ordinalgmifs {ordinalgmifs}

Ordinal Generalized Monotone Incremental Forward Stagewise Regression

Description

This function can fit a cumulative link, adjacent category, forward and backward continuation ratio, and stereotype ordinal response model when the number of parameters exceeds the sample size, using the the generalized monotone incremental forward stagewise method.

Usage

ordinalgmifs(formula, data, x = NULL, subset, epsilon = 0.001, tol = 1e-05, 
	scale = TRUE, probability.model = "Cumulative", link = "logit", 
	verbose=FALSE, assumption=NULL, ...)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The left side of the formula is the ordinal outcome while the variables on the right side of the formula are the covariates that are not included in the penalization process. Note that if all variables in the model are to be penalized, an intercept only model formula should be specified.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model.

x

an optional matrix of predictors that are to be penalized in the model fitting process.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

epsilon

small incremental amount used to update a coefficient at a given step.

tol

the iterative process stops when the difference between successive log-likelihoods is less than this specified level of tolerance.

scale

logical, if TRUE the penalized predictors are centered and scaled.

probability.model

the type of ordinal response model to be fit. Can be "Cumulative", "AdjCategory", "ForwardCR", "BackwardCR", or "Stereotype"

link

the link function used. Allowable links for "Cumulative", "ForwardCR", and "BackwardCR" are "logit", "probit", and "cloglog". For an "AdjCategory" model only a "loge" link is allowed; for a "Stereotype" model only a "logit" link is allowed.

verbose

logical, if TRUE the step number is printed to the console (default is FALSE).

assumption

integer, only use with probability.model = "ForwardCR" and link = "cloglog" to denote the assumption to use for discrete censored survival modeling. If assumption = 1, assume the observation was censored at the end of the discrete time interval in which the censoring occurred; if assumption = 2, assume the observation was censored at the beginning of the interval in which censoring occurred; if assumption = 3, assume constant hazard rate within the interval in which the censoring occurred; if no censoring occurs, do not specify a value for assumption.

...

additional arguments

Details

A model specified as response~terms, x=penalized.terms where response is the ordinal response vector and terms is the series of variables in the model that are not to be penalized and x is a matrix of variables that are to be penalized. For example, terms may include the variables age and gender while x includes hundreds to thousands of features from a high-throughput genomic experiment. In the event that no baseline demographic/clinical characteristics/subject level variables are available or needed in terms (all variables are to be penalized) then the model is specified as response~1, x=penalized.terms.

Value

AIC

a vector of AIC values for each step (if x is specified).

BIC

a vector of BIC values for each step (if x is specified).

alpha

the ordinal threshold estimates for the fitted model.

theta

the coefficient estimates for the unpenalized variables (if terms are specified on the right hand side of the model formula).

beta

the coefficient estimates for the penalized variables (if x is specified in the model).

phi

the scaling coefficient estimates (if a "Stereotype" logit model is fit).

logLik

a vector of log-likelihood values for each step(if terms are specified on the right hand side of the model formula).

link

the link function used in the model fit.

model.select

the step at which the minimum AIC was observed (if terms are specified on the right hand side of the model formula).

probability.model

the model fit.

scale

logical indicating whether penalized variables were centered and scaled.

w

the unpenalized variables in the model (if any).

x

the penalized variables in the model (if any).

y

the ordinal response.

Author(s)

Kellie J. Archer, Jiayi Hou, Qing Zhou, Kyle Ferber, John G. Layne, Amanda Gentry

References

Hastie T., Taylor J., Tibshirani R., and Walther G. (2007) Forward stagewise regression and the monotone lasso. Electronic Journal of Statistics, 1, 1-29.

See Also

See Also coef.ordinalgmifs, summary.ordinalgmifs, plot.ordinalgmifs, predict.ordinalgmifs

Examples

data(hccframe)
# To minimize processing time, MPO_E302_R is coerced into the model and only a subset of 
# two CpG sites (DDIT3_P1313_R and HDAC9_P137_R) are included as penalized covariates
# in this demonstration, and epsilon is set to 0.01
hcc.fit <- ordinalgmifs(group ~ MPO_E302_R, x = c("DDIT3_P1313_R", "HDAC9_P137_R"), 
	data = hccframe, epsilon = 0.01)
coef(hcc.fit)
summary(hcc.fit)
phat <- predict(hcc.fit)
head(phat$predicted)
table(phat$class, hccframe$group)