Multivariate Analysis

Inhaltsverzeichnis

1. Frontmatter

2. 1. Introduction to Empirical Data Analysis

   Klaus Backhaus, Bernd Erichson, Sonja Gensler, Rolf Weiber, Thomas Weiber

   Abstract

   This chapter introduces, characterizes and classifies the eight methods of multivariate data analysis (MVA) covered in this book. When using MVA, several variables are considered simultaneously and their relationship is analyzed quantitatively. MVA aims to describe and explain these relationships or to predict future developments. Bivariate analyses that consider just two variables at a time are a special case of MVA. However, reality is usually much more complex and requires the consideration of more than just two variables. Furthermore, this chapter presents the fundamentals of empirical data analysis that are relevant to all methods discussed in the book. Since most readers will be familiar with these basics, these presentations serve primarily as a repetition or as an opportunity to look up important aspects of quantitative data analysis, such as basic statistical concepts (e.g. mean, standard deviation, covariance), the difference between correlation and causality, and the basics of statistical testing. Finally, the handling of outliers and missing values is discussed and the statistical package IBM SPSS Statistics, which is used in this book, is briefly introduced.

3. 2. Regression Analysis

   Klaus Backhaus, Bernd Erichson, Sonja Gensler, Rolf Weiber, Thomas Weiber

   Abstract

   Regression analysis is one of the most flexible and most frequently used multivariate methods. It is employed to analyze relationships between a metrically scaled dependent variable and one or more metrically scaled independent variables. In particular, it is used to describe relationships quantitatively and to explain them. As a result, we can estimate or predict values of the dependent variable. Regression analysis is of eminent importance for science and practice.

4. 3. Analysis of Variance

   Klaus Backhaus, Bernd Erichson, Sonja Gensler, Rolf Weiber, Thomas Weiber

   Abstract

   Analysis of variance is a procedure that examines the effect of one (or more) independent variable(s) on one (or more) dependent variable(s). For the independent variables, which are also called factors or treatments, only a nominal scaling is required, while the dependent variable (also called target variable) is scaled metrically. The analysis of variance is the most important multivariate method for the detection of mean differences across more than two groups and is thus particularly useful for the evaluation of experiments. The chapter deals with both the one-factorial (one dependent and one independent variable) and the two-factorial (one dependent and two independent variables) analysis of variance and extends the considerations in the case study to the analysis with two (nominally scaled) independent factors and two (metrically scaled) covariates. Furthermore, contrast analysis and post-hoc testing are also covered.

5. 4. Discriminant Analysis

   Klaus Backhaus, Bernd Erichson, Sonja Gensler, Rolf Weiber, Thomas Weiber

   Abstract

   Discriminant analysis is a multivariate procedure for the analysis of group differences. It allows examining the difference between two or more groups with respect to a variety of variables in order to answer questions such as: Do the considered groups differ significantly from each other with respect to the variables? Which variables are suitable or unsuitable for distinguishing between the groups? While the analysis of group differences serves primarily scientific purposes, the determination or prediction of the group membership of new elements (classification) is of direct practical relevance. The question then is: Which group does a ‘new’ observation belong to based on its describing variables? The chapter describes discriminant analysis for cases with two or more groups.

6. 5. Logistic Regression

   Klaus Backhaus, Bernd Erichson, Sonja Gensler, Rolf Weiber, Thomas Weiber

   Abstract

   In many problems in science and practice, the following questions arise: Which one of two or more alternative states is present or which event will occur? Which factors are suitable for the decision or prognosis and what influence do they have on the occurrence of a state or event? Often, only two alternative states or events are involved, as in the question whether a patient has a certain disease or not. Logistic regression can be used to answer such questions. The logistic regression is similar to discriminant analysis with regard to the problem definition. The main difference between the two methods is that logistic regression directly provides probabilities for the occurrence of the alternative states or the affiliations to the individual groups.

7. 6. Contingency Analysis

   Klaus Backhaus, Bernd Erichson, Sonja Gensler, Rolf Weiber, Thomas Weiber

   Abstract

   Contingency analysis is used to detect and investigate relationships between nominally scaled variables. Typical examples are the investigation of associations between income class, profession or gender and consumer behavior, or the examination of whether the level of education or the family background (social class) is associated with the membership in a particular political party. Questions arising in this context may include: Is there a significant association between the variables? Is it possible to make a statement about the strength or even the direction of the association? This chapter describes contingency analysis for the simple 2 × 2 case as well as for larger cross tables. Furthermore, the role of confounding variables is discussed.

8. 7. Factor Analysis

   Klaus Backhaus, Bernd Erichson, Sonja Gensler, Rolf Weiber, Thomas Weiber

   Abstract

   The explorative factor analysis is a procedure of multivariate analysis which aims at identifying structures in large sets of variables. Large sets of variables are often characterized by the fact that as the number of variables increases, it may be assumed that more and more variables are correlated. The exploratory factor analysis aims to structure the relationships in a large set of variables to the extent that it identifies groups of variables that are highly correlated with each other and separates them from less correlated groups. The groups of highly correlated variables are called factors. Apart from the structuring function, factor analysis is also used for data reduction. At the end of the chapter, there is also a brief outlook on confirmatory factor analysis, in which predefined factor structures are examined.

9. 8. Cluster Analysis

   Klaus Backhaus, Bernd Erichson, Sonja Gensler, Rolf Weiber, Thomas Weiber

   Abstract

   Cluster analysis is a procedure for grouping cases (objects of investigation) in a data set. For this purpose, the first step is to determine the similarity or dissimilarity (distance) between the cases by a suitable measure. The second step searches for the fusion algorithm which combines the individual cases successively into groups (clusters). The goal is to combine such cases into groups which are similar with respect to the considered segmentation variables (homogenous groups). At the same time, the groups should be as dissimilar as possible. The procedures of cluster analysis can handle variables with metric, non-metric as well as mixed scales. The focus of the chapter is on hierarchical agglomerative clustering methods, with the single-linkage method and Ward’s method presented in detail. Finally, k-means clustering and _two-step cluster analysis, two partitioning cluster methods, are also explained. These methods offer particular advantages when working with large amounts of data.

10. 9. Conjoint Analysis

    Klaus Backhaus, Bernd Erichson, Sonja Gensler, Rolf Weiber, Thomas Weiber

    Abstract

    The (traditional) conjoint analysis is a procedure for measuring and analyzing consumers’ preferences for specific objects. The test persons evaluate different objects stating their preferences using metric or ordinal scales. The measured preferences are used as proxies for the utility value of an object. The goal of conjoint analysis is to identify the utility contribution of each attribute level that decsribes an object. Conjoint analysis is used in the context of new product development and is a method of multivariate analysis frequently used in practice. This chapter describes both the traditional conjoint analysis and the choice-based conjoint (CBC) analysis.

11. Backmatter