What's the appropriate coding/model for this data?

I'm looking at a language at time X and Y. I identify 20 changes between time X and Y. The question is what the best account is for those changes. Theory 1 says it's all due to "external factors", and is able to account for them all in that way: 20/20. Theory 2 says that some of the changes (let's say 5) could also be due to "internal factors", so it adds that to the story: 5/20.

Here I want to make a very basic argument that theory 2 is entirely superfluous, since it simply adds another independent variable ("internal factors") to the model, even though the already existing independent variable ("external factors") explains all the data.

What would be the appropriate way to encode this toy example? I could imagine something like the following:

Changes ExternalFactors InternalFactors
20      20              5


But even though the number in ExternalFactors matches the number in the dependent variable, both independent variables "explain" the dependent variable (the number 5 could just as easily predict the number 20 as the number 20 could).

I am sorry to say that you may need to return to the drawing board. Both your EF and IF will explain Changes perfectly because:

$Change = 0 + 1 * ExternalFactors$

$Change = 0 + 4 * InternalFactors$

If you put both of them into the model, most software packages will just pick one for you, either by the order you have fed them in or by the alphabetical order of your variable names.

In order to make this question testable, you'd probably need some validated tools to assess the external and internal factors separately. They are latent variables, and we cannot simply assign a constant to them without measuring them. Using that two values, you can then use regression to find out which one is more predictive, and if the internal factor matters in the presence of the external factor.

What do you have in mind when you say that I'd "need some validated tools to assess the external and internal factors separately"?

Well, I am not a linguistic specialist (actually not a specialist in anything) so I can't tell you what to use. But if I were tasked to examine this phenomenon, I'd first document the linguistic change like you did. And then I'll either look for or design an instrument to capture the "external factors" such as change in social status, change in education, change in weather, etc. Whatever you feel is a significant contributor to the "externality." And then I'll do the same for the internality, but with another specific instrument. (Notice that some instruments can capture both constructs at the same time, they don't have to be two separate tools.) With these three variable, I can then run some tests.

The major challenges I can see is what to classify as internal and external. For that you may need to consult some experts in this matter.

Without any empirical data, your argument would still be valid. If something can 100% explain an outcome, adding anything else is going to be useless. If you'd like get away from this coding dilemma, think from $R^2$ (search "coefficient of determination"). If what you said is right, the $R^2$ of the model using EF as a predictor would be $1$, and the $R^2$ of the model using IF as a predictor would only be $.25$. As EF has already perfected the model, IF is then unnecessary.

• I agree with everything you say, since I've realized that I can't code it in the way I sketched. So the question is how it should be coded (and modeled). What do you have in mind when you say that I'd "need some validated tools to assess the external and internal factors separately"? Sep 26 '13 at 14:51
• @Sverre I've edited the answer to address your question. Good luck. Sep 26 '13 at 15:09
• I see what you mean, and I've thought along those lines. The problem is that, say, a certain internal factor that could explain one change would not be the same internal factor that explains another change. Plus the factors themselves are not quantifiable. But since I'm not interested in looking at the variables for each change individually, but for the overall picture, I can't see how I should do it. I think the conclusion is that although the example is statistical in principle, it cannot be in practice, since it doesn't involve variables that by themselves are quantifiable. Sep 26 '13 at 15:22
• @Sverre What you described would itself be a good research direction. If we cannot quantify the IF itself, how do you know that there are different subfactors within IF, and they contribute differently? It is perhaps getting a bit philosophical, but if we cannot quantify an array of things, even very so arbitrarily, then perhaps we should not use "more" or "stronger" to compare them. If you decide to use statistics as a tool to study this, I'd suggest starting to look into how to operationalize your factors. Sep 26 '13 at 15:28
• This is just one of my many arguments against using these IF, since their advocates cannot quantify them (not are they trying to). I just wanted to add another statistical argument as well, but I see that it needs to be more of a general conceptual argument instead. Sep 26 '13 at 15:32