What is Multivariate Data Analysis?

Introduction

 

We have access to huge amounts of data in today’s world and it is very important to analyze and manage the data in order to use it for something important. The words data and analysis go hand in hand, as they depend on each other. 

 

Data analysis and research are also related as they both involve several tools and techniques that are used to predict the outcome of specific tasks for the benefit of any company. The majority of business issues include several factors. 

 

When making choices, managers use a variety of performance indicators and associated metrics. When selecting which items or services to buy, consumers consider a variety of factors. The equities that a broker suggests are influenced by a variety of variables. 

 

When choosing a restaurant, diners evaluate a variety of things. More elements affect managers' and customers' decisions as the world grows more complicated. As a result, business researchers, managers, and consumers must increasingly rely on more sophisticated techniques for data analysis and comprehension. 

 

One of those analytical techniques that are used to read huge amounts of data is known as Multivariate Data Analysis.

 

(Also read: Binary and multiclass classification in ML)

 

In statistics, one might have heard of variates, which is a particular combination of different variables. Two of the common variate analysis approaches are univariate and bivariate approaches. 

 

A single variable is statistically tested in univariate analysis, whereas two variables are statistically tested in bivariate analysis. When three or more variables are involved, the problem is intrinsically multidimensional, necessitating the use of multivariate data analysis. In this article, we are going to discuss:

 

• What is multivariate data analysis? Objectives of MVA.

• Types of multivariate data analysis.

• Advantages of multivariate data analysis.

• Disadvantages of multivariate data analysis.

 

(Recommended read: What is Hypothesis Testing? Types and Methods)

 

Multivariate data analysis

 

Multivariate data analysis is a type of statistical analysis that involves more than two dependent variables, resulting in a single outcome. Many problems in the world can be practical examples of multivariate equations as whatever happens in the world happens due to multiple reasons. 

 

One such example of the real world is the weather. The weather at any particular place does not solely depend on the ongoing season, instead many other factors play their specific roles, like humidity, pollution, etc. Just like this, the variables in the analysis are prototypes of real-time situations, products, services, or decision-making involving more variables. 

 

Wishart presented the first article on multivariate data analysis (MVA) in 1928. The topic of the study was the covariance matrix distribution of a normal population with numerous variables. 

 

Hotelling, R. A. Fischer, and others published theoretical work on MVA in the 1930s. multivariate data analysis was widely used in the disciplines of education, psychology, and biology at the time. 

 

As time advanced, MVA was extended to the fields of meteorology, geology, science, and medicine in the mid-1950s. Today, it focuses on two types of statistics: descriptive statistics and inferential statistics. We frequently find the best linear combination of variables that are mathematically docile in the descriptive region, but an inference is an informed estimate that is meant to save analysts time from diving too deeply into the data.

 

Till now we have talked about the definition and history of multivariate data analysis. Let us learn about the objectives as well.

 

Objectives of multivariate data analysis:

 

1. Multivariate data analysis helps in the reduction and simplification of data as much as possible without losing any important details.

2. As MVA has multiple variables, the variables are grouped and sorted on the basis of their unique features. 

3. The variables in multivariate data analysis could be dependent or independent. It is important to verify the collected data and analyze the state of the variables.

4. In multivariate data analysis, it is very important to understand the relationship between all the variables and predict the behavior of the variables based on observations.

5. It is tested to create a statistical hypothesis based on the parameters of multivariate data. This testing is carried out to determine whether or not the assumptions are true.

 

(Must read: Hypothesis testing)

 

Advantages of multivariate data analysis:

 

The following are the advantages of multivariate data analysis:

 

1. As multivariate data analysis deals with multiple variables, all the variables can either be independent or dependent on each other. This helps the analysis to search for factors that can help in drawing accurate conclusions.

2. Since the analysis is tested, the drawn conclusions are closer to real-life situations.

 

Disadvantages of multivariate data analysis:

 

The following are the disadvantages of multivariate data analysis:

 

1. Multivariate data analysis includes many complex computations and hence can be laborious.

2. The analysis necessitates the collection and tabulation of a large number of observations for various variables. This process of observation takes a long time.

 

(Also read: 15 Statistical Terms for Machine Learning)

 

7 Types of Multivariate Data Analysis

 

According to this source, the following types of multivariate data analysis are there in research analysis:

 

1. Structural Equation Modelling:

 

SEM or Structural Equation Modelling is a type of statistical multivariate data analysis technique that analyzes the structural relationships between variables. This is a versatile and extensive data analysis network. 

 

SEM evaluates the dependent and independent variables. In addition, latent variable metrics and model measurement verification are obtained. SEM is a hybrid of metric analysis and structural modeling. 

 

For multivariate data analysis, this takes into account measurement errors and factors observed. The factors are evaluated using multivariate analytic techniques. This is an important component of the SEM model.

 

(Look also: Statistical data analysis)

 

 

2. Interdependence technique:

 

The relationships between the variables are studied in this approach to have a better understanding of them. This aids in determining the data's pattern and the variables' assumptions.

 

 

3. Canonical Correlation Analysis:

 

The canonical correlation analysis deals with the relations of straight lines between two types of variables. It has two main purposes- reduction of data and interpretation of data. Between the two categories of variables, all probability correlations are calculated. 

 

When the two types of correlations are large, interpreting them might be difficult, but canonical correlation analysis can assist to highlight the link between the two variables.

 

 

4. Factor Analysis:

 

Factor analysis reduces data from a large number of variables to a small number of variables. Dimension reduction is another name for it. Before proceeding with the analysis, this approach is utilized to decrease the data. The patterns are apparent and much easier to examine when factor analysis is completed.

 

 

5. Cluster Analysis:

 

Cluster analysis is a collection of approaches for categorizing instances or objects into groupings called clusters. The data is divided based on similarity and then labeled to the group throughout the analysis. This is a data mining function that allows them to acquire insight into the data distribution based on each group's distinct characteristics.

 

 

6. Correspondence Analysis:

 

A table with a two-way array of non-negative values is used in a correspondence analysis approach. This array represents the relationship between the table's row and column entries. A table of contingency, in which the column and row entries relate to the two variables and the numbers in the table cells refer to frequencies, is a popular multivariate data analysis example.

 

 

7. Multidimensional Scaling:

 

MDS, or multidimensional scaling, is a technique that involves creating a map with the locations of the variables in a table, as well as the distances between them. There can be one or more dimensions to the map. 

 

A metric or non-metric answer can be provided by the software. The proximity matrix is a table that shows the distances in tabular form. The findings of the trials or a correlation matrix are used to update this tabular column.

 

Conclusion

 

From the rows and columns of a database table to meaningful data, multivariate data analysis may be used to read and analyze data contained in various databases. This approach, also known as factor analysis, is used to gain an overview of a table in a database by reading strong patterns in the data such as trends, groupings, outliers, and their repetitions, producing a pattern. This is used by huge organizations and companies. 

 

(Must read: Feature engineering in ML)

 

The output of this applied multivariate statistical analysis is the basis for the sales plan. Multivariate data analysis approaches are often utilized in companies to define objectives.