusion
From the result, the calculation in Table 5 shows that four independent variables significantly spatially influence to the second case that is malnutrition and malnutrition prevalence in under-fives using a 5 0.05, that is chronic energy deficiency prevalence in woman of child-bearing age (X9), proportion of family planning (X10), percentage of households with PHBS (X11), and coverage of access to clean water (X12).
Figure 1.Anemia Catches Tematic Map in Banda Aceh Figure 2. Map of Neighboring Relationships between Districts Figure 3. k-Nearest Neighborhood Location Figure 4. Prevalence Distribution of Poor Nutrition and Nutrition less in Sumatera Island
Figure 5. Plot of Moran Directions Value of Standards of Sumatra Island

Table 5 .
access in 125 regencies/cities of Sumatra Island is 97%, and the average coverage of sanitation access on the island of Sumatra is 55.41%. water