Coming in JMP 12: Multiple Correspondence Analysis
Mar 9, 2015 12:16 PM
In multivariate analysis, dimension reduction into a small number of factors is the most important step for capturing the variability among a large number of variables. In JMP, we have the Principal Components (PC) platform to do dimension reduction for continuous variables. However, when we have categorical variables, we cannot use the PC platform for dimension reduction. The new Multiple Correspondence Analysis (MCA) platform in JMP 12 takes multiple categorical variables as input variables and seeks to identify associations between the levels of those variables.
Multiple correspondence analysis is frequently used in the social sciences; it is particularly popular in France and Japan. It can be used in survey analysis to identify question agreement. It is also used in consumer research to identify potential markets for products. Microarray studies in genetics also use MCA to identify potential relationships between genes.
Example of Multiple Correspondence Analysis
The Car Poll.jmp sample data in JMP contains data collected from car polls. The data include aspects about the individuals polled, such as sex, marital status and age. The data also include aspects about the car that respondents own, such as the country of origin, the size, and the type. We may want to explore relationships between sex, marital status, country and size of car to identify consumer preferences.
A key part of correspondence analysis is the multidimensional map produced as part of the output. The correspondence map allows you to visualize the relationships among categories spatially on dimensional axes. In other words, you can see which categories are close to other categories on empirically derived dimensions.
The Correspondence Analysis map from Car Poll data shows the cloud of categories of the four variables as projected onto the two principal axes. From this cloud, you can see that Americans have a strong association with the large car size, while Japanese are highly associated with the small car size. Also, males and single people are strongly associated with the small car type, and females and married people are associated with the medium car size. This information could be used in market research to identify target audiences for advertisements.
Once JMP 12 becomes available later this month, I hope you can explore the new MCA platform with your own categorical variables. I look forward to your feedback.