5
$\begingroup$

In a simple experiment I asked participants to make acceptability judgements (9-point Likert scale) when they observed different animated virtual characters. I have two factors: character (7 levels) and motion (5 levels).

Two-way ANOVA showed significant interaction between the above factors, so I want to explore this interaction better. I've run a post-hoc Tukey test and looked at critical differences between mean acceptability ratings for all characters, and all levels of motion. It's a large matrix (rough example can be seen in this post in stackoverflow) that might not be entirely clear for the interpretation. It's been suggested to me that maybe I could have visualize or statistically explore this interaction between characters and motion better.

Any suggestions how I could do that (preferably in R)?

| cite | improve this question | |
$\endgroup$
  • 2
    $\begingroup$ We won't eat you alive :) $\endgroup$ – chl Dec 18 '11 at 22:32
  • 2
    $\begingroup$ One way is to plot the mean of fitted values from your model, conditional on values of these predictors of interest. You could make the x-axis one of the predictors, and then use a different color for different values of the other predictor (with the y-axis being the mean of the fitted values). You can do this with R basic graphics, lattice, ggplot, or other packages; e.g. jstatsoft.org/v08/i15/paper $\endgroup$ – Michael Bishop Dec 24 '11 at 22:44
  • $\begingroup$ @MichaelBishop (+1) Besides basic interaction plot, John Fox's paper has interesting discussion about marginalization over higher-order interaction terms, etc. I feel like you could expand your comment into a reply, with some illustrations. $\endgroup$ – chl Dec 25 '11 at 19:52
  • $\begingroup$ @MichaelBishop (+1) Yes, as chl pointed out, it's a great little article, and I also feel you could show some example on how you would use it, if you don't mind... $\endgroup$ – Geek On Acid Feb 16 '12 at 16:22
6
$\begingroup$

If you are interested in visualizing an interaction effect specifically, you can subtract main effects (i.e., average factor effect, say $x_i$ and $x_j$) from each treatment mean (combination of factor levels, indexed by $i$ and $j$) based on the relation

$$\gamma_{ij} = \bar x_{ij} - \bar x_i - \bar x_j + \bar x$$

This will yield $i$ (or $j$) curves where every value are expressed as deviation from a baseline which is simply the grand mean ($\bar x$). This idea is developed in Howell, Statistical Methods for Psychology. Below is an illustration with one of Howell's dataset (a study on number of words recalled as a function of subjects' age and recall condition, N=100).

enter image description here

| cite | improve this answer | |
$\endgroup$
8
$\begingroup$

In R, there is a function coplot which plots your main effect and outcome in a grid of domains for each conditioning factor in a scatter-plot matrix. By examining the change between trends in the panel of plots, you can assess the extent of interaction present in the data.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ (+1) Interesting idea. I always think of coplots as a way to show trivariate relationships between numerical variables. Re-reading the help page, I see there are examples of use with factors. $\endgroup$ – chl Dec 25 '11 at 19:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.