# Multivariate Data Analysis

### Multivariate Data Analysis

Multivariate data analysis consists of a set of statistical models. These models examine patterns in multidimensional data by considering several data variables at once. It is an extension of bivariate data analysis which only considers two variables in its models. Multivariate models can examine complicated phenomena and identify patterns that accurately represent the real world. This is possible because multivariate data analysis considers more variables.

Multivariate Data Analysis Techniques

Multivariate data analysis has two categories. Each of them pursues a different type of relationship in the data. The relationships are:

• Dependence – Relates to cause-effect situations. It tries to find if one set of variables can describe or predict the values of the other variables
• Interdependence – This is the structural intercorrelation. It aims to understand the underlying patterns of the data.

There is a myriad of multivariate models that can be used to find these relationships.  Also, many factors distinguish them. When choosing a technique, the nature of the data variables is one of the primary factors that must be taken into account. The data variables can be metric or non-metric.

• Metric Data Variables

These data variables are always of the numeric type. Metric data variables represent information that can be measured by some scale. For example, age can be 30years, profit registered is 2000 US dollars, the temperature recorded is 25 degrees Celsius, etc. The magnitude of the value on a given scale is specified by the number.

• Non-metric Data Variable

These variables categorize the data but do not specify its magnitude. For example, operation systems (can be Windows, Linux, macOS), house size can be (small, medium, large), etc. Non-metric data variables assume a list of options called levels or categories. As long as there is no magnitude associated with the variable, it remains non-metric. It doesn’t matter whether the levels have an inherent order.

Several multivariate data analysis techniques compute results that need numbers as inputs. But the question is, can a multivariate technique work with non-metric data? The answer to this question is simple. The non-metric variable can become a dichotomic metric variable where each level becomes a new metric variable that can only have binary values. 0 as false and 1 as true.

Dependence techniques

The analyst feeds a model with input data in dependence techniques. He or she also specifies which variables are independent and those that are dependent. The model tries to explain or predict independent variables. On the other hand, the dependent variables are studied by the analyst to know how much they affect the independent variables.

Dependence techniques strive to establish a cause-effect relationship. They only differ in the number of variables they support and the nature of the variables involved. Dependence techniques include:

• Multiple regression
• Conjoint analysis
• Multiple discriminant analysis
• Linear probability models
• Multivariate analysis of variance and covariance
• Canonical correlation analysis
• Structural equation modeling

Our multivariate data analysis can help you with all the techniques mentioned above and many more. So do not hesitate to contact us.

Interdependence techniques

Interdependence techniques aim to understand the underlying structure of data instead of solving cause-effect problems. This means that they are very distinguishable and differ in goals and needs. Examples include:

• Factor analysis
• Cluster analysis
• Multidimensional scaling
• Correspondence analysis

How do you design a multivariate data analysis?

Designing an effective multivariate data analysis study requires more than just selecting a multivariate technique. The analyst needs to define the specific aspects that are inherent to the selected technique after defining the conceptual problem. Some of these inherent aspects include estimation methods and distance metrics. Furthermore, he or she must be well-versed in the model assumptions and transform the data if need be. Also, the analyst must define the sample size by pondering the statistical significance, effect size, and statistical power if the data was not collected yet.

It is only after all these that the analyst can apply the technique to produce results. However, on rare occasions does the model gives satisfactory results in the first run. Sometimes, because of type I and type II errors, the model fails to accept or reject a hypothesis. Also, the model can sometimes not generalize its results for new entries because it fits too heavily with the input data. This process is classed overfitting.

Checking and correcting the errors in the model is an iterative process. You should only proceed when the results are generalizable and solid. To learn more about this process of building robust models , take our multivariate data analysis assignment help.