Iso (version 0.0-18)

ufit: Unimodal isotonic regression.

Description

A "divide and conquer" algorithm is applied to calculate the isotonic regression of a set of data, for a unimodal order. If the mode of the unimodal order is not specified, then the optimal (in terms of minimizing the error sum of squares) unimodal fit is calculated.

Usage

ufit(y, lmode=NULL, x=NULL, w=NULL, lc=TRUE, rc=TRUE,
        type=c("raw","stepfun","both"))

Arguments

y

Vector of data whose isotonic regression is to be calculated.

lmode

Gives the location of the mode if this is specified; if the location is not specified, then all possible modes are tried and that one giving the smallest error sum of squares is used.

x

A largely notional vector of \(x\) values corresponding to the data vector y; the value of the mode must be given, or will be calculated in terms of these \(x\) values. Conceptually the model is y = m(x) + E, where m() is a unimodal function with mode at lmode, and where E is random "error". If x is not specified, it defaults to an equi-spaced sequence on [0,1].

w

Optional vector of weights to be used for calculating a weighted isotonic regression; if w is not given, all weights are taken to equal 1.

lc

Logical argument; should the isotonization be left continuous? If lc==FALSE then the value of the isotonization just before the mode is set to NA, which causes line plots to have a jump discontinuity at (just to the left of) the mode. The default is lc=TRUE.

rc

Logical argument; should the isotonization be right continuous? If rc==FALSE then the value of the isotonization just after the mode is set to NA, which causes line plots to have a jump discontinuity at (just to the right of) the mode. The default is rc=TRUE.

type

String specifying the type of the output; see “Value”. May be abbreviated.

Value

If type=="raw" then the value is a list with components:

x

The argument x if this is specified, otherwise the default value.

y

The fitted values.

lmode

The argument lmode if this is specified, otherwise the value of lmode which is found to minimize the error sum of squares.

mse

The mean squared error.

If type=="both" then a component h which is the step function representation of the isotonic regression is added to the foregoing list.

If type=="stepfun" then only the step function representation h is returned.

Details

Dynamically loads fortran subroutines "pava", "ufit" and "unimode" to do the actual work.

References

Mureika, R. A., Turner, T. R. and Wollan, P. C. (1992). An algorithm for unimodal isotonic regression, with application to locating a maximum. University of New Brunswick Department of Mathematics and Statistics Technical Report Number 92 -- 4.

Robertson, T., Wright, F. T. and Dykstra, R. L. (1988). Order Restricted Statistical Inference. Wiley, New York.

Shi, Ning-Zhong. (1988) A test of homogeneity for umbrella alternatives and tables of the level probabilities. Commun. Statist. --- Theory Meth. vol. 17, pp. 657 -- 670.

Turner, T. R., and Wollan, P. C. (1997) Locating a maximum using isotonic regression. Computational Statistics and Data Analysis vol. 25, pp. 305 -- 320.

See Also

pava() biviso()

Examples

# NOT RUN {
x <- c(0.00,0.34,0.67,1.00,1.34,1.67,2.00,2.50,3.00,3.50,4.00,4.50,
       5.00,5.50,6.00,8.00,12.00,16.00,24.00)
y <- c(0.0,61.9,183.3,173.7,250.6,238.1,292.6,293.8,268.0,285.9,258.8,
       297.4,217.3,226.4,170.1,74.2,59.8,4.1,6.1)
z <- ufit(y,x=x,type="b")
plot(x,y)
lines(z,col="red")
plot(z$h,do.points=FALSE,col.hor="blue",col.vert="blue",add=TRUE)

# }