Understanding Multivariate Statistical Analysis

Multivariate analysis refers to the statistical techniques that simultaneously analyze multiple measurements or objects under research. In this statistical method, the variables must be random and interrelated in a way that their different effects cannot be estimated and interpreted separately. If you are looking for expert guidance on multivariate data analysis, our experts conduct rigorous analysis and apply the advanced features of statistical software such as the Statistical Package of Software Sciences (SPSS) and R to produce accurate and actionable insights.

Multivariate analysis aims to measure, explain, and predict the degree to which variates are related. Variates are a weighted combination of variables. This article begins by describing the types of multivariate analysis methods, giving a comparison of univariate analysis and multivariate analysis, then demonstrates how to build a multivariate model, how to prepare data for analysis, and an example of multivariate analysis.

What is Multivariate Analysis?

Multivariate analysis refers to the statistical techniques used to evaluate the simultaneous relationship that exists between two or more variables/phenomena. Multivariate techniques are among the advanced methods of statistical analysis. Though it involves complex mathematical procedures, our experts perform multivariate analysis using advanced statistical software packages to simplify the analysis process and gain meaningful insights.

Types of Multivariate Analysis

(1). Exploratory Factor Analysis

Exploratory factor analysis is a statistical approach used to analyze the relationship between a large number of variables and then explain these variables based on their common underlying dimensions. This technique aims to condense the information contained in the original variables into smaller factors without losing information. It combines both principal component analysis and common factor analysis.

(2). Cluster Analysis

Cluster analysis is a technique used for developing meaningful groups of individuals or objects under research. It aims to classify a small sample of the objects/participants under study into a smaller number of mutually exclusive groups based on the similarities among them. The data analyst begins by measuring some form of similarity among the respondents to determine how groups exist, then they partition them into groups, and finally, label the variables to determine the composition.

(3). Multivariate Analysis of Variance (MANOVA）

Multivariate analysis of variance (MANOVA) is a technique used to simultaneously explore the relationship between multiple independent variables and two or more dependent variables. It is an extension of the Univariate Analysis of Variance (ANOVA).

The main difference between MANOVA and ANOVA is that ANOVA assesses differences in time and group for one continuous variable, while MANOVA is utilized to assess differences in time or group for multiple continuous variables.

MANOVA is mostly applied in situations where the analyst designs an experimental situation to test a hypothesis regarding the variance in group responses on multiple dependent variables.

(4). Multivariate Regression Analysis

The multivariate regression analysis technique evaluates the linear relationship between a dependent variable and one or more independent variables. It is mainly used to identify risk factors and predict outcomes in a study.

(5). Multivariate Time Series Analysis

Multivariate time series analysis technique involves the analysis of data that consists of multiple independent variables recorded at different times. It is applied when an analyst wants to explain the interactions among a group of time series variables. Each variable can have undergone a different sampling procedure having different numbers of measurements.

Univariate Vs. Multivariate Analysis

Univariate analysis is the analysis of a single variable, while multivariate analysis involves analyzing multiple variables simultaneously. The table below shows the differences between univariate and multivariate analysis.

Get Help Conduct Multivariate Analysis in Research

Our multivariate statistical analysis services offer personalized solutions that enable you to identify associations, differences, and significance in your data set. Our experts are familiar with all the multivariate analysis techniques and apply advanced statistical software to set up complex models and perform statistical analysis of large data sets. In this section, we demonstrate how our experts build a multivariate model and an example.

How to Build a Multivariate Model

The successful completion of a multivariate analysis involves more than the selection of the correct method because issues such as problem definition and results diagnosis must be addressed. Building a multivariate model focuses the analysis on a well-defined research plan and illustrates the process in conceptual terms. This enables the selection of a multivariate technique relevant to the data set. The steps involved in this process are:

Step 1: Define the Research Problem

The model-building process begins by defining the research problem as a simple representation of the relationships being studied. Our data analyst defines the concept and states the research objective. After specifying both factors, the researcher chooses the appropriate multivariate technique based on the measurements of the variables.

Step 2: Develop an Analysis Plan

With the multivariate technique and conceptual model specified, our analyst develops an analysis plan. This comprises the desired sample sizes, required variables, and the estimation procedures. The variables can be metric or non-metric.

Step 3: Evaluate the Assumptions Underlying the Analysis

Before model estimation, our data analysts evaluate the underlying statistical assumptions that may affect the ability to represent multivariate relationships. Some of these assumptions are multivariate normality, linearity, independence of error terms, and equality of variance. All the assumptions must be met to ensure the accuracy of the output.

Step 4: Estimate the Multivariate Model

In the estimation process, our analyst may choose to choose options to meet specific characteristics of the data or make the model fit the data as closely as possible. After estimation, the model is evaluated to confirm whether it identifies the proposed relationship and achieves practical significance. The analyst also determines whether the results are affected by any single small set of factors.

Step 5: Interpret the Variates

Interpreting the variates demonstrates the nature of the multivariate relationship. This step aims to identify evidence in the sample data that can be generalized to the whole population. It is done by examining the estimated coefficients for each variable in the variate.

Step 6:Validate the Multivariate Model

Validating the multivariate model involves assessing the degree of the generalizability of the results. The aim of validating the model is to demonstrate the generalization of the sample to represent the whole population.

Multivariate Analysis Example in Research

A survey was conducted on a group of children in a rescue center to evaluate how three measured variables (height, weight, and middle-upper arm circumference) affect nutritional status. The data analyst also noted the sex of each child and their social class. They used a multivariate analysis technique, MANOVA, to evaluate the relationship between the independent and dependent variables and discover whether the nutritional indicators are based on sex and social class or their interaction.

Summary

Multivariate analysis refers to all statistical techniques that analyze multiple variables under research. It aims to measure, explain, and predict the degree to which a set of variables are related. These statistical techniques are an advanced form of statistical analysis that deals with massive data sets. Examples are exploratory factor analysis, cluster analysis, multivariate regression, and time series analysis.

Suppose you are looking for multivariate statistical analysis services. Our experts offer personalized solutions designed to acquire actionable, meaningful insights. We are available 24/7 to ensure we serve you at any time based on your convenience. Our friendly customer support team takes you through our order process and gives prompt responses to your inquiries. Reach out to our expert data analysts via our live chat today for help with statistical analysis!