# Logistic regression with a quadratic penalization on the coefficients This function fits a logistic regression model penalizing the size of the L2 norm of the coefficients. ```r plr(x, y, weights = rep(1,length(y)), offset.subset = NULL, offset.coefficients = NULL, lambda = 1e-4, cp = "bic") ``` ## Arguments - `x`: matrix of features - `y`: binary response - `weights`: optional vector of weights for observations - `offset.subset`: optional vector of indices for the predictors for which the coefficients are preset to `offset.coefficients`. If `offset.coefficients` is not `NULL`, `offset.subset` must be provided. - `offset.coefficients`: optional vector of preset coefficient values for the predictors in `offset.subset`. If `offset.coefficient` is not `NULL`, `offset.coefficients` must be provided. - `lambda`: regularization parameter for the L2 norm of the coefficients. The minimizing criterion in `plr` is -log-likelihood+$\lambda*\|\beta\|^2$. Default is `lambda=1e-4.` - `cp`: complexity parameter to be used when computing the score. `score=deviance+cp*df.` If `cp="aic"` or `cp="bic",` these are converted to `cp=2` or `cp=log(sample size),` respectively. Default is `cp="bic".` ## Returns A `plr` object is returned. `predict, print,` and `summary` functions can be applied. - **coefficients**: vector of the coefficient estimates - **covariance**: sandwich estimate of the covariance matrix for the coefficients - **deviance**: deviance of the fitted model - **null.deviance**: deviance of the null model - **df**: degrees of freedom of the fitted model - **score**: deviance + cp*df - **nobs**: number of observations - **cp**: complexity parameter used when computing the score - **fitted.values**: fitted probabilities - **linear.predictors**: linear predictors computed with the estimated coefficients - **level**: If any categorical factors are input, level - the list of level sets - is automatically generated and returned. See `step.plr` for details of how it is generated. ## Details We proposed using logistic regression with a quadratic penalization on the coefficients for detecting gene interactions as described in "Penalized Logistic Regression for Detecting Gene Interactions (2008)" by Park and Hastie. However, this function `plr` may be used for a general purpose. ## References Mee Young Park and Trevor Hastie (2008) Penalized Logistic Regression for Detecting Gene Interactions ## Author(s) Mee Young Park and Trevor Hastie ## See Also predict.plr, step.plr ## Examples ```r n <- 100 p <- 10 x <- matrix(rnorm(n * p), nrow=n) y <- sample(c(0, 1), n, replace=TRUE) fit <- plr(x, y, lambda=1) p <- 3 z <- matrix(sample(seq(3), n * p, replace=TRUE), nrow=n) x <- data.frame(x1=factor(z[, 1]), x2=factor(z[, 2]), x3=factor(z[, 3])) y <- sample(c(0, 1), n, replace=TRUE) fit <- plr(x, y, lambda=1) # 'level' is automatically generated. Check 'fit$level'. ```

plr function