Influence of overweight and obesity on the diabetes in the world on adult people using spatial regression

Diabetes, obesity, and overweight are now a staggering global burden and are approaching the scale of other forms of malnutrition. The prevalence of adult overweight, obesity, and diabetes is rising for every region and nearly every country. Based on data World Health Organization in the Global Nutrition Report 2015 [1] showed that an increasing number of people with Obesity, Overweight, and Diabetes in the world.


I. Introduction
Diabetes, obesity, and overweight are now a staggering global burden and are approaching the scale of other forms of malnutrition.The prevalence of adult overweight, obesity, and diabetes is rising for every region and nearly every country.Based on data World Health Organization in the Global Nutrition Report 2015 [1] showed that an increasing number of people with Obesity, Overweight, and Diabetes in the world.
A regression modeling analysis to determine the factors that affect the rate of diabetes that influenced by the characteristic of region is important.In some cases, the response variable that observed has associated with observations in different areas, especially area that adjacent.The presence of spatial relationships in the response variable will cause estimation becomes inaccurate because the assumption of randomness an error is violated.To resolve these problems required a regression model that insert the spatial relationships between regions into the model.The presence of spatial relationships among area led to any spatial diversity into the model, so that the models were used is the regression model spatially.Some methods have been developing are Spatial Autoregressive Model (SAR), Spatial Error Model (SEM), and Spatial Autoregressive Moving Average (SARMA).SAR, SEM, and SARMA are based on the effects of spatial lag and spatial error by using the approach area.The fundamental component from spatial model is spatial weighting matrix, this matrix reflects the relationship between a region with other regions [2].In this research, the spatial weighting matrix that used is a spatial weighting Queen.
Based on the above, this research is solved using spatial regression with Spatial Autoregressive Model (SAR) and Spatial Error Model (SEM) to determine the factors that influence diabetes worldwide.

II. Literature Review
The regions are usually interrelated because of their proximity [3].The similar performances in healthy field are usually attributed to their location.The spatial auto-correlation in the geographic approach is taken into account in the new healthy models used to forecast healthy issues.Therefore, the spatial approach is not important only for analyzing the economic and social phenomena, but also for the policy decisions [4], such as looking for the factors that influencing the poverty status of districts in Java island for making government easier to prioritized the appropriate disctrict based on current condition [5].
According to the Indonesia's Endocrinologist Association (PERKENI) diagnostic criteria in 2015 [6], to suffer from diabetes if have fasting blood glucose levels > 126 mg/dL and at 2 hours after ate (postprandial) > 200 mg/dL.Blood glucose level varies for every individual every day where the number of blood glucose content will increase after the individual eat and will return to normal within 2 hours after eat.In normal condition, approximately 50% of glucose from food eaten will have perfect metabolism into carbon dioxide (CO2) and water, 10% into glycogen and 20% to 40% is converted into fat.In people with diabetes mellitus, all metabolic process disrupted by deficiency of insulin.The absorption of glucose into the cells decreased and the metabolism disturbed.This condition causes most of glucose remains in the blood circulation, causing hyperglycemia.
Obesity can be defined as excess body fat.The determinant that used is Body Mass Index (BMI).Whereas Overweight is stage before clinically obese.Based on WHO criteria [7], underweight was identified as BMI < 18.5 kg/m2, overweight as BMI 25.0-29.9kg/m2, and obese as BMI ≥ 30.0 kg/m2.According to WHO [7], body mass index (BMI) is the calculation of number from a person's weight and height.BMI obtained from the weight in kilograms divided by the square from height in meters (kg/m2).The value of the BMI in adults does not depend on age or sex.However, BMI may not correspond to the degree of obesity in different populations, due to differences in their body proportions.

III. Material and Methodology
The data that used in this research is secondary data that obtained from The 2016 Global Nutrition Report from WHO [8].The data that obtained is data distribution of adult patients with Diabetes, Overweight, and obesity in 190 countries around the world in 2015.The data were collected through survey taken from each country.
In this research there are one dependent variable and two independent variables Diabetes (y), Overweight (xoverweight), and Obesity (xobesity).
We started the research by looking for the classic regression model, the general model of spatial regression equation [9], [10] stated on (1) and (2).
where Y is response variable matrix (n x 1), X for independen variable matrix (n x (p+1)), β for coefficients vector parameter regression (p+1)x1, spatial lag coefficient autoregression stated with ρ, λ for autoregression lag coefficient in error valued | λ | < 1, μ for vector error that assumed contain autocorrelation sized n x 1, ε for vector error sized nx1, normal distribution with mean zero and variance σ2I, W is spatial weighting matrix sized n x n, and number of observations / location stated with n.
There are several types of Spatial Weight (W): binary W, uniform W, invers distance W (non uniform weight) and and some W from real case of economics condition or transportation condition from the area.Binary weight matrix has values 0 and 1 in off-diagonal entries; uniform weight is determined by the number of sites surrounding a certain site in ℓ-th spatial order; and non-uniform weight gives unequal weight for different sites.The element of the uniform weight matrix is formulated as, ) is the number of neighbor locations with site-i in ℓ-th order.The non-uniform weight may become uniform weight when some conditions are met.One method in building non-uniform weight is based on inverse distance.The weight matrix of spatial lag k is based on the inverse weights 1/(1+d_ij ) for sites i and j whose Euclidean distance  lies within a fixed distance range, and otherwise is weight zero.Kernel Gaussian Weight follow this formulla : with d is distance between location i and j, then b is bandwith which is a parameter for smoothing function [5].
The models that have been obtained is then performed selecting best model.Selection of best model is done to get the most supportive factor of research.The criteria for selection of best model used is Akaike's Information Criteria corrected (AICc).

IV. Results and Discussion
Fig. 1 shows the mapping that rates of diabetes most occurred in middle eastern areas.Based Conditional Map of Diabetes, Overweight, and Obesity (Fig. 2) in 190 Countries rates of Diabetes, Overweight, and Obesity many occur in the Northern Hemisphere and Australia.While at least in the region of Southeast Asia and each country in Africa.Based on Table 1, there is one variable that have significant influence to the response variable (Diabetes) that is obesity.So variable that affects the number of adult people with diabetes from overweight and obesity is obesity.

Fig. 3 .
Fig. 3. Moran's I index of diabetes rate in 190 counties However, a strong spatial auto-correlation can be observed between the diabetes rate in 2015 in 190 counties compared to the values for obesity and overweight.A bivariate Moran's I index of 0.514 for obesity (Fig. 4(a)) and 0.585 for overweight confirms a strong positive spatial autocorrelation (Fig. 4(b)).

Fig. 4 .
Fig. 4. Bivariate Moran's I index of diabetes, overweight, and obesity rate in 190 counties