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  • 1.  Checking Model Assumptions for Equal Slopes in ANCOVA - Complicated Model

    Posted 05-01-2014 15:05
    I have run into this situation twice in the same week and would like some input.

    To check the model assumption of equal slopes for a simple ANCOVA with one discrete factor (A) and one continuous covariate (X) is pretty straightforward.  I would include the interaction A*X in the model.  If the interaction is not significant, I would assume that the equal slopes assumption is satisfied.  (I would also check some other diagnostics and not rely exclusively on the statistical test of interaction.)

    What would you recommend if there are four factors (A, B, C, and D) and three continuous covariates (W, X, Z)?  Do we check all possible interactions between the 4 factors and 3 covariates?  Or is there a subset of those interactions that could be tested? Or, could we test the interaction between each covariate and a single super-variable (A||B||C||D) consisting of a*b*c*d levels (where factor A has a levels, B has b levels, etc.)?   Other ideas?  I would appreciate any help you can give me.

    Thank you,

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    Beverly Grunden
    Statistical Consultant
    Wright State University
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  • 2.  RE:Checking Model Assumptions for Equal Slopes in ANCOVA - Complicated Model

    Posted 05-01-2014 15:22

    Beverly:

    If possible, I would probably first try and simplify the model by considering main effects first and also asking subject matter experts which interactions would be the most plausible.

    Roy Tamura
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    Roy Tamura
    Associate Professor
    University of South Florida
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  • 3.  RE:Checking Model Assumptions for Equal Slopes in ANCOVA - Complicated Model

    Posted 05-01-2014 15:40


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    Raymond Hoffmann
    Professor
    Medical College of Wisconsin
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    It is not an answerable question without a sample size.  That's because the strategy depends on whether it is a large or small sample.
    But if you think of it instead as a multiple linear regression problem you can use a forward (or your favorite!) stepwise regression analysis,
    use CART, use the LASSO, etc. and then you can build the model while checking for co-linearity, etc.

    Ray




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  • 4.  RE:Checking Model Assumptions for Equal Slopes in ANCOVA - Complicated Model

    Posted 05-01-2014 16:48


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    George Milliken
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    Beverly:  Unfortunately there are no easy short cuts.  What I do is put all of the effects in the model, A B A*B ... A*B*C*D and then include X and X interacting with all of the effects, same for Y and Z providing a model with 63 terms.  Then I do a backward elimination process with the terms involving the covariates, focusing on the higher order interactions first.  Not an easy process, but you can use proc glmselect to do some model building.







  • 5.  RE:Checking Model Assumptions for Equal Slopes in ANCOVA - Complicated Model

    Posted 05-01-2014 17:41
    Here is another case of ask a big group of statisticians and get a wide range of answers.

    The two proposed methods seem to leave something to be desired.  It would be nice to have a method that is free of sample size and doesn't require fitting a model with all the higher order interactions.  Certainly different strokes for different folks and different types of data require different considerations.  In clinical or experimental settings you might be able to elucidate good reasons from clinicians for or not for testing certain interactions, but there can be a lot of observational studies where you may not have as rich clinical thought.

    May I suggest an initial screening of your data using trees, either classification or decision or regression tress (whatever you use and/or call them).  They have been shown to be very versatile in both a separate analysis of the data and for model building.  However in the ANCOVA setting with many variables the trees will help see which categorical/quantitative variables  might interact in a regression model.

    With the ABCD and XWZ model you said you were looking at then if a tree analysis finds many splits along ABC variables but only X splits when C splits then you may have an interaction worth putting into a regression model.  However if there seems to be no method to where XWZ split or the split levels are around the same in different parts of the tree then you may not have any real interactive effects.  It's not perfect but it is more exploratory in nature which lets see how tenable a equal slopes assumption is with the data you have.

    Good luck!

    Jason

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    Jason Brinkley
    East Carolina University
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