What to do when assumption of ANCOVA doesn´t check up?

#1
Hi,
I am doing an ANCOVA because i have a continuous and a categorical explanatory variable, however found during analysis that my explanatory variables are correlated. How should i proceed? Do i drop the covariate and do a regular ANOVA, with risking overemphasizing the effect of the categorical variable on the response? Or do i interpret the regression coefficient but can´t say anything definit about the categorical explanatory variables effect on the response?
 
#2
welcome back to talk stats, the Internet's premiere statistical chat forum.

How correlated are we talking about? Is the rainfall or whatever it was you were adjusting for completely different in each of the categories, or just a bit different. That is is there any overlap in rainfalls?

If not, I think the thing is that you can still adjust for it in the manner of ANCOVA, but it essentially implies a counterfactual, in the sense that you would be comparing two categories at a rain level that is not actually observed, or may not exist in reality (ie factual). So if the correlation is too high, yes I would think to not adjust for the continuous response, and the effect of the category and the rainfall will just be indistinguishible, and that may be a physical reality as much as a statistical boo boo, if it makes you feel better. Such is the nature of observational data.
 
#3
I do not know how correlated, only that when i change the order of the explanatory variables and compare the anova tables, the significance level of the categorical explanatory variable shifts from non-significant to significant, whereas the covariate value stays the same.
 

noetsi

Fortran must die
#4
Warning, I don't think there is an agreed on way to do this (well there are several and which to do is not clear). From ancient memory ...One possibility is to do factor analysis and create factors that combine your variables into one variable. Then use the factors not the original variables. Finding a new variable to replace one of the variables that are correlated is another option although I doubt many do that. For Multicolinearity, which may mirror this issue, some suggest ridge regression although that gives other statisticians fits (John Fox comes to mind) since it builds bias into your results.

You might just have to accept that in the real world some predictors are correlated. So you can not determine their unique effect, because there is no unique effect. They work together.

I suspect structural equations might also address this maybe, but you would need spunky to advice you and he is lost in a SQL virtual world :(
 
#5
I do not know how correlated
What does it look like if you scatter plot the watering covariate by category? Big diff or no...

when i change the order of the explanatory variables
sounds like you may be running the 'Type I' analysis? That the category shifted to being significant is probably good/expected.

suggest ridge regression
I think the issue will not be col linearity in this case, I doubt the situation is dire enough to warrant this.

structural equations
if this isn't already accepted practice in a field, it'll probably just confuse reviewers. Now you have 2 problems, correlated covariates and explaining what a SEM model is.
 
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noetsi

Fortran must die
#6
I would hope reviewers chosen for their expertise, would know what SEM is :p If they don't I think you have larger issues.
 
#7
If they don't I think you have larger issues.
I don't know i guess ecologists tend to like stats so maybe. But if you get into some molecular biology areas or laboratory science, if it doesn't rhyme with 'ANOVA' or look like <famous statistician>-test, it doesn't register.