Every once in a while, I work with a client who is stuck between a particular statistical rock and hard place. It happens when they’re trying to run an analysis of covariance (ANCOVA) model because they have a categorical independent variable and a continuous covariate.
The problem arises when a coauthor, committee member, or reviewer insists that ANCOVA is inappropriate in this situation because one of the following ANCOVA assumptions are not met:
1. The independent variable and the covariate are independent of each other.
2. There is no interaction between independent variable and the covariate.
If you look them up in any design of experiments textbook, which is usually where you’ll find information about ANOVA and ANCOVA, you will indeed find these assumptions. So the critic has nice references.
However, this is a case where it’s important to stop and think about whether the assumptions apply to your situation, and how dealing with the assumption will affect the analysis and the conclusions you can draw. (more…)
It’s really easy to mix up the concepts of association (as measured by correlation) and interaction. Or to assume if two variables interact, they must be associated. But it’s not actually true.
In statistics, they have different implications for the relationships among your variables. This is especially true when the variables you’re talking about are predictors in a regression or ANOVA model.
Association
Association between two variables means the values of one variable relate in some way to the values of the other. It is usually measured by correlation for two continuous variables and by cross tabulation and a Chi-square test for two categorical variables.
Unfortunately, there is no nice, descriptive measure for association between one (more…)
Centering predictor variables is one of those simple but extremely useful practices that is easily overlooked.
It’s almost too simple.
Centering simply means subtracting a constant from every value of a variable. What it does is redefine the 0 point for that predictor to be whatever value you subtracted. It shifts the scale over, but retains the units.
The effect is that the slope between that predictor and the response variable doesn’t (more…)
I recently received this great question:
Question:
Hi Karen, ive purchased a lot of your material and read a lot of your pdf documents w.r.t. regression and interaction terms. Its, now, my general understanding that interaction for two or more categorical variables is best done with effects coding, and interactions cont v. categorical variables is usually handled via dummy coding. Further, i may mess this up a little but hopefully you’ll get my point and more importantly my question, i understand that
1) given a fitted line Y = b0 + b1 x1 + b2 x2 + b3 x1*x2, the interpretation for b3 is the diff of the effect of x1 on Y, when x2 changes one unit, if x1 and x2 are cont. ( also interpretation can be reversed in terms of x1 and x2). (more…)
Need to dummy code in a Cox regression model?
Interpret interactions in a logistic regression?
Add a quadratic term to a multilevel model?
This is where statistical analysis starts to feel really hard. You’re combining two difficult issues into one.
You’re dealing with both a complicated modeling technique at Stage 3 (survival analysis, logistic regression, multilevel modeling) and tricky effects in the model (dummy coding, interactions, and quadratic terms).
The only way to figure it all out in a situation like that is to break it down into parts. (more…)
One of the tricky parts about dummy coded (0/1) variables is keeping track of what’s a 0 and what’s a 1.
This is made particularly tricky because sometimes your software switches them on you.
Here’s one example in a question I received recently. The context was a Linear Mixed Model, but this can happen in other procedures as well.
I dummy code my categorical variables “0” or “1” but for some reason in the (more…)
