Non-negative regression fits with a sparse overparameterized model matrix

Assuming z = t(x) %*% y + noise, a non-negatively modified least squares estimate of t(x) %*% y is made.

Usage

LSfitNonNeg(x, z, limit = 1e-10, viaQR = FALSE, printInc = TRUE)

Arguments

x: A matrix
z: A single column matrix
limit: Lower limit for non-zero fits. Set to NULL or -Inf to avoid the non-zero restriction.
viaQR: Least squares fits obtained using qr when TRUE.
printInc: Printing "..." to console when TRUE.

Value

A fitted version of z

Details

The problem is first reduced by elimination some rows of x (elements of y) using GaussIndependent. Thereafter least squares fits are obtained using solve or qr. Possible negative fits will be forced to zero in the next estimation iteration(s).

Author

Øyvind Langsrud

Examples

set.seed(123)
data2 <- SSBtoolsData("z2")
x <- ModelMatrix(data2, formula = ~fylke + kostragr * hovedint - 1)
z <- t(x) %*% data2$ant + rnorm(ncol(x), sd = 3)
LSfitNonNeg(x, z)
#> (-)..........-z......
#> 20 x 1 Matrix of class "dgeMatrix"
#>                           [,1]
#> 1-Total-Total        124.16486
#> 4-Total-Total         53.15576
#> 5-Total-Total        121.52242
#> 6-Total-Total        204.05782
#> 8-Total-Total        104.23415
#> 10-Total-Total        99.99149
#> Total-300-Total      599.12021
#> Total-400-Total      108.00628
#> Total-Total-annet     87.11441
#> Total-Total-arbeid    52.20565
#> Total-Total-soshjelp 344.18318
#> Total-Total-trygd    223.62325
#> Total-300-annet       71.44359
#> Total-300-arbeid      52.20565
#> Total-300-soshjelp   282.23779
#> Total-300-trygd      193.23318
#> Total-400-annet       15.67083
#> Total-400-arbeid       0.00000
#> Total-400-soshjelp    61.94538
#> Total-400-trygd       30.39007
LSfitNonNeg(x, z, limit = NULL)
#> (-)..........
#> 20 x 1 Matrix of class "dgeMatrix"
#>                            [,1]
#> 1-Total-Total        124.083059
#> 4-Total-Total         53.073953
#> 5-Total-Total        121.440610
#> 6-Total-Total        203.976011
#> 8-Total-Total        104.152349
#> 10-Total-Total        99.909680
#> Total-300-Total      599.283822
#> Total-400-Total      107.351839
#> Total-Total-annet     87.332560
#> Total-Total-arbeid    51.060386
#> Total-Total-soshjelp 344.401322
#> Total-Total-trygd    223.841393
#> Total-300-annet       71.143636
#> Total-300-arbeid      53.269117
#> Total-300-soshjelp   281.937840
#> Total-300-trygd      192.933228
#> Total-400-annet       16.188924
#> Total-400-arbeid      -2.208732
#> Total-400-soshjelp    62.463482
#> Total-400-trygd       30.908165

if (FALSE) { # \dontrun{
mf <- ~region*mnd + hovedint*mnd + fylke*hovedint*mnd + kostragr*hovedint*mnd
data4 <- SSBtoolsData("sosialFiktiv")
x <- ModelMatrix(data4, formula = mf)
z <- t(x) %*% data4$ant + rnorm(ncol(x), sd = 3)
zFit <- LSfitNonNeg(x, z)
} # }