# Multivariate Analysis

**Quick definition**

Multivariate analysis (MVA) involves evaluating multiple variables (more than two) to identify any possible association among them.

**Key takeaways:**

- Multivariate analysis offers a more complete examination of data by looking at all possible independent variables and their relationships to one another.
- It helps companies predict future outcomes, improve efficiency, make decisions about policies and processes, correct errors, and gain new insights.
- It builds upon univariate (one variable) analysis and bivariate (two variable) analysis.
- The more a company invests in ensuring quality data collection, the more accurate multivariate analysis will be.

Answers to the following questions were provided in an interview with John Bates, Director of Product Management for Adobe Marketing Cloud.

What is multivariate analysis?

What are different types of multivariate analysis?

Why do companies use multivariate analysis?

How do you conduct multivariate analysis with regression models?

What are the advantages of multivariate analysis?

What are the disadvantages of multivariate analysis?

What is the process of conducting multivariate analysis?

What best practices can companies follow to ensure better multivariate analysis results?

How will multivariate testing change in the future?

## What is multivariate analysis?

Multivariate analysis is a method of gathering multiple sets of data and drawing cause-and-effect conclusions about their constituent parts.

Companies must gather all the relevant data they can to make data-driven decisions. Sometimes that involves taking three or more sets of data into account — and that’s where MVA comes in.

## What are the different types of multivariate analysis?

To classify different types of multivariate analysis, you must first understand if the variables involved are independent or dependent.

Data scientists use certain techniques specifically with dependent variables, and others with independent variables. Identify how many variables you’re testing — dependent versus independent. You’ll then arrive at two families of techniques.

One is the family of dependence methods, which includes predictive analytic models. The other method is based on interdependence.

With each of these techniques, you’re making strong assumptions about both independent and dependent variables up front.

## Why do companies use multivariate analysis?

Conducting multivariate analyses can help companies forecast future opportunities, risks, and demand for products. This helps with investment strategies, business decisions, and setting expectations.

The information you derive from multivariate analysis can also support data-driven decision making (DDDM) and eliminate speculation in terms of corporate policies and processes. Businesses often have large quantities of financial, operational, customer, and purchase data to help inform business decisions based on statistical significance rather than intuition. By relying on this type of analysis, you can decrease your overall risk and chance of failure.

A company may also use MVA to gain new insights. This could include uncovering new customer targets or identifying market patterns that exist during certain times of the year or hours of the day. Without MVA, opportunities might get buried beneath an avalanche of unorganized data.

## Conducting multivariate analysis with regression models

Data scientists can use regression models to prove everyday facts.

For example, to analyze relationships between the wait-time of callers and the number of complaints at a call center.

Regression modeling can help support management decisions, but it can also help identify errors in judgment. A retail store manager may believe that extending shop hours will increase sales, but regression modeling may indicate that increased revenue might not be sufficient to support the rise in operating expenses due to longer working hours.

## What are the advantages of multivariate analysis?

The main advantage of multivariate analysis is that it considers more than one factor in data analysis. It looks at the various independent variables that influence the dependent variable.

The conclusions you draw from MVA are also more likely to be accurate. There will always be errors, but by considering all the possible variables that could influence your data, you are less likely to miss something and make an incorrect assumption.

## What are the disadvantages of multivariate analysis?

Multivariate analysis sometimes requires more complex computations to arrive at an answer, and you must make sure you have enough data for all the variables you’re analyzing. The sort of governance and prep required for MVA is typically much more complex, time consuming, and costly.

Because you're accounting for multiple variables with MVA, you're uncovering the relative influence or impact of one variable on another set of variables. It gives you a better sense of reality.

A simple bivariate correlation model might predict that if a company spends 10 times more money on marketing, they will see a 5% increase in sales. But with MVA, there might be other constraints or factors that play into that, which could give you a more realistic prediction. You might see that the actual increase in sales wouldn’t be 5%, because you need to take into account the quality of the marketing spend, the channels, or the time of year.

### When is multivariate analysis unnecessary?

There are cases where multivariate analysis may be unnecessary. If you're trying to get to something like a simple insight or forecast of a metric, you don't need MVA. By looking at historical revenue data, for example, you can make a basic prediction for the next quarter or year. However, if you want to understand the levers you can pull and the factors that cause or influence those predictions, that's when you would want to expand to MVA.

It might be a smart option to do univariate or bivariate analysis first. You can start by analyzing trending data, which is a univariate analysis, to get the statistical mean and median. Once you have that information, then you can perform analysis to understand the relationship between that data and other variables.

## What is the process of conducting multivariate analysis?

The process of conducting multivariate analysis depends on which techniques you're using and the objective of the MVA. Generally, when performing MVA, you’re trying to achieve one of five different objectives:

**Data reduction or structural simplification**: MVA focused on this objective helps simplify data as much as possible without sacrificing valuable information, which helps with interpretation.**Sorting and grouping**: When you have multiple variables, you may want to group similar ones together based on common characteristics. An example of a method used to achieve this objective would be cluster analysis.**Investigation of dependents among variables**: This is an exploratory analysis technique. You're trying to explore the data and better understand the relationships between the variables of interest. For example, are they mutually independent, or is there a cause-effect relationship between them? Are one or more variables dependent on the others?**Prediction**: You might want to predict a relationship between variables. For example, you may use past observations of other variables or current observations of one variable to make a prediction on an unknown variable. If clicks to your website go up by 10%, you might use that information to predict how many more sales you’re going to get — but in the context of other variables, like the time of year or marketing channel.**Testing a hypothesis**: For specific statistical hypotheses, you want to formulate them in terms of the parameters of the populations. You want to test the hypotheses with certain assumptions or prior convictions. You also want to test out the influence or impact of a particular treatment, such as on a sample, and then be able to infer that upon the population.

When it comes to the model-building process, there are a few steps you always must follow. First, you must define the research problem, objective, and the potential, and then map these to the multivariate technique you will use. The next step is to develop the analysis plan.

You then want to evaluate the assumptions underlying the multivariate techniques themselves. Whichever multivariate technique you choose, there are certain model assumptions that you must account for, such as:

- Linearity
- Independence
- The shape of the independent variables

You may need to assess whether there are relationships between the independent variables that are undesirable.

Next, you want to estimate the multivariate model and assess its overall model fit. Then you will interpret the model and validate it, executing the information in some way, according to your original objective.

## What best practices can companies follow to ensure better multivariate analysis results?

By investing in high-quality and consistent data collection, you will get a more accurate analysis that facilitates informed business decisions and data models. You won’t have to reinvent the wheel each time you perform an analysis or constantly check the quality of your underlying data.

Also, because companies continue to work with larger quantities of data, there is a tendency to want to use more sophisticated techniques like neural networks or deep-learning type techniques.

It might take more computation power and more time to arrive at the output — and that comes at a real cost. You also can't distribute or disseminate the potential insights or the interpretation of the output to the organization because of the added complexity of all of the different variables you need to include.

There may be a different sweet spot for different departments or use cases.

## How will multivariate analysis change in the future?

In the past, multivariate analysis has been largely left to actuaries or statisticians. But in the future, the model-building process will likely become more automated.

We're already starting to see this with some software where you simply state an objective or metric and a definitive variable that you're trying to maximize or optimize in some way, and the software is able to quickly compute many different models simultaneously for immediate evaluation. This process will cut out a lot of that manual work and achieve the most accurate or best model for a given objective much more quickly.

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