However you do need to know what is behind these estimate, there is a mathematical foundation between them that you need to be aware of before being able to derive explanations.I plan to make two post on this issue, this first one will deal with interpreting interactions coefficients from classical linear models, a second one will look at the F-ratios of these coefficients and what they mean. You have four categories, but you can write the model several different ways, e.g., let 1 be a constant term, with variables $(1, x_1, x_2, x_1*x_2)$ or $(x_1, x_2, x_1*x_2, (1-x_1)*(1-x_2)$, or others. And why the results from these two approaches are different?The results are different because the way lm sets up the model with the interaction is different from how it is set up when you set it up yourself.

If you look at the residual sd, it's the same, which indicates (not definitively) that the underlying models are the same, just expressed (to the lm internals) differently. Detailed answers to any questions you might have Interaction are the funny interesting part of ecology, the most fun during data analysis is when you try to understand and to derive explanations from the estimated coefficients of your model. Interaction are the funny interesting part of ecology, the most fun during data analysis is when you try to understand and to derive explanations from the estimated coefficients of your model. When you look at these matrices, you can compare the constellations of For instance, executing the following code gives you exactly the same output as using the automatic setting of R: This also provides a quick answer to your question: the really only reason to change the way factors are set up is to provide expositional clarity. In most (but not all) situations, a single dependent (lefthand) variable is also needed.Thus we can construct a formula quite simply by just typing:Note: Spaces in formulae are not important.And, like any other object, we can store this as an R variable and see that it is, in fact, a formula:More commonly, we want to express a formula as a relationship between an outc… R for loop in a formula. I will only look at two-way interaction because above this my brain start to collapse. Here is an example: But tests of interactions can have low power - some people perform them by relaxing the significance level to guard against this (e.g., increase the significance level from 0.05 to 0.10). ... Regression model with all possible two way interaction terms in r. 2. The coefficient estimates will be different, but the model is really the same.Therefore, although different, both approaches are correct, aren't it?Right. For example to get the mean shoot length for High temperature and nitrogen B we do: 0.97+3-1.97+0.98, this 0.98 is then the added difference for tese particular cases.So in this context the interaction coefficient cannot be interpreted alone, we need to look at the other main effects coefficient to understand their effects.ii) Interaction between one continuous and one categorical variablesNow let’s turn to another case, there we are weighting standardize soil samples, we added a temperature treatment with two levels (Low, High) and we measured the soil nitrogen concentration, we would like to see the effects of the nitrogen concentration and its interaction with temperature on soil weight.This is an easy case, the first coefficient is the intercept, the second is the slope between the weight and the soil nitrogen concentration, the third one is the difference when the nitrogen concentration is 0 between the means for the two temperature treatments, and the fourth is the change in the slope weight~nitrogen between the Low and High temperature treatment.Now the last possible case could be something like a study where we measured the attack rates of carabids beetles on some prey and we collected two continuous variable: the number of prey item in the proximity of the beetles and the air temperature. Consider the following data:Two equivalent ways to specify the model with interactions are:My question is if I could specify the interaction considering a new variable (rs) with the same levels of interaction:What advantages/disadvantages have this approach? The basic structure of a formula is the tilde symbol (~) and at least one independent (righthand) variable.

Predicting new data using glm and cv.glmnet in R (including interactions and categorical variables ) Hot Network Questions