Ordinary and Canonical Biplots for Province Mapping Based on IPB Students’ Achievement.

Abstract

Biplot is a graphical display of the rows and columns of a data matrix. Ordinary biplot is the biplot that was introduced by Gabriel (1971). The most general method for discrimination among groups using multiple observed variables is canonical variate analysis (CVA). CVA allows us to derive linear combinations that successively maximize the ratio of ‘between-groups’ to ‘pooled within-group’ sample variance. Biplot representation for CVA is called canonical biplot. Ordinary and canonical biplots are multivariate analyses that can be used for mapping of objects. Procrustes analysis is an analysis tool based on the principle of least squares that can be used to measure the maximum similarity of point of configurations through a series of linear transformations of translation, rotation and dilation. Unfortunately, implementation of canonical biplot and goodness of fit of two matrix configurations with Procrustes analysis has not yet been integrated in statistical package program. The objectives of this study are to examine ordinary biplot, canonical biplot and Procrustes analysis; implement the canonical biplot and Procrustes analysis using functional programming techniques; and compare provincial mapping using ordinary biplot analysis with the analysis of canonical biplot based on IPB students’ achievement. As the first result this study, a program has been written using software Mathematica 8.0 to integrate the ordinary and canonical biplot with Procrustes analysis. For implementation purposes, the data used in this study are IPB students’ achievement in 2009/2010 academic year. Province mapping is an important effort to get an overview of relative position of the province compared to other provinces based on students’ academic achievement. The results from Procrustes analysis of the data matrix with its matrix approximation show that in this case the canonical biplot relatively more suitable to be used. The goodness of fit of configuration of ordinary and canonical biplot with Procrustes analysis is relatively high for data, as well as variables and objects, i.e. more than 91%. This means that the results of ordinary and canonical biplot analysis for mapping the province based on TPB IPB students’ achievement showed relatively more similarities than differences. Extreme difference of the object's position (province) of variables is the province of Sulawesi Utara, Jawa Barat, Banten and Sumatera Selatan in ordinary biplot has superior in Bahasa Indonesia and Pengantar Ilmu Pertanian course, whereas the canonical biplot has superior in Bahasa Inggris and Pendidikan Kewarganegaraan course.

Analisis biplot merupakan salah satu bentuk Analisis Peubah Ganda (APG) yang dapat memberikan gambaran secara grafik dari suatu matriks data tentang kedekatan antar objek, keragaman peubah, korelasi antarpeubah serta keterkaitan objek dengan peubah. Biplot biasa yang dipelajari dalam penelitian ini adalah biplot yang diperkenalkan oleh Gabriel (1971), sedangkan biplot kanonik merupakan representasi grafis dari analisis peubah kanonik (APK, Canonical Variate Analysis). APK merupakan analisis data dengan peubah ganda yang berbasis analisis pengelompokan data, digunakan untuk memperoleh kombinasi linear dari peubah-peubah asal yang akan memberikan nilai sedekat mungkin bagi objek-objek dalam kelompok yang sama dan sebesar mungkin bagi objek-objek antarkelompok.