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

2.1. 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 S₁, S₂, . . . , S_n and area D ⊂ Rd. The random process is shown in n measurements:

And there is a random process {Z (s); s∈D, where D is fixed (nonrandom), but there are random states because it relates to the value of the variables measured in each location. Process Time series {Z (t); - ~ <t <~} for the purple room process is determined by {Z (s, t); s∈D (t), t∈T, where Z, D, T is a geostatistical random beyond the interpolation problem, taking into account the phenomena studied in unknown locations as a set of correlated random variables.

2.2. Modeling of spastic stained pattern data

Spatial stochastic is a widely used tool for describing and analyzing the spatial pattern, i.e. how geographical objects occur and change in a location. It can also compare the pattern of these objects with the pattern of objects found in other locations. Some methods for detecting spatial patterns are quadrant analysis, kernel density estimation (K means), and nearest neighbor distance. These methods only analyze the spread of the location from a point but do not differentiate the point based on its attributes (Fradinata, 2012).

2.3. 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 auto-correlation) 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).

3.1. 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 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:

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Figure 1.

Anemia Catches Tematic Map in Banda Aceh

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).

3.2. 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.

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Figure 2.

Map of Neighboring Relationships between Districts

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.

3.3. 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 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 = 0.2239 means p-value> α = 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 sub-district 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 auto-correlation. This is indicated by the value of p-value > α = 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).

3.3.1. Case of nutrition of under-five children in sumatera Island (Spatial Auto-correlation).

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.

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Figure 3.

k-Nearest Neighborhood Location

3.3.2. Spatial weighted matrix.

Based on the distribution of malnutrition prevalence, Figure 4 shows a spatial weighted (W) matrix of 125 × 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 = 4 using trial and error, for k = 4 means that each district/city will have four nearest neighbors, where the spatial-weighted matrix is formed according to the matrix equation W (5d), and the matrix is not symmetric with the size 125 × 125.

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Figure 4.

Prevalence Distribution of Poor Nutrition and Nutrition less in Sumatera Island

3.3.3. Modeling stochastic for the nutritional status of under-five children.

Beginning with the data of prevalence of malnutrition and underweight nutrition in under-fives with the under-five condition, mother condition, and environmental condition for 125 regency/city profile in Sumatera Island consists of 13 causes (variable) as seen in Table 5.

Table 5.

Lagrange Multiplier Test

Test statistics	Value	P-Value
Lagrange multiplier (SAR)	5.4921	0.0191*
Lagrange multiplier (SEM)	3.0231	0.08208
Lagrange multiplier (SARMA)	5.5067	0.06371

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Figure 5.

Plot of Moran Directions Value of Standards of Sumatra Island

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 water 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%.

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:

(3) y^i=47,157+0,24335 ∑j=1,j≠i125wijyj+0,139X9−0,370X10−0,136X11−0,254X12

where y_i = prevalence of malnutrition and under-nutrition in under-fives in the 1st district/city for i = 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 = 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 × 125 spatial weighted matrix and value ρ = 0.24355.