The motivation for this post was to create a pipeline for generating publication-ready plots entirely within ggplot and avoid post-generation touch-ups in Illustrator or Inkscape. These scripts are a start. The ideal modification would be turning the chunks into functions with personalized detail so that a research team could quickly and efficiently generate multiple plots. I might try to turn the scripts into a very-general-but-not-ready-for-r-package function for my students.
Continue to the whole post
A factorial experiment is one in which there are two or more factor variables (categorical \(X\)) that are crossed, resulting in a group for each combination of the levels of each factor. Factorial experiments are used to estimate the interaction effect between factors. Two factors interact when the effect of one factor depends on the level of the other factors. Interactions are ubiquitous, although sometimes they are small enough to ignore with little to no loss of understanding.
motivating source: Integration of two herbivore-induced plant volatiles results in synergistic effects on plant defense and resistance
What is synergism or antagonism? (this post is a follow up to What is an interaction?)
In the experiment for Figure 1 of the motivating source article, the researchers were explicitly interested in measuring any synergistic effects of hac and indole on the response. What is a synergistic effect? If hac and indole act independently, then the response should be additive – the HAC+Indole effect should simply be the sum of the independent HAC and Indole effects.
In R, so-called “Type I sums of squares” are default. With balanced designs, inferential statistics from Type I, II, and III sums of squares are equal. Type III sums of squares are returned using car::Anova instead of base R anova. But to get the correct Type III statistics, you cannot simply specify car:Anova(m1, type = 3). You also have to set the contrasts in the model matrix to contr.sum in your linear model fit.
Background Comparing marginal effects to main effect terms in an ANOVA table First, some fake data Comparison of marginal effects vs. “main” effects term of ANOVA table when data are balanced Comparison of marginal effects vs. “main” effects term of ANOVA table when data are unbalanced When to estimate marginal effects keywords: estimation, ANOVA, factorial, model simplification, conditional effects, marginal effects
Background I recently read a paper from a very good ecology journal that communicated the results of an ANOVA like that below (Table 1) using a statement similar to “The removal of crabs strongly decreased algae cover (\(F_{1,36} = 17.
I was googling around and somehow landed on a page that stated “When effect coding is used, statistical power is the same for all regression coefficients of the same size, whether they correspond to main effects or interactions, and irrespective of the order of the interaction”. Really? How could this be? The p-value for an interaction effect is the same regardless of dummy or effects coding, and, with dummy coding (R’s default), the power of the interaction effect is less than that of the coefficients for the main factors when they have the same magnitude, so my intuition said this statement must be wrong.
