This post isn’t really very anole-specific, but because lots of studies of anoles use principal component analyses, I think it’s at least tangentially relevant.
PCA is a way of to reduce the variation in a data set to a few dimensions by constructing new variables that emphasize variables that are highly correlated with each other. I won’t go into the details of the method here, because Ambika Kamath explains all in a post she wrote on her blog a while back.
What I want to mention here is how we interpret these new statistical axes. Back in my day, computer programs spit out a matrix of numbers like the one above, which we called “loadings.” These values represent how strongly each variable was correlated with each of the new axes. So, for example, in the table above, values for PCA axis one correlate most strongly with “fats and oil” and “animal protein” content and most weakly with Vitamin B1.In other words, the regression line determining the PCA (a PCA axis is a linear regression of all the variables), was determined the most by fats and oils and animal protein and the least by Vitamin B1.
Now, everyone uses the computer program R to conduct PCAs, and R, too, spits out “loadings.” But those are not your father’s loadings (or my loadings). Rather, those values are the coefficients of the new equation that defines the PCA axis. Thus, in the example above, hot dogs that scored high on PCA 1 would have the largest (positive or negative, depending on size) fat and oil and animal protein content. Back in the day, we could also access those values, but we called them “coefficients.”
Does this really matter? Only to the extent that what much of the literature used to call “coefficients” is now called “loadings” and what used to be called “loadings” apparently isn’t routinely spit out by R. And, more importantly, most R users are completely unaware of the switcheroo.
Ambika did a very preliminary analysis to see whether the values of coefficients (new “loadings”) and correlations (old “loadings”) are very different. Her tentative conclusion is that they aren’t, so maybe this doesn’t matter much, but it might be worth looking into more.