The Implementation of Nonlinear Principal Component Analysis to Acquire the Demography of Latent Variable Data (A Study Case on Brawijaya University Students)

Solimun Solimun,Retno Ayu Cahyoningtyas,Adji Achmad Rinaldo Fernandes

doi:10.13189/ms.2020.080410

Abstract

Nonlinear principal component analysis is used for data that has a mixed scale. This study uses a formative measurement model by combining metric and nonmetric data scales. The variable used in this study is the demographic variable. This study aims to obtain the principal component of the latent demographic variable and to identify the strongest indicators of demographic formers with mixed scales using samples of students of Brawijaya University based on predetermined indicators. The data used in this study are primary data with research instruments in the form of questionnaires distributed to research respondents, which are active students of Brawijaya University Malang. The used method is nonlinear principal component analysis. There are nine indicators specified in this study, namely gender, regional origin, father's occupation, mother's occupation, type of place of residence, father's last education, mother's last education, parents' income per month, and students' allowance per month. The result of this study shows that the latent demographic variable with samples of a student at Brawijaya University can be obtained by calculating its component scores. The nine indicators formed in PC1 or X1 were able to store diversity or information by 19.49%, while the other 80.51% of diversity or other information was not saved in this PC. From these indicators, the strongest indicator in forming latent demographic variables with samples of a student of Brawijaya University is the origin of the region (I2) and type of residence (I5).

Highlights

Multivariate analysis is one type of statistical analysis that simultaneously analyzes multiple variables on an individual or object [1]
The Nonlinear Principal Component Analysis used in this research has a mixed scale that comprises of nominal, ordinal, and ratio measurement scales
Based on the findings achieved, the conclusion is the data of demographic latent variables with mixed scales using students of Brawijaya University as the sample can be acquired by calculating the principal component score through the Nonlinear Principal Component Analysis

Summary

Introduction

Multivariate analysis is one type of statistical analysis that simultaneously analyzes multiple variables on an individual or object [1]. By using the multivariate analysis, the influence of several variables toward other variables can be done simultaneously for each object of research [5]. Based on the measurement process, variables can be categorized into manifest variables (observable) and latent variables (unobservable) [2][3]. Latent variables are defined by the variables that cannot be measured directly, yet those variables must be through the indicator that reflects and constructs it [11]. Demography is research regarding the human population in a particular area, especially about the composition of a community and its development [10]. [10] To measure the data of latent variables using the formative indicator model, it can be used primary component score acquired through the Principal Component Analysis The indicator model that forms or constructs the variables is known as the formative indicator model wherein this indicator model that constructs it is not obliged to have common factors [7]. [10] To measure the data of latent variables using the formative indicator model, it can be used primary component score acquired through the Principal Component Analysis

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