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3 AN OVERVIEW OF MULTIVARIATE DATA ANALYSIS AND ITS APPLICATION Steph Subanidja* A first literature of multivariate object under investigation. Moreover, data analysis was published almost 20 any simultaneous analysis of more than years ago. Recently, it has been two variables can be loosely considered becoming a comprehensive method to multivariate analysis. What kinds of data analyze complex data and multiple should be analyzed by using multivariate correlations among variables. As an analysis? improvement of some software packages There are two basic kinds of in a computer program, researchers and data: non-metric for qualitative data and decision makers, become easier to metric for quantitative data. Non-metric analyze the complex data and data are attributes, characteristics or phenomena accurately. categorical data. Non-metric The computer technology has measurements can be made with either a made possible extraordinary advances in nominal or an ordinal scale. Nominal the analysis of, for example, scales, also known as categorical scale, sociological, psychological and other provide the number of occurrences in types of behavioral data. Almost any each class or category of the variable research problem is easily analyzed by being studied. Ordinal scales, on the any number of statistical programs on other hand, are the next higher level of microcomputers. measurement precision. Variables can be This article tries to know, at a ordered or ranked with ordinal scales in glance, what are multivariate data relation to the amount of the attribute analysis and its application on research possessed. activities. Metric measurement can be made with either interval or ratio scales. The What is Multivariate Analysis? most familiar interval scales, for Multivariate analysis is not easy example, are the Fahrenheit and Celsius to define. However, some experts in the temperature scales. Each has a different area of data analysis, such as Hair, arbitrary zero point, and either indicates Anderson, Tatham and Black, said that a zero amount or lack of temperature broadly speaking, multivariate analysis because we can register temperatures refers to all statistical methods that below the zero point on each scale. Ratio simultaneously analyze multiple scales represent the highest form of measurements on each individual or measurement precision because they An Overview of Multivariate Data Analysis ….. (Steph Subanidja) 4 possess the advantages of all lower scales plus an absolute zero point. The objective of the multiple regression analysis is to predict the changes in the Application of Multivariate Data dependent variable in response the Analysis (MDA) change in the independent variables. So, There are at least 11 applications it is suggested, do not using the of MDA, namely 1) principal regression, if you do not want to predict components and factor analysis, 2) the changes in the dependent variable. multiple regressions and correlations, 3) Multiple discriminant analysis multiple discriminant analysis, 4) (MDA) is the appropriate multivariate multivariate analysis of variance and technique if the single dependent covariance, 5) conjoint analysis, 6) variable is dichotomous such as male- canonical correlation, 7) cluster analysis, female or multichotomous such as high- 8) multidimensional scaling, 9) medium- low. Therefore, the dependent correspondence analysis, 10) linear variable is non-metric scale. The primary probability models and 11) structural objectives of MDA are to understand equation modeling. group differences and to predict values Principal components and factor of group based on several metric analysis are a statistical approach that independent variables. So, the equation can be used to analyze interrelationships of MDA is: among a large number of variables. This approach is appropriate to analyze, for y (for non-metric scale) = f (X1, X2, …, example, market segmentation. So, we Xn ) for non-metric scale. have independent variable with a large number of indicators or factors, with Multivariate analysis of variance either nominal, ordinal, interval or ratio (MANOVA) is a statistical technique to scales. simultaneously explore the relationship Multiple regression is between several categorical independent appropriate method to analyze a single variables and two or more metric metric dependent variable related to two dependent variables. The mathematical or more metric independent variables. equation of MANOVA is: By using mathematical equation, the regression is: y1 + y2 + … + yn (for metric scale) = X1 + X2 + …+ Xn (for non-metric scale). y (for metric scale) = f (X1, X2, …, Xn) for metric scale. Ingenious, Vol. 1, No. 1, August 2003: 3 - 6 5 Whereas, multivariate analysis of of mutually exclusive groups based on covariance (MANCOVA) can be used to the similarities among the entities that is remove the effect of any uncontrolled individuals or objects. metric dependent variables toward the Multidimensional scaling (MDS) dependent variables. ANOVA, is usually used to transform consumer furthermore, represents a single metric judgments or similarity or preference dependent variable based on several into distances represented in non-metric independent variables. multidimensional space. MDS is also Conjoint analysis is the called as perceptual mapping of the relationship between a single non-metric similarities. dependent variable and several non- Correspondence analysis (CA) is metric independent variables. The a special form of MDS. In the basic mathematical function as follows form, CA employs a contingency table, which is a cross-tabulation of two y (for non-metric or metric scale) = X1 + categorical variables. It provides a X2 + …+ Xn (for non-metric scale). multivariate representation of interdependence for non-metric data that Canonical correlations analysis is not possible with other methods. can be viewed as a logical extension of Linear probability models, which multiple regression analysis in order to often referred to as logit -analysis, are a correlate simultaneously several metric combination of multiple regressions and or non-metric dependent variables and multiple discriminant analysis. The several metric or non-metric independent technique to analyze the data is similar variables. So that the equation of the to multiple regression analysis. relationship of the canonical correlation Structural equation modeling is: (SEM), often called as LISREL (the name of one of software packages), is a y1 + y2 + … + yn (for metric and non technique that allows separate metric scale) = X1 + X2 + …+ Xn (for relationship for each of a set of metric and non-metric scale). dependent variables. There are two basic component of SEM: the structural model Cluster analysis is a statistical and the measurement model. The technique to develop meaningful structural model is usually called as the subgroups of individuals or objects. The Path Analysis model, which relates objective of cluster analysis is to classify independent to dependent variables. a sample of entities into a small number Whereas, measurement model allows to An Overview of Multivariate Data Analysis ….. (Steph Subanidja) 6 use several variables for a single independent or dependent variables. The mathematical equation of the SEM is shown as follows: y1 = X11 + X12 + …+ X1n y2 = X21 + X22 + …+ X2n …………………………. Ym = Xm1 + Xm2 + …+ Xmn Variable y is for metric scale and variable X for both metric and or non- metric scale. From the information above, it can be seen that multivariate data analysis is a comprehensive method of a statistical technique to analyze relationship among variables. The types of the techniques can be used for almost all relationships based on the objectives of the researchers or decision makers. So, the problem is, now, not how to analyze the data, but how to construct the relationship among variables based on the exploring some literatures or phenomena such as journals, books, studies, or researcher’s managerial experiences. * is now a doctorate student of University of Padjadjaran Bandung Ingenious, Vol. 1, No. 1, August 2003: 3 - 6