| Title: | Performs Monotone Regression |
|---|---|
| Description: | The monotone package contains a fast up-and-down-blocks implementation for the pool-adjacent-violators algorithm for simple linear ordered monotone regression, including two spin-off functions for unimodal and bivariate monotone regression (see <doi:10.18637/jss.v102.c01>). |
| Authors: | Frank Busing [aut, cre], Juan Claramunt Gonzalez [aut] |
| Maintainer: | Frank Busing <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.2 |
| Built: | 2024-10-15 06:15:45 UTC |
| Source: | https://github.com/cran/monotone |
bimonotone performs bivariate monotone regression.
The function uses the up-and-down-blocks implementation (Kruskal, 1964)
of the pool-adjacent-violators algorithm (Ayer, Brunk, Ewing, Reid, and Silverman, 1955),
with additional lookaheads, repeatedly, for both rows and columns, until convergence.
bimonotone( x, w = matrix(1, nrow(x), ncol(x)), maxiter = 65536, eps = 1.49011611938477e-08 )bimonotone( x, w = matrix(1, nrow(x), ncol(x)), maxiter = 65536, eps = 1.49011611938477e-08 )
x |
a real-valued matrix. |
w |
a real-valued matrix with positive weights (default a matrix with ones). |
maxiter |
maximum number of iterations (default = 65536) |
eps |
precision of estimates (default = 1.4901161193847656e-08) |
Error checking on x, w, maxiter, or eps is not present.
Returns a real-valued matrix with values of both rows and columns of x in monotone order.
Bril G, Dykstra R, Pillers C, Robertson T (1984). Algorithm AS 206: isotonic regression in two independent variables. Journal of the Royal Statistical Society. Series C (Applied Statistics), 33(3), 352-357. URL https://www.jstor.org/stable/pdf/2347723.pdf.
Busing, F.M.T.A. (2022). Monotone Regression: A Simple and Fast O(n) PAVA Implementation. Journal of Statistical Software, Code Snippets, 102 (1), pp. 1-25. (<doi:10.18637/jss.v102.c01>)
Dykstra R.L., Robertson T. (1982). An algorithm for isotonic regression for two or more independent variables. The Annals of Statistics, 10(3), 708-716. URL https: //projecteuclid.org/download/pdf_1/euclid.aos/1176345866.
Turner, T.R. (2019). Iso: Functions to Perform Isotonic Regression. R package version 0.0-18. URL https://cran.r-project.org/package=Iso
G <- matrix( c( 1, 5.2, 0.1, 0.1, 5, 0, 6, 2, 3, 5.2, 5, 7, 4, 5.5, 6, 6 ), 4, 4 ) print( G ) H <- bimonotone( G ) print( H ) y <- c( 8, 4, 8, 2, 2, 0, 8 ) x <- bimonotone( as.matrix( y ) ) print( x ) x <- bimonotone( t( as.matrix( y ) ) ) print( x )G <- matrix( c( 1, 5.2, 0.1, 0.1, 5, 0, 6, 2, 3, 5.2, 5, 7, 4, 5.5, 6, 6 ), 4, 4 ) print( G ) H <- bimonotone( G ) print( H ) y <- c( 8, 4, 8, 2, 2, 0, 8 ) x <- bimonotone( as.matrix( y ) ) print( x ) x <- bimonotone( t( as.matrix( y ) ) ) print( x )
legacy provides some functions for monotone regression from the past.
Current implementations have been translated into C for proper comparison in Busing (2022).
legacy(x, w = rep(1, length(x)), number = 0)legacy(x, w = rep(1, length(x)), number = 0)
x |
a real-valued vector. |
w |
a real-valued vector with positive weights (default a vector with ones). |
number |
function number (specifications below). |
Legacy implementations by number, function, author, and year:
0 = default (do nothing)
1 = fitm() by Kruskal (1964).
2 = wmrmnh() by van Waning (1976).
3 = amalgm() by Cran (1980).
4 = pav() by Bril (1984).
5 = isoreg() by Gupta (1995).
6 = iso_pava() by Turner (1997).
7 = isotonic() by Kincaid (2001).
8 = isomean() by Strimmer (2008).
9 = pooled_pava() by Pedregosa (2011).
10 = linear_pava() by Tulloch (2014).
