CODEWITHSUNDEEP
rregressionlm
Abhishek Baikadi
Abhishek Baikadi

Reputation:

Regression of Higher order

I want to fit a model $Y = X_1^2 + X_2^2 + X_1 + X_2 + X_1\cdot X_2$

How to build this in R

glm(Y ~ poly(X1,2) * poly(X2,2)

how to generalise it to higher order ? eg. $Y = X_1^3 + X_2^3 + X_1\cdot X_2^2 + X_1^2 \cdot X_2 + X_1^2 + X_2^2 + X_1 + X_2 + X_1\cdot X_2$

Upvotes: 0

Views: 1051

Answers (1)

Sven Hohenstein
Sven Hohenstein

Reputation: 81713

You can use glm with the following formula:

glm(Y ~ poly(X1, 2) + poly(X2, 2) + X1:X2)

The function poly creates polynomials. In your example, poly(X1, 2) results in $X_1$ and $X_1^2$. Note that poly creates orthogonal polynomials. If you want raw polynomials, you have to use the argument raw = TRUE.

The term X1:X2 is the interaction between $X_1$ and $X_2$, i.e., $X_1 \cdot X_2$.

Furthermore, your formula doesn't contain an intercept. I suppose this was not intended. However, you you really want to create a model without an intercept in R, you have to change the command to glm(Y ~ 0 + poly(X1, 2) + poly(X2, 2) + X1:X2).

Note that unless you specify a family in glm, the function will fit a linear model.

The formula you proposed (Y ~ poly(X1,2) * poly(X2,2)) creates all the terms of the formula above and additional terms, namely all interactions between the polynomials of first and second order of $X_1$, and $X_2$, i.e., $X_1 \cdot X_2^2$, $X_1^2 \cdot X_2$, and $X_1^2 \cdot X_2^2$.

Upvotes: 1

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