6

Any universal approximators can do it. You need a term like $A(\beta_A+\beta_{A\times C}\times C)$ to appear, so the interaction between $A$ and $C$ suffices. $$A\times C = \frac{(A+C)^2-A^2-C^2}{2}$$ If you have an universal approximator, it can (locally) approximate the quadratic form somewhere in its formulation, giving you the interaction without ...


5

MARS (Multivariate Adaptive Regression Splines) are able to detect automatically non-linear interactions between explanatory variables without manually adding them in the model


4

Using Gaussian error propagation: summary(fit <- lm(Y ~ X + M + X*M)) sigma2mat <- vcov(fit)[-c(1, 3), -c(1, 3)] sum(coef(fit)[-c(1, 3)]) + c(-1.96, 1.96) * sqrt(sum(sigma2mat)) #[1] 147.3562 226.2858 Using bootstrapping: library(boot) DF <- data.frame(X, M, Y) set.seed(42) myboot <- boot(DF, function(DF, i) { fit <- lm(Y ~ X + M + X*M, ...


3

It's certainly possible to have a situation in which only the interaction is significant. A trivial example is: > set.seed(12) > x1 <- rnorm(100,0,1) > x2 <- rnorm(100,0,1) > cor(x1,x2) [1] 0.01592198 > y <- x1*x2 + rnorm(100,0,.3) > modFull <- lm(y~x1+x2+x1:x2) > modIntOnly <- lm(y~x1:x2) > anova(modIntOnly,modFull) ...


3

With an interaction, the big problem is interpreting the lower-order coefficients. For simplicity let's call your continuous "B/A", "B/C" and "SVO" simply "A" and "C" and "S", and call "Mag," your dichotomous predictor, "M". As lower-order terms should be included along with ...


3

It looks like other responses have already addressed the fact that there is no absolute rule that an interaction needs to be included. I'll just echo briefly that the decision of including an interaction should be driven by theory, and I'd like to use my answer to just fill in some context about why that matters. First, consider what you are analyzing when ...


3

There are two different definitions or understandings of the term ANCOVA. The first and a broader one is "Any linear model containing continuous/scale predictors besides factors (categorical predictors). The continuous predictor then receives an argot name "covariate". Often it this broader sense "covariate" is just a quantitative ...


3

There is nothing in statistical theory or practice which requires you to include any interaction, or any main effect for that matter. You include in your model the variables which your scientific theory has suggested and you include any interaction which that theory has suggested. You would then present that model to the reader. If you now decide to modify ...


2

The results are different because moderation and mediation are two fundamentally different phenomena. (more details here: http://davidakenny.net/cm/mediate.htm) In your mediation code, you're stating that moderator_idx is a function of the interaction between different_sex and sex (this makes no sense to me...) and that outgroup_feelings_diff is a function ...


2

I cannot replicate your estimates with the R code provided, but you can verify your manual calculations by testing the null that linear combination of two coefficients is zero: set.seed(101) n <- 2000 dv <- sample(0:1,n,rep=TRUE) condition <- sample(c("control","treat"),n,rep=TRUE) gender <- sample(c("male","...


2

My understanding is that, by including siteyear as random effect, the interaction is accounted for as well I don't think this is correct. The random effects (1|siteyear/block) will account for interactions between siteyear and block but not between siteyear and the fixed factors. Since you seem to have interest in the estimates for the interaction between ...


1

These are completely different models. The first: regress y x x1 fits fixed effects for x and x1 The second: regress y x#x1 fits a fixed effect for the interaction between the variables only (that is, the main effects in the first model are omitted). It very rarely makes sense to fit the 2nd model. This has been discussed here several times before. If you ...


1

In regression there is a danger of omitted-variable bias. In linear regression, if you omit a predictor that is associated both with outcome and with a predictor that is in the model, your results will be biased. With A and B highly correlated, your results are what you thus might expect. Model 1 attributes to A both its own contribution to outcome and a ...


1

The concept of significance is quite subtle, particularly when more than one test is run. If you estimate more parameters, this means that under null hypothesis there will be more variation in the estimators. This means that the threshold for significance is higher (because more deviation from null values will happen by random variation even if the H0 is ...


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