Penerapan Multivariate Adaptive Regression Spline (MARS) Pada Kasus Indeks Pembangunan Manusia di Kawasan Timur Indonesia

Abstract

Human Development Index (HDI) is an important indicator to measure success in effort to build the quality of human life. Multivariate Adaptive Regression Spline (MARS) is a regression approach developed from the Recursive Partitioning Regression (RPR) method and combined with the spline method to produce a model that is continuous on knots. MARS modeling is determined based on trial and error for a combination of basis function (BF), maximum interaction (MI), and minimum observation (MO) to get the value of minimum smoothing parameter. Automatic determination of knots on MARS uses a forward stepwise and backward stepwise algorithm based on minimum Generalized Cross Validation (GCV) values. The results of this study, obtained a combination value of BF = 52, MI = 3, and MO = 2 with a minimum GCV of 0,00049 then the best MARS model is as follows.Y = –1,045 + 0,446*BF1 – 0,592*BF2 + 0,234*BF3 – 0,352*BF4 + 0,218*BF5 – 0,254*BF6 + 0,338*BF7 – 0,304*BF8 – 3,974*BF9 + 0,097*BF13 – 1,267*BF15 – 41,784*BF16 – 1,845*BF18 – 0,519*BF19 – 0,046*BF21 + 1,275*BF23 – 0,006*BF24 – 0,110*BF25 + 0,021*BF26 + 0,153*BF27 + 14,607*BF28 – 9,276*BF30 – 5,335*BF32 – 0,053*BF34 – 0,219*BF35 – 0,111*BF36 + 0,033*BF37 – 0,238*BF38 + 0,037*BF39 – 0,017*BF41 – 0,039*BF42 – 0,632*BF43 + 0,096*BF45 – 0,147*BF46 + 0,070*BF48 + 0,339*BF49 + 0,017*BF50. The factors that influence HDI based on the level of importance in the best MARS model are per capita expenditure (X9), life expectancy (X7), long school expectations (X8), average school length (X6), poverty severity index (X4), percentage of poor people (X5), percentage of per capita expenditure for food (X12), population density per km2 (X1), and percentage of poor people aged 15 years and over do not work (X11).