In a previous post, Interpreting Interactions in Regression, I said the following:

In our example, once we add the interaction term, our model looks like:

Height = 35 + 4.2*Bacteria + 9*Sun + 3.2*Bacteria*Sun

Adding the interaction term changed the values of B1 and B2. The effect of Bacteria on Height is now 4.2 + 3.2*Sun. For plants in partial sun, Sun = 0, so the effect of Bacteria is 4.2 + 3.2*0 = 4.2. So for two plants in partial sun, a plant with 1000 more bacteria/ml in the soil would be expected to be 4.2 cm taller than a (more…)

The way to follow up on a significant two-way interaction between two categorical variables is to check the simple effects.  Most of the time the simple effects tests give a very clear picture about the interaction.  Every so often, however, you have a significant interaction, but no significant simple effects.  It is not a logical impossibility. They are testing two different, but related hypotheses.

Assume your two independent variables are A and B.  Each has two values: 1 and 2.  The interaction is testing if A1 - B1 = A2 - B2 (the null hypothesis). The simple effects are testing whether A1-B1=0 and A2-B2=0 (null) or not.

If you have a crossover interaction, you can have A1-B1 slightly positive and A2-B2 slightly negative. While neither is significantly different from 0, they are significantly different from each other.

And it is highly useful for answering many research questions to know if the differences in the means in one condition equal the differences in the means for the other. It might be true that it’s not testing a hypothesis you’re interested in, but in many studies, all the interesting effects are in the interactions.

Just a reminder that our free monthly teleseminar is tomorrow.  The topic this month is Interpreting Regression Coefficients: A Walk Through Output.

Always free, but you have to register…

http://www.analysisfactor.com/learning/teletraining4.html.

This month we’ll be doing two things differently–we’re trying out a new webinar system, adding visuals; and we’re going over the actual output of one of my current clients.

It’s a great example, because it contains lots of fun, but confusing terms, two dummy-coded categorical predictors, a centered predictor, and a few interactions.  And technically, the analysis was an ANCOVA, but she needed to be able to interpret the regression parameters to understand the results.

Interpreting the coefficients is one of the most commonly asked questions I’ve received in 10 years of consulting, even among clients who’ve taken regression classes.  It’s just not the same when the output is in front of you.

The other bonus is you’ll get a glimse of what we’ll be doing in much deeper detail in my upcoming 4 week workshop on Interpreting Regression Coefficients.

A Linear Regression Model with an interaction between two predictors (X1 and X2) has the form:

Y = B0 + B1X1 + B2X2 + B3X1*X2.

It doesn’t really matter if X1 and X2 are categorical or continuous, but let’s assume they are continuous for simplicity.

One important concept is that B1 and B2 are not main effects, the way they would be if (more…)

The reason for centering a continuous covariate is that it can improve interpretability.

For example, say you had one categorical predictor with 4 categories and one continuous covariate, plus an interaction between them.

First, you’ll notice that if you center your covariate at the mean, there is (more…)

Adding interaction terms to a regression model can greatly expand understanding of the relationships among the variables in the model and allows more hypotheses to be tested.

The example from Interpreting Regression Coefficients was a model of the height of a shrub (Height) based on the amount of bacteria in the soil (Bacteria) and whether the shrub is located in partial or full sun (Sun). Height is measured in cm, Bacteria is measured in thousand per ml of soil, and Sun = 0 if the plant is in partial sun and Sun = 1 if the plant is in full sun. The regression equation was estimated as follows:

Height = 42 + 2.3*Bacteria + 11*Sun

It would be useful to add an interaction term to the model if we wanted to (more…)