Package 'RAMP'

Model prediction based on a fitted RAMP object.

Description

Similar to the usual predict methods, this function returns predictions from a fitted 'RAMP' object.

Usage

## S3 method for class 'RAMP'
predict(object, newdata = NULL, type = c("link",
  "response", "class"), allpath = FALSE, ...)

Arguments

object	Fitted 'RAMP' model object.
newdata	Matrix of new values for x at which predictions are to be made, without the intercept term.
type	Type of prediction required. Type 'response' gives the fitted values for 'gaussian', fitted probabilities for 'binomial', fitted mean for 'poisson', and the fitted relative risk for 'cox'. Type 'link' returns the linear predictors for 'binomial', 'poisson' and 'cox' models; for 'gaussian' models it is equivalent to type 'response'. Type 'class' applies only to 'binomial' models, and produces the class label corresponding to the maximum probability (0-1 labels).
allpath	allpath = T will output all the predictions on the solution path. allpath = FALSE will only output the one the criterion selected in the 'RAMP' object.
...	Not used. Other arguments to predict.

Value

The object returned depends on type.

See Also

RAMP,print.RAMP

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Result summary of a fitted RAMP object.

Description

Similar to the usual print methods, this function summarize results from a fitted 'RAMP' object.

Usage

## S3 method for class 'RAMP'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

x	Fitted 'RAMP' model object.
digits	The number of significant digits for the coefficient estimates.
...	Not used. Other arguments to predict.

Value

No value is returned.

See Also

RAMP

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Regularization Algorithm under Marginality Principle (RAMP) for high dimensional generalized quadratic regression.

Description

Regularization Algorithm under Marginality Principle (RAMP) for high dimensional generalized quadratic regression.

Usage

RAMP(X, y, family = "gaussian", penalty = "LASSO", gamma = NULL,
  inter = TRUE, hier = "Strong", eps = 1e-15, tune = "EBIC",
  penalty.factor = rep(1, ncol(X)), inter.penalty.factor = 1, lam.list,
  lambda.min.ratio, max.iter = 100, max.num, n.lambda = 100,
  ebic.gamma = 1, refit = TRUE, trace = FALSE)

Arguments

X	input matrix, of dimension nobs x nvars; each row is an observation vector.
y	response variable, of dimension nobs x 1. continous for family='gaussian', binary for family='binomial'.
family	response type. Default is 'gaussian'. The other choice is 'binomial' for logistic regression.
penalty	Choose from LASSO, SCAD and MCP. Default is 'LASSO'.
gamma	concavity parameter. If NULL, the code will use 3.7 for 'SCAD' and 2.7 for 'MCP'.
inter	whether to select interaction effects. Default is TRUE.
hier	whether to enforce strong or weak heredity. Default is 'Strong'.
eps	the precision used to test the convergence. Default is 1e-15.
tune	tuning parameter selection method. 'AIC', 'BIC', 'EBIC' and 'GIC' are available options. Default is EBIC.
penalty.factor	A multiplicative factor for the penalty applied to each coefficient. If supplied, penalty.factor must be a numeric vector of length equal to the number of columns of X. The purpose of penalty.factor is to apply differential penalization if some coefficients are thought to be more likely than others to be in the model. In particular, penalty.factor can be 0, in which case the coefficient is always in the model without shrinkage.
inter.penalty.factor	the penalty factor for interactions effects. Default is 1. larger value discourage interaction effects.
lam.list	a user supplied $\lambda$ sequence. typical usage is to have the program compute its own lambda sequence based on lambda.min.ratio and n.lambda. supplying a value of $\lambda$ overrides this.
lambda.min.ratio	optional input. smallest value for lambda, as a fraction of max.lam, the (data derived) entry value. the default depends on the sample size n relative to the number of variables p. if n > p, the default is 0.0001. otherwise, the default is 0.01.
max.iter	maximum number of iteration in the computation. Default is 100.
max.num	optional input. maximum number of nonzero coefficients.
n.lambda	the number of lambda values. Default is 100.
ebic.gamma	the gamma parameter value in the EBIC criteria. Default is 1.
refit	whether to perform a MLE refit on the selected model. Default is TRUE.
trace	whether to trace the fitting process. Default is FALSE.

Value

An object with S3 class RAMP.

a0	intercept vector of length(lambda).
mainInd	index for the selected main effects.
interInd	index for the selected interaction effects
beta.m	coefficients for the selected main effects.
beta.i	coefficients for the selected interaction effects.

See Also

predict.RAMP,print.RAMP

Examples

set.seed(0)
n = 500
p = 10 #Can be changed to a much larger number say 50000
x = matrix(rnorm(n*p),n,p)
eta = 1 * x[,1] + 2 * x[,3]  + 3*x[,6]  + 4*x[,1]*x[,3] + 5*x[,1]*x[,6]
y =  eta + rnorm(n)
xtest = matrix(rnorm(n*p),n,p)
eta.test = 1 * xtest[,1] + 2 * xtest[,3]  + 3*xtest[,6] +
4*xtest[,1]*xtest[,3] + 5*xtest[,1]*xtest[,6]
ytest =  eta.test + rnorm(n)
fit1 = RAMP(x, y)
fit1    ###examine the results
ypred = predict(fit1, xtest)
mean((ypred-ytest)^2)

#fit1.scad = RAMP(x, y, penalty = 'SCAD')
#fit1.scad    ###examine the results

#fit1.mcp = RAMP(x, y, penalty = 'MCP')
#fit1.mcp    ###examine the results

##Now, try a binary response
#y = rbinom(n, 1, 1/(1+exp(-eta)))
#fit2 = RAMP(x, y, family='binomial')  ###for binary response

## Weak heredity
eta = 1 * x[,1] + 3*x[,6]  + 4*x[,1]*x[,3] + 5*x[,1]*x[,6]
y =  eta + rnorm(n)
eta.test = 1 * xtest[,1] +  3*xtest[,6] + 4*xtest[,1]*xtest[,3] +
5*xtest[,1]*xtest[,6]
ytest =  eta.test + rnorm(n)

fit3 = RAMP(x, y, hier = 'Strong')
fit3    ###examine the results
ypred3 = predict(fit3, xtest)
mean((ypred3-ytest)^2)
fit4 = RAMP(x, y, hier = 'Weak')
fit4
ypred4 = predict(fit4, xtest)
mean((ypred4-ytest)^2)

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