glmpathcr {glmpathcr}

Fit Penalized Continuation Ratio Model

Description

This function fits a penalized backward (default) or forward continuation ratio model using the glmpath framework.

Usage

glmpathcr(x, y, data, method="backward", weight = rep(1, n), offset = rep(0, n), 
lambda2 = 1e-05, max.steps = 10 * min(n, m), max.norm = 100 * m, 
min.lambda = (if (m >= n) 1e-06 else 0), max.vars = Inf, max.arclength = Inf, 
frac.arclength = 1, add.newvars = 1, bshoot.threshold = 0.1, relax.lambda = 1e-08, 
standardize = TRUE, function.precision = 3e-13, eps = .Machine$double.eps, trace = FALSE, 
nopenalty=NULL)

Arguments

x

a matrix of predictor variables

y

ordinal response

data

optional; list that includes x and y components

method

select between fitting a backward (default) versus a forward continuation ratio model

weight

an optional vector of weights for observations

offset

an optional vector of offset. If a column of x is used as offset, the corresponding column must be removed from x

lambda2

regularization parameter for the L2 norm of the coefficients. Default is 1e-5.

max.steps

an optional bound for the number of steps to be taken. Default is 10 * min{nrow(x), ncol(x)}

max.norm

an optional bound for the L1 norm of the coefficients. Default is 100 * ncol(x)

min.lambda

an optional (lower) bound for the size of \lambda. Default is 0 for ncol(x) < nrow(x) cases and 1e-6 otherwise

max.vars

an optional bound for the number of active variables. Default is Inf

max.arclength

an optional bound for arc length (L1 norm) of a step. If max.arclength is extremely small, an exact nonlinear path is produced. Default is Inf

frac.arclength

Under the default setting, the next step size is computed so that the active set changes right at the next value of \lambda. When frac.arclength is assigned some fraction between 0 and 1, the step size is decreased by the factor of frac.arclength in arc length. If frac.arclength=0.2, the step length is adjusted so that the active set would change after five smaller steps. Either max.arclength or frac.arclength can be used to force the path to be more accurate. Default is 1.

add.newvars

add.newvars candidate variables (that are currently not in the active set) are used in the corrector step as potential active variables. Default is 1.

bshoot.threshold

If the absolute value of a coefficient is larger than bshoot.threshold at the first corrector step it becomes nonzero (therefore when \lambda is considered to have been decreased too far), \lambda is increased again. i.e. A backward distance in \lambda that makes the coefficient zero is computed. Default is 0.1

relax.lambda

A variable joins the active set if |l(\beta)| > \lambda*(1-relax.lambda). Default is 1e-8. If no variable joins the active set even after many (>20) steps, the user should increase relax.lambda to 1e-7 or 1e-6, but not more than that. This adjustment is sometimes needed because of the numerical precision/error propagation problems. In general, the paths are less accurate with relaxed lambda.

standardize

If TRUE, predictors are standardized to have a unit variance

function.precision

function.precision parameter used in the internal solver. Default is 3e-13. The algorithm is faster, but less accurate with relaxed, larger function precision

eps

effective zero

trace

If TRUE, the algorithm prints out its progress

nopenalty

a set of indices for the predictors that are not subject to the L1 penalty

Details

The glmpathcr function is largely borrowed from the glmpath package and differs only in that (1) the ordinal dataset is first restructured to represent the K-1 conditionally independent likelihoods and (2) the family is specified to be binomial and the nopenalty.subset is specified to be the thresholds for the ordinal classes.

Value

A glmpathcr object is returned.

lambda

vector of \lambda values for which the exact coefficients are computed

lambda2

\lambda_2 used

step.length

vector of step lengths in \lambda

core

matrix of l(\beta) values (derivatives of the log-likelihood)

new.df

vector of degrees of freedom (to be used in the plot function)

df

vector of degrees of freedom at each step

deviance

vector of deviance computed at each step

aic

vector of AIC values from fitted logistic regression on restructured data; use summary for AIC from continuation ratio model

bic

vector of BIC values from fitted logistic regression on restructured data; use summary for AIC from continuation ratio model

b.predictor

matrix of coefficient estimates from the predictor steps

b.corrector

matrix of coefficient estimates from the corrector steps

new.A

vector of boolean values indicating the steps at which the active set changed (to be used in the plot/predict functions)

actions

actions taken at each step

means

means of the columns of x

sdx

standard deviations of the columns of x

xnames

column names of x

family

family used

weight

weights used

offset

offset used

nopenalty.subset

nopenalty.subset used

standardize

TRUE if the predictors were standardized before fitting

x

the matrix of predictor variables used in fitting the model

y

the ordinal outcome

method

either forward of backward method

Note

For further details about the fitting algorithm, see the glmpath package.

Author(s)

Kellie J. Archer

References

Ralf Bender and Axel Benner (2000) Calculating ordinal regression models in SAS and S-Plus. Biometrical Journal 42, 677–699.

See Also

See also as predict.glmpathcr, coef.glmpathcr

Examples

data(diabetes)
x <- diabetes[, 2:dim(diabetes)[2]]
y <- diabetes$y
fit <- glmpathcr(x, y)