Introduction to gglasso
Install the package
Least squares regression
library(gglasso)
# load bardet data set
data(bardet)
group1 <- rep(1:20, each = 5)
fit_ls <- gglasso(x = bardet$x, y = bardet$y, group = group1, loss = "ls")
plot(fit_ls)
## s89 s90 s91 s92 s93
## (Intercept) 8.099354325 8.098922472 8.098531366 8.098175719 8.097849146
## V1 -0.119580203 -0.120877799 -0.122079683 -0.123223779 -0.124310183
## V2 -0.113742329 -0.114834411 -0.115853997 -0.116837630 -0.117782854
## V3 -0.002584792 -0.003487571 -0.004328519 -0.005134215 -0.005904892
## V4 -0.084771705 -0.088304073 -0.091674509 -0.094978960 -0.098212775
## s94 s95 s96 s97 s98
## (Intercept) 8.097574095 8.097295166 8.097058895 8.096833259 8.096637676
## V1 -0.125274109 -0.126284595 -0.127173301 -0.128011016 -0.128738414
## V2 -0.118630121 -0.119526679 -0.120326451 -0.121086672 -0.121754134
## V3 -0.006593702 -0.007323107 -0.007970047 -0.008583011 -0.009116809
## V4 -0.101161988 -0.104349829 -0.107241330 -0.110045942 -0.112543755
## s99
## (Intercept) 8.096455264
## V1 -0.129453437
## V2 -0.122415680
## V3 -0.009645386
## V4 -0.115058449Cross-Validation
## 1
## (Intercept) 8.188159e+00
## V1 -2.920404e-02
## V2 -6.260109e-02
## V3 3.778408e-02
## V4 8.687388e-03
## V5 -8.859391e-02
## V6 -1.917990e-04
## V7 1.154126e-03
## V8 1.134775e-03
## V9 1.375735e-04
## V10 -1.803483e-03
## V11 3.013438e-02
## V12 -4.004602e-02
## V13 -6.794145e-03
## V14 8.109610e-03
## V15 -5.928599e-02
## V16 -1.546346e-03
## V17 4.609510e-02
## V18 -2.604565e-02
## V19 -4.389721e-03
## V20 -6.305305e-02
## V21 4.003787e-02
## V22 9.184201e-02
## V23 -4.403054e-02
## V24 -2.419818e-02
## V25 -1.597623e-01
## V26 1.237461e-01
## V27 2.623245e-02
## V28 -3.587628e-02
## V29 1.594558e-02
## V30 -1.875068e-01
## V31 -2.663886e-02
## V32 1.306416e-02
## V33 4.911749e-03
## V34 1.682876e-02
## V35 2.623702e-02
## V36 4.044955e-02
## V37 -1.269815e-02
## V38 5.584653e-03
## V39 1.161722e-02
## V40 -5.532465e-02
## V41 -2.726735e-03
## V42 -3.547834e-03
## V43 1.317188e-03
## V44 8.437427e-03
## V45 4.023073e-03
## V46 -1.063313e-01
## V47 8.810500e-02
## V48 1.009493e-01
## V49 1.711919e-02
## V50 2.499672e-02
## V51 -9.420268e-03
## V52 1.250468e-02
## V53 9.582327e-02
## V54 1.612372e-01
## V55 3.603498e-02
## V56 5.235399e-04
## V57 -1.333945e-05
## V58 -1.657585e-03
## V59 2.294992e-03
## V60 6.384236e-04
## V61 -5.603876e-02
## V62 3.572879e-02
## V63 3.379915e-03
## V64 8.641343e-02
## V65 2.367518e-01
## V66 -3.549915e-02
## V67 1.250114e-02
## V68 2.605464e-02
## V69 4.405841e-02
## V70 2.679824e-03
## V71 -7.724819e-03
## V72 -1.259015e-03
## V73 2.855898e-02
## V74 -5.028518e-03
## V75 6.201713e-03
## V76 -1.765083e-02
## V77 2.514867e-02
## V78 5.464928e-02
## V79 -1.087780e-02
## V80 1.661320e-02
## V81 5.503388e-03
## V82 -1.814688e-02
## V83 8.430385e-03
## V84 8.898539e-03
## V85 -2.486413e-02
## V86 4.534706e-03
## V87 -6.503766e-02
## V88 -2.233163e-03
## V89 4.839429e-02
## V90 -7.798514e-02
## V91 2.161202e-02
## V92 -7.751690e-03
## V93 -8.403776e-03
## V94 2.150891e-02
## V95 -2.723838e-02
## V96 -5.745993e-03
## V97 5.749582e-03
## V98 -8.963615e-04
## V99 6.827704e-04
## V100 8.933803e-03Weight Least squares regression
We can also perform weighted least-squares regression by specifying
loss='wls', and