I have been examining Variables A and B with Variable X. I have found modest correlations but also evidence for heteroskedasticity. Generally, I believe, based on prior research, that those with high levels of A and B can have high or low levels of X, while those with low levels of A and B will generally have low levels of X.
Would running a two step-cluster analysis be a suitable alternative?
John -
If you are interested in linear relationships between variables where there is heteroscedasticity, perhaps you might explore weighted least squares regression (WLS). I haven't done cluster analysis, at least, not in a long time anyway, so I don't know how you might look at it that way, but WLS regression might be relatively easily interpreted.
Perhaps see https://www.researchgate.net/publication/263036348_Properties_of_Weighted_Least_Squares_Regression_for_Cutoff_Sampling_in_Establishment_Surveys
If you want to run a regression where one of those variables is considered dependent, and the others are independent, then to consider heteroscedasticity, you could form a size variable from the independent variables, and use that and a coefficient of heteroscedasticity in the regression weights. - For an example using multiple linear regression with an often robust coefficient of heteroscedasticity, see Appendix IV, page 36 in https://www.researchgate.net/publication/242677296_Quasi-Cutoff_Sampling_and_Inference.
You could experiment. Note that one regressor may impact with the other. Scatterplot graphics often offer insight.
This may be off topic for what you want, but I thought it might be useful.
Cheers - Jim
Article Properties of Weighted Least Squares Regression for Cutoff S...
Article Quasi-Cutoff Sampling and Inference
You better remove heteroskedasticity by using the appropriate transformation of variables before applying cluster analysis.
If you use a different transformation for each variable, won't you just be working with a different set of variables?
Dear Prof., Knaub
You are right and 100% correct. In transforming variables for removing heteroskedasticity we do usually end with different set of variables which affect the interpretation of multiple regression. But since the researcher in the current case is interested in breaking elements into groups (clusters) therefore I recommend that he uses transformation before using cluster analysis
I understand. I was/am just wondering if the transformed variables would form into irrelevant groups.
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