Multivariate Statistics: How Variables are Related to Each Other? (Research Paper Sample)

Multivariate Statistics
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Multivariate analyses are that part of statistics that deals with the observation made on many variables. The prime purpose is to study how variables are related to each other. As a result, multivariate analyses can predict the results when one of the variables changes. There are several multivariate techniques used in business. However, this article will focus only on three – factor analysis. Cluster analysis and multidimensional scaling.
Factor analysis is a statistical technic used in reducing the number of variables to a set of elements. It is an independent technique in that there is no dependent variable. Rather, while using this technique, the researcher looks at the underlying structure of the data matrix. Usually, the independent variables are continuous and normal loading into one factor. Multicollinearity is preferred between the variables. This is mainly because correlations are key to data reduction. An MSA of 90 and above is good while that below 50 is considered poor.
There are two-factor analysis methods – principle concept analysis and common factor analysis. The later derives factors based on the variance shared by them. The former on the other hand, derives elements based on the total variance. Principle concept analysis is used to look for the least number of variables that explains the highest variance. The first factor extracted explains the most variance. Common factor analysis is used to find the underlying factors.
There are several ways in which factor analyses can be applied. Firstly, during advertising. This method can be used to analyze and better comprehend media habits over various customers. Factor analysis is also used in pricing. This is where it helps establish various traits of prestige – sensitive and price – sensitive consumers. Furthermore, it is used in distribution, where it can be employed to determine channel selection criteria among distribution channel members. Finally, it can be used in product analyses. This is where brand attributes that influences customer choice are identified.
The benefits of factor analyses include the feasibility of perpetual maps, a more concise representation of the marketing situation thus enhanced communication, and the fewer number of questions that may arise in future surveys. There are disadvantages as well for this technique. Firstly, it is usually difficult to decide on how many factors to include. There are several methods of determining this, and there is little agreement as to which is best. The other con is where it becomes difficult to tell if the factors that emerge reflect the data or are simply part of the power of factor analysis to find patterns.
The other technique is cluster analysis. Its primary purpose is to reduce a large data set to meaningful subgroups of objects or individuals. The division is achieved from the similarity of the objects across a set of specified features. The main problem with this technique is outliers. Too many inconsistent variables often cause These. The sample should be one that is representative of the whole population. Uncorrelated factors are desirable.
There are three main clustering methods – hierarchical, none – hierarchical and a combination of both. The hierarchical approach is like a tree process, appropriate for small sets of data. Non – hierarchical needs specification of the number of clusters. This technique has four rules for determining and developing clusters. They are: clusters ought to be reachable, they should be measurable, should be different and the clusters should be profitable. The technique is best for market segmentation (Noh, Ghouch, & Van Keilegom, 2014).
There are several applications of cluster analysis. The method can be used to identify hidden patterns and structures in the data without formulating a particular hypothesis. Clustering is also performed to determine similarities to specific dimension or behavior. In other cases, it can be used to discover structures in data without providing explanations or interpretations. This is simply recognizing patterns of data without explaining where they exist.
This multivariate technique has its advantages. Firstly, it is very flexible and responds to the shifting of a marketplace. Cluster analyses help businesses and companies direct their recruiting efforts and economic development. Businesses understand that the best way to expand their economies and those of the surrounding region is to support a cluster of firms rather than to try to attract companies one at a time to an area. Cluster analyses also help attract foreign investments.
The disadvantages of this technique are mainly associated with the hierarchical cluster analysis. The drawback comes in when it different partitions result into different final groups. The fact that this method can be used to discover structures in data without providing interpretations is a limitation.
Multidimensional scaling is a technique that transforms consumer judgments of similarity into distances represented in multidimensional space. The approach in this technique is decompositional and uses perennial mapping to present the dimensions. It is essential in examining unknown aspects about products and in revealing comparative evaluations of goods when the basis for comparison is unrecognized. There must be at the very least four times as many objects being evaluated as dimensions (Barakat, 2009).
Typically, the pairing comparison is used. This is where the objects with nonmetric preference rankings or metric similarities ratings are evaluated. A stress percentage of over 20 is usually a poor fit while that of 0 percentage is a perfect fit. The dimensions can be interpreted objectively or subjectively. The former is where t...