Level: Intermediate
The "least squares means" and "prediction profile" obtained by "fitting a model" in JMP are essential for displaying the results of exploratory analysis. However, they are like a dialect that is not even listed in the index of the "Dictionary of Statistics" by Takeuchi et al. (1989), and it is difficult to explain them. Recently, we have found that a simple and clear explanation can be obtained by complementing the "least squares means" and "prediction profile" in "analysis of covariance" that includes qualitative and quantitative factors and interactions. The data used is an example of "regression analysis including stratified factors" from "Multivariate Analysis Methods, Revised Edition" by Okuno et al. (1981) (observation results of a sulfur dioxide gas recovery tower, concentration of the recovery liquid is y, temperature of the washing water is x, and operation period A has four levels). In the original paper, the graph is displayed as if the slope of the operation period (January and February) is different from other periods. Using a model including interactions, the change in the profile of the temperature x of the cleaning water is tracked while changing the operating season A in the prediction profile, and the average concentration y in operating season A is compared while changing the temperature x. It can be clearly shown that when the total average of temperature x is given, it coincides with the least squares mean for operating season A.
https://www.yukms.com/biostat/takahasi2/rec/009-13.htm
I have been using SAS since before JMP4. At my previous company, I provided statistical education using various versions of JMP and promoted JMP within the company. I introduced the results of this at JMPer's meetings as appropriate. After retiring, I established a self-employed consulting company and continue to work there. Recently, I have realized that the ability to perform statistical analysis of real data in many academic fields in Japan (excluding clinical statistics) is declining collectively. Analysis of covariance is an old yet new topic for me. I needed to seriously tackle analysis of covariance including interactions. Analysis of covariance is well established as an analytical model when there are no interactions. I realized that historically, cases including interactions were also discussed, and I realized that this is extremely useful when explaining the least squares method, which is a dialect of SAS, and the prediction profile, which is a dialect of JMP.
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