1 vote
3k views

### Why prefer poly() to I() ? Are they different? [duplicate]

A post "Fitting Polynomial Regression in R" used two ways to model the polynomial regression: (a) poly(..., ...); (b) I(...). ...
• 1,027
4k views

### R formula for higher order polynomials and interactions, only allowing polynomial of degree 1 to interact

I am trying to build a (mixed) model using several predictor variables, and including some interactions and potentially higher degree polynomial versions of the continuous variables. The model formula ...
647 views

### When including a linear interaction between two continuous predictors, should one generally also include quadratic predictors?

Suppose I am fitting a linear model, and I have two continuous predictors x1 and x2. I think that they might interact, so I add ...
250 views

### Perfect multicollinearity with a cubic term in the model?

I'm trying to figure out why adding a cubic term in the model doesn't guarantee a perfect multicollinearity. If $X$ is known, then $X^3$ is known in both magnitude and sign and vice versa. It may not ...
• 769
1 vote
664 views

### What are 'Polynomial feature expansions'?

I have a question where I am explaining what polynomial regression is and have been asked to make sure I cover certain points, one of which is 'Polynomial feature expansions' what exactly does this ...
• 11
637 views

### Poly() function in R for linear models

I am working with some data on which I used the poly() function to get 4th degree polynomials. I had one model that only had significance for the first degree, so I ...
363 views

### Why do we need to model lower-order effects in models with interactions?

I recently saw a paper with a four-way interaction. That already is difficult to interpret (maybe if you have 1 or more categorical variables but definitely near impossible to interpret if all ...
• 910
1 vote
280 views

### Effect of basis functions on the dimension of a linear regression model

In Scikit-learn I can use polynomial features to create polynomial linear regression models. Scikit-learn transforms my original ...
• 216
Suppose that there are 2 models, $y$ ~ $x_1+x_2+x_2^2+x_1:x_2+x_1:x_2^2$ $y$ ~ $x_1+x_2+x_2^2+x_1:x_2^2$ For both models, their adjusted $R^2$ values are the same and BIC values are similar with the ...