transform_plaqr {plaqr}

Transformation for Partially Linear Additive Quantile Regression

Description

Returns the estimated transformation parameter for the one-parameter symmetric transformation (Geraci and Jones, 2015). Confidence intervals for the transformation parameter can also be created using the bootstrap. The response variable must be strictly positive; a constant can be added to the variable to ensure that all values are positive.

Usage

transform_plaqr(formula, nonlinVars=NULL, tau=.5, data=NULL, lambda=seq(0,1,by=.05),
                confint=NULL, B=99, subset, weights, na.action, method = "br", 
                contrasts = NULL, splinesettings=NULL)

Arguments

formula

a formula object, with the response on the left of a ~ operator, and the linear terms, separated by + operators, on the right. Any terms on the right of the ~ operator that also appear in nonlinVars will be included in the model as spline terms, not linear terms.

nonlinVars

a one-sided formula object, with a ~ operator to the left of the nonlinear terms seperated by + operators. A term appearing in both formula and nonlinVars will be treated as a nonlinear term. If nonlinVars is not NULL, then an intercept will automatically be included in the model (despite a -1 or 0 term included in formula).

tau

the quantile to be estimated, this is a number strictly between 0 and 1 (for now).

data

a data.frame in which to interpret the variables named in the formula, or in the subset and the weights argument. If this is missing, then the variables in the formula should be on the search list. This may also be a single number to handle some special cases – see below for details.

lambda

a real-valued sequence of possible transformation parameters. 0 corresponds to the log transformation and 1 corresponds to the identity. The transformation is symmetric so a negative transformation parameter is redundant and can be avoided. See Geraci and Jones (2015) for more information on the one-parameter, symmetric transformation.

confint

a confint confidence interval for the transformation parameter will be created if confint is a number between 0 and 1 (otherwise automatically creates 95% CI). Otherwise, no confidence interval will be created. The bootstrap is used to create the confidence interval.

B

the number of bootstrap replications for the confidence interval. If no confidence interval is being created, this argument is ignored.

subset

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

weights

vector of observation weights; if supplied, the algorithm fits to minimize the sum of the weights multiplied into the absolute residuals. The length of weights must be the same as the number of observations. The weights must be nonnegative and it is strongly recommended that they be strictly positive, since zero weights are ambiguous.

na.action

a function to filter missing data. This is applied to the model.frame after any subset argument has been used. The default (with na.fail) is to create an error if any missing values are found. A possible alternative is na.omit, which deletes observations that contain one or more missing values.

method

the algorithmic method used to compute the fit. There are several options: The default method is the modified version of the Barrodale and Roberts algorithm for l_1-regression, used by l1fit in S, and is described in detail in Koenker and d'Orey(1987, 1994), default = "br". This is quite efficient for problems up to several thousand observations, and may be used to compute the full quantile regression process. It also implements a scheme for computing confidence intervals for the estimated parameters, based on inversion of a rank test described in Koenker(1994). For larger problems it is advantagous to use the Frisch–Newton interior point method "fn". And very large problems one can use the Frisch–Newton approach after preprocessing "pfn". Both of the latter methods are described in detail in Portnoy and Koenker(1997). There is a fifth option "fnc" that enables the user to specify linear inequality constraints on the fitted coefficients; in this case one needs to specify the matrix R and the vector r representing the constraints in the form Rb \geq r. See the examples. Finally, there are two penalized methods: "lasso" and "scad" that implement the lasso penalty and Fan and Li's smoothly clipped absolute deviation penalty, respectively. These methods should probably be regarded as experimental.

contrasts

a list giving contrasts for some or all of the factors default = NULL appearing in the model formula. The elements of the list should have the same name as the variable and should be either a contrast matrix (specifically, any full-rank matrix with as many rows as there are levels in the factor), or else a function to compute such a matrix given the number of levels.

splinesettings

a list of length equal to the number of nonlinear effects containing arguments to pass to the bs function for each term. Each element of the list is either NULL or a list with named elements correpsonding to the arguments in bs. If not NULL, the first element of splinesettings corresponds to the first nonlinear effect and so on.

Value

Returns the following:

parameter

The transformation parameter

Y

The values of the transformed response

confint

If a confidence interval is created, this is the confidence interval for the transformation parameter. Otherwise, NULL.

U

If a confidence interval is created, a B by n matrix containing the indices used in each bootstrap sample. Otherwise, NULL.

P

If a confidence interval is created, a B length vector containing the transformation parameter estimated in each bootstrap sample. Otherwise, NULL.

Author(s)

Adam Maidman

References

Geraci, M. and Jones, M. (2015). Improved transformation-based quantile regression. Canadian Journal of Statistics 43, 118-132.

Maidman, A., Wang, L. (2017). New Semiparametric Method for Predicting High-Cost Patients. Preprint.

Examples

data(simData)

simData$Y <- exp(simData$y)

transform_plaqr(Y~x1+x2+x3, nonlinVars=~z1+z2, data=simData) 

transform_plaqr(Y~x1+x2+x3, nonlinVars=~z1+z2, confint=.95, data=simData)