I am investigating if variable A (categorical ) has effect on variable B (continuous) with controlling of covariate C (continuous). My plan is to run an ANCOVA, so I first examine if there is significant interaction between A and C ( check the equal regression slope assumption), which I did. Most materials on ANCOVA provided examples where this interaction is insignificant and that is the ideal result. some recommend if the interaction is significant, just stop interprete the effect of A.
In two-way ANOVA, we can do simple-effect analysis of variable A when significant interaction is found. However, here, it is impossible to run simple effect analysis of A at each level of C which has hundreds of values.
Does anyone has suggestions on how to work further on answering my research question? Thanks lot!
An ANCOVA is a general linear model with binary predictors (if more than one, then also with interaction variables) and continuous variables. There is no sich thing as an "ideal" case. "Controlling" is unfortunately a slilt misleading term, what you do is to explicitly model a linaer relationship between the continous variable and the criterion. If there is a theoretic reason, why this should be included, then statistical significance should not change one's treatment of the model. Use any software package that is able to accept covariates in the glm or ANOVA procedure to estimate the coefficients for the factorial part of your design. In your case you seem to have added.a technical variable ghat captures the interactin between a factor and the continuous predictor, in other words you explicitly allow for diffferent slopes in your model for the groups defined by your factor. The coefficient for the binary variable can still be interpreted as a difference between groups, but now the relationship between the sets of continuous predictor values (are both groups comparable on the predictor dimension) and the relationship of slopes, but none of that changes the estimation procedures. I personally would recommend plotting the relationship between continuous predictor and criterion with the factor variable determining the markers, so you can get an idea of what is going on. You could even plot the model predictin lines (for each factorial combination) into the graph. You can also search for answers on cross validated, e.g.
http://stats.stackexchange.com/questions/151668/difference-between-a-random-slope-intercept-model-and-an-ancova-with-an-interact
I also find useful this article:
Miller, G. A., & Chapman, J. P. (2001). Misunderstanding analysis of covariance. Journal of Abnormal Psychology, 110(1), 40.
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