Correspondence Analysis

Due to the number of combinations of questions and answers within a dataset, identifying the most interesting connections in the data can become really challenging. Fortunately, statistical models provide us with relevant tools that help uncover patterns that may not be visible at first glance. Enter Correspondence Analysis - a powerful technique used to map relationships in a 2D space.

Correspondence Analysis is a statistical technique available in the Query module that visually represents the associations between two sets of categorical data within a single two-dimensional chart. It is especially useful when you want to see, at a glance, how two questions relate to each other, for example, how car brands are perceived in terms of characteristics such as “Luxurious”, “Sporty”, or “Environmentally friendly”. Correspondence Analysis converts a crosstabulation of two variables into a perceptual map that makes patterns, clusters, and outliers immediately visible. Halo Reports’ implementation of Correspondence Analysis enriches the chart with additional interactions, which help to interpret the results and increase the analytical value of the chart. Let’s use an example of survey data, including questions that identify the product analyzed (e.g., Make of new car) and ones that present the image perceptions of those products (e.g., Car characteristics).

Correspondence Analysis in Halo Reports is available within the Query module for all report authors. You can convert an existing tab to a Correspondence Analysis chart (note that this may result in the need to adjust some of the query elements), or you can change your empty Crosstab to a Correspondence Analysis tab and set up the query directly from there.

The two main panels you will find here are the Items and Attributes:

- Items – the first set of categorical values, typically the who or what being analyzed (for example, the product: brand, model, group, or segment, such as Make of new car). By default, items are displayed on the chart as filled circles.

- Attributes – the second set of categorical values, typically describing how the items are perceived or characterized (for example, Car Characteristics such as Luxurious, Sporty, or Environmentally friendly). By default, attributes are displayed on the chart as diamonds.

You can drag and drop questions to those panels, just like for any other type of Query. In our use case, it will be important to use Make of new car question in Items, and Car characteristics in Attributes.

As soon as you fill in the items and attributes panels, the Correspondence Analysis chart will be generated on the right side of the Query module. Such a chart is immediately usable, and the information presented is the result of the statistical analysis processed on top of the 2 questions selected. In many cases, this will be all you need, but let’s see what else the module offers to increase the value of data insights.

Both the Items and Attributes panels expect a categorical question as the input. Nesting is not allowed - only one question can be analyzed at a time for each of the fields. As with any other tab, you can define additional filters for the input data. If you are only interested in data based on a specific engine type or demographic cluster, you can use the standard Filters panel. Anything you include there will change the data input for the Correspondence Analysis statistical model, and therefore, you should expect the chart to reload automatically with positions of the points recalculated accordingly. Similarly, you may want to exclude specific elements from the questions included as Items and Attributes, for example, if you have identified outliers that heavily impact the analysis, obscuring interesting findings among other data points. Applying a subset to a question in the Items or Attributes panel will also regenerate the chart, with the excluded answers not being passed as the input for the statistical analysis. The same logic applies to the “Include missing” options - you may decide whether you want to keep the “No response” as one of the analyzed data points or fully exclude it from the analysis.

It is important to note that the query definition can take advantage of all the dynamic features Halo Reports offers, just as any other query type. If needed, dynamic connections to datasets can be set up, and any question in the query can be parameterized, allowing for a more dynamic analysis.

Interpreting the correspondence analysis chart is quite intuitive, thanks to the 2D map representation of the results; however, it is easy to fall into some traps if not analyzed carefully. To help avoid this, we present some useful reading tips by default on the right side of the chart. To help draw the right conclusions, Halo Reports includes a focused view, available when you click on a specific point.

This view presents visually which of the points from the other series are positively or negatively associated (point color), and also how strong that association is (percentage of fill for the point markers). The association strength is represented by 5 levels of fills, ranging from empty markers (weak associations) to fully filled markers (very strong associations) - the additional explainer on the right side includes a related legend. This explainer also summarizes the strongest associations for the given point - strongest are defined as levels 4 or 5, on either the positive or negative side.

There are also several options to strengthen visual aspects. 

You can: