Heteroscedasticity Detection in Cross-Sectional Diabetes Pedigree Function: A Comparison of Breusch-Pagan-Godfrey, Harvey and Glejser Tests

Omotayo Oluwatosin ILORI1*, & Fatai Olalekan TANIMOWO2
1,*Department of Mathematics and Statistics, Austin Peay State University, Clarksville, Tennessee, USA.
2Department of Mathematics and Statistics, Austin Peay State University, Clarksville, Tennessee, USA.
DOI – http://doi.org/10.37502/IJSMR.2022.51211

Abstract

Diabetes is a serious defect that does not make the body to have enough insulin, and thereby allowing blood sugar to stay in the bloodstream more than the body requires and over time causes serious problems relating to health. So, predicting if a person has diabetes or not using the linear model surface, but a major challenge arises if there is heteroscedasticity in the model, which can make the least square estimates inefficient. So, there is a need to know the method that is best for detecting heteroscedasticity so as not to rely on inefficient model for predicting diabetes. This research therefore aimed at comparing the Breusch-Pagan-Godfrey (BPG), Harvey and Glejser tests for detecting heteroscedasticity in cross-sectional data. To achieve this, data were collected on Diabetes Pedigree Function (DPF), Plasma glucose concentration a 2 hours in an oral glucose tolerance test (G), 2-Hour serum insulin (mu U/ml) (I), and Triceps skin fold thickness (mm) (S) from National Institute of Diabetes and Digestive and Kidney Diseases (1990) comprising 768 observations. The data was divided into two, small sample and large sample. The result of the regression analysis showed that skin fold thickness is the most important factor that can predict diabetes in a patient, followed by plasma glucose concentration, and then by insulin. The result for heteroscedasticity showed that, heteroscedasticity is not present in small dataset using the three tests. However, for the large sample, both the Breusch-Pagan-Godfrey and Glejser detect heteroscedasticity, but Harvey did not. Hence, it is advisable to use either Breusch-pagan or Glejser tests because they are more sensitive to heteroscedasticity in diabetes patient data.

Keywords: Cross-sectional, Diabetes pedigree function, Heteroscedasticity, Ordinary Least square, Residual.

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