**Introduction**

First, let us understand what multivariate analysis is. In multivariate analysis (MVA), numerous variables (more than two) are analysed to find any potential relationships between them. By examining every potential independent variable and how it relates to other independent variables, the multivariate analysis provides a more thorough interpretation of the data. In this blog, we are going to describe multivariate analysis in depth along with using and analysing it in a PhD research.

**Defining Multivariate analysis**

In a broad sense, multivariate analysis refers to a group of statistical techniques used to examine many datasets at once. The goal of multivariate analysis is to use various statistical techniques to apply and interpret the inherent structure and meaning that are revealed within large collections of variables.

When using a multivariate technique, two important considerations must be made: the data matrix's multidimensionality and the goal of maintaining its intricate structure. This is predicated on the idea that because the variables are connected, only a set of the same test may give a more comprehensive picture of the topic being researched while gathering data that univariate and bivariate statistical approaches cannot. Let me give you an example to simplify multivariate analysis.

An investigation is being conducted to identify potential causes of a medical illness, such as heart disease. Data on age, height, weight, serum cholesterol, phospholipids, blood glucose, nutrition, and many other potential determinants are gathered from a preliminary survey of healthy guys. These boys' medical histories are monitored in order to ascertain whether and when they might be given a heart disease diagnosis.

**Figure 1: Multivariate analysis**

**Using multivariate analysis in PhD research**

The multivariate technique is being used in 8 factors in a PhD research such as cluster analysis, discriminant analysis, factor analysis, CHAID, regression analysis, correspondence analysis, structural modelling of equations and statis. The types of analysis are described below:

*Cluster analysis - *

It is a technique used for categorising distinct groupings of cases that are connected. Another use is to depict groups of related cases in a data compilation. Dissection is the name of this cluster analysis method.

*Discriminant analysis - *

It is a statistical technique used to group exhaustively and mutually exclusive individuals or things based on a set of independent factors.

*Factor analysis -*

It is a Statistical approach used to explain the variability between studied variables in terms of a possibly smaller set of unknown variables that are referred to as factors."

*CHAID - *

It is a form of decision tree strategy that is based on the Bonferroni testing approach to adjusted significance testing.

*Regression analysis - *

It refers to any techniques for modelling and examining multiple variables where the emphasis is on the link between a dependent variable and one or more independent variables.

*Correspondence analysis - *

The process of creating visual representations of interactions between the modalities (or "categories") of two categorical variables.

*Structural modelling of equation -*

Using a combination of statistical information and qualitative causal hypotheses, structural equation modelling (SEM) is a statistical technique for testing and estimating causal links.

*Statis -*

When at least one three-way table dimension is shared by all tables, Statis is used. The method's initial step involves doing a PCA on each table and creating a table that compares the units in each table.

**Capabilities and limitations of multivariate analysis in PhD research**

**Figure 2: Regression of Multivariate analysis**

**Capabilities**

Researchers can use multivariate techniques to quantify the link between variables and examine relationships between variables in a broad sense. Cross tabulation, partial correlation, and multiple regressions can be used to control the association between variables, and they can also introduce new variables to establish the relationships between the independent and dependent variables or to define the circumstances under which the association occurs. Multivariate analysis has the benefit of providing a more accurate image than single variable analysis. Comparatively to univariate procedures, multivariate techniques offer a strong test of significance.

**Limitations **

A statistical programme is needed to examine the data using multivariate approaches because they are intricate and involve advanced mathematics. It can be expensive for an individual to purchase these statistical applications. The fact that the results of statistical modelling are not always simple for students to understand is one of the main drawbacks of multivariate analysis. Large samples of data are required for multivariate approaches to produce conclusions that are relevant; otherwise, results with high standard errors are useless. The level of confidence in the results is determined by the standard errors, and the results from a large sample can be trusted more than those from a small sample. Although running statistical algorithms is pretty simple, understanding the data requires statistical training.

**Conclusion**

Finally, we can conclude that multivariate analysis is helpful to examine datasets and also to make relationships between them. The different uses of multivariate analysis have been described along with a critically analysing of its limitations and capacities of it. We, at Regent Statistics, provide you with high-quality PhD dissertations at an affordable price that covers all your needs.