I planned several ANCOVA analyses with 8 covariates to be included in each one. However, the homogeneity of regression slopes assumption was violated for some covariates but not others.
E.g. for my depression outcome, some of the covariates violated the homogeneity of regression slopes assumption. I removed these from the analysis and kept the covariates that did not violate this assumption. Is this justifiable? Has anyone heard of this being done and possibly has an academic reference for it?
Thank you all
I would not advise doing that because you have changed your experimental design, which you have not described. Your university is well regarded in Statistics.. I would check with an experimental design person there or at least look at this reference: Montgomery, D C, Design and Analysis of Experiments
you might also look at your residual plots. Best, D. Booth
ANCOVA with multiple covariates, can you drop some covariates that violated assumptions and keep those that met the assumptions
I think you should drop the covariates that violate the assumption [many would say don't, it explains this..], except the covariate is so important and will lead to a more accurate estimate of the real relationship between the independent variable and the outcome.
If you would retain them, then test for interaction please, (and if significant) forget ANCOVA, and run the covariate as a predictor,... multiple regression! {Infact, if there is an interaction between a factor and a covariate then there will be a violation of the assumption of homogeneity of regression slopes!}
You can as well try the factorial ANCOVA (with reduced covariates), it allows additional control of covariates that might influence the outcome but have nothing to do with the IVs.
David Eugene Booth Hello, sorry for the late reply, I am wondering what you mean by 'I have changed the experimental design'? I have included my 8 covariates in order to see if my intervention is still effective after accounting for those covariates. But I cannot include the covariates that have violated assumptions. I will check the textbook thank you.
Abiodun Christian Ibiloye Hello, do you mean that I should run the analysis as a multiple regression instead, and include the covariates as predictors? However, this will completely change my experimental design...
If i do a factorial ANCOVA, I could drop the covariates that violated assumptions and include the ones that met the assumption?
Every design has a model most easily written as a regression. if you drop terms it may no longer represent the experiment. see the book i suggested. Best, D. Booth
BTW this is what Prof Christian is talking about too.
I don't think this is general a good strategy. The homogeneity of covariance "assumption" isn't really an assumption in my view. It just means that those covariates interact with one or more grouping variables. The best option in this case is probably to include the interactions and see how much impact this has on the interpretation of the model. It may be helpful to centre the covariates and use effect coding for the grouping variables (though your software may do that or something equivalent by default).
The test of homogeneity of covariance should just be a comparison of the model with and without the interaction. All ANCOVA and ANOVA models are special cases of multiple regression, so an ANCOVA model without the interactions is equivalent to a multiple regression without the interactions. They may look different - but this is mainly just an issue of using different parameterisations by default.
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