gpava: Generalized Pooled-Adjacent-Violators Algorithm (PAVA)

In isotone: Active Set and Generalized PAVA for Isotone Optimization

Generalized Pooled-Adjacent-Violators Algorithm (PAVA)

Description

Pooled-adjacent-violators algorithm for general isotone regression problems. It allows for general convex target function, multiple measurements, and different approaches for handling ties.

Usage

gpava(z, y, weights = NULL, solver = weighted.mean, ties = "primary", p = NA)

Arguments

z	Vector of abscissae values
y	Vector or list of vectors of responses
weights	Vector of list of vectors of observation weights
solver	Either weighted.mean, weighted.median, weighted.fractile, or a user-specified function (see below)
ties	Treatment of ties, either "primary", "secondary", or "tertiary"
p	Fractile value between 0 and 1 if weighted.fractile is used

Details

A Pool Adjacent Violators Algorithm framework for minimizing problems like

∑_i ∑_{J_i} w_{ij} f(y_{ij}, m_i)

under the constraint m_1 ≤ ... ≤ m_n with f a convex function in m. Note that this formulation allows for repeated data in each block (i.e. each list element of y, and hence is more general than the usual pava/isoreg ones.

A solver for the unconstrained ∑_k w_k f(y_k, m) -> min! can be specified. Typical cases are f(y, m) = |y - m|^p for p = 2 (solved by weighted mean) and p = 1 (solved by weighted median), respectively.

Using the weighted.fractile solver corresponds to the classical minimization procedure in quantile regression.

The user can also specify his own function foo(y, w) with responses and weights as arguments. It should return a single numerical value.

Value

Generates an object of class gpava.

x	Fitted values
y	Observed response
z	Observed predictors
w	Weights
solver	Convex function
call	Matched call
p	Fractile value

Author(s)

Kurt Hornik, Jan de Leeuw, Patrick Mair

References

de Leeuw, J., Hornik, K., Mair, P. (2009). Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods. Journal of Statistical Software, 32(5), 1-24.

Examples

data(pituitary)
##different tie approaches
gpava(pituitary[,1],pituitary[,2], ties = "primary")
gpava(pituitary[,1],pituitary[,2], ties = "secondary")
gpava(pituitary[,1],pituitary[,2], ties = "tertiary")

##different target functions
gpava(pituitary[,1],pituitary[,2], solver = weighted.mean)
gpava(pituitary[,1],pituitary[,2], solver = weighted.median)
gpava(pituitary[,1],pituitary[,2], solver = weighted.fractile, p = 0.25)


##repeated measures
data(posturo)
res <- gpava(posturo[,1],posturo[,2:4], ties = "secondary")
plot(res)

isotone documentation built on March 7, 2023, 3:17 p.m.