11 = inplace_pava() by Varoquaux (2016).
12 = md_pava() by Danish (2016).
13 = reg_1d_l2() by Xu (2017).
14 = jbkpava() by de Leeuw (2017).
Error checking on w or x is not present.
Returns a real-valued vector with values of x in increasing order.
Busing, F.M.T.A. (2022). Monotone Regression: A Simple and Fast O(n) PAVA Implementation. Journal of Statistical Software, Code Snippets, 102 (1), pp. 1-25. (<doi:10.18637/jss.v102.c01>)
y <- c( 8, 4, 8, 2, 2, 0, 8 ) x <- legacy( y, number = 1 ) print( x )y <- c( 8, 4, 8, 2, 2, 0, 8 ) x <- legacy( y, number = 1 ) print( x )
monotone performs simple linear ordered monotone or isotonic regression.
The function follows the up-and-down-blocks implementation (Kruskal, 1964)
of the pool-adjacent-violators algorithm (Ayer, Brunk, Ewing, Reid, and Silverman, 1955)
with additional lookaheads (Busing, 2022).
monotone(x, w = rep(1, length(x)))monotone(x, w = rep(1, length(x)))
x |
a real-valued vector. |
w |
a real-valued vector with positive weights (default a vector with ones). |
Error checking on x or w is not present.
Returns a real-valued vector with values of x in increasing order.
Ayer M., H.D. Brunk, G.M. Ewing, W.T. Reid, and E. Silverman (1955). An empirical distribution function for sampling with incomplete information. The Annals of Mathematical Statistics, pp. 641-647. URL https://www.jstor.org/stable/pdf/2236377.pdf.
Busing, F.M.T.A. (2022). Monotone Regression: A Simple and Fast O(n) PAVA Implementation. Journal of Statistical Software, Code Snippets, 102 (1), pp. 1-25. (<doi:10.18637/jss.v102.c01>)
Kruskal, J.B. (1964). Nonmetric multidimensional scaling: a numerical method. Psychometrika, 29(2), pp. 115-129. URL http://cda.psych.uiuc.edu/psychometrika_highly_cited_articles/kruskal_1964b.pdf.
y <- c( 8, 4, 8, 2, 2, 0, 8 ) x <- monotone( y ) print( x )y <- c( 8, 4, 8, 2, 2, 0, 8 ) x <- monotone( y ) print( x )
unimonotone performs unimodal monotone regression.
The function follows the up-and-down-blocks implementation (Kruskal, 1964)
of the pool-adjacent-violators algorithm (Ayer, Brunk, Ewing, Reid, and Silverman, 1955)
for both isotonic and antitonic regression,
and the prefix isotonic regression approach (Stout, 2008)
with additional lookaheads and progressive error sum-of-squares computation.
unimonotone(x, w = rep(1, length(x)))unimonotone(x, w = rep(1, length(x)))
x |
a real-valued vector. |
w |
a real-valued vector with positive weights (default a vector with ones). |
Error checking on x or w is not present.
Returns a real-valued vector with values of x in umbrella order.
Bril G, Dykstra R, Pillers C, Robertson T (1984). Algorithm AS 206: isotonic regression in two independent variables. Journal of the Royal Statistical Society. Series C (Applied Statistics), 33(3), 352-357. URL https://www.jstor.org/stable/pdf/2347723.pdf.
Busing, F.M.T.A. (2022). Monotone Regression: A Simple and Fast O(n) PAVA Implementation. Journal of Statistical Software, Code Snippets, 102 (1), pp. 1-25. (<doi:10.18637/jss.v102.c01>)
Stout, Q.F. (2008). Unimodal Regression via Prefix Isotonic Regression. Computational Statistics and Data Analysis, 53, pp. 289-297. URL https://doi:10.1016/j.csda.2008.08.005
Turner, T.R. and Wollan, P.C. (1997). Locating a maximum using isotonic regression. Computational statistics and data analysis, 25(3), pp. 305-320. URL https://doi.org/10.1016/S0167-9473(97)00009-1
Turner, T.R. (2019). Iso: Functions to Perform Isotonic Regression. R package version 0.0-18. URL https://cran.r-project.org/package=Iso
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 ) x <- unimonotone( y ) print( x )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 ) x <- unimonotone( y ) print( x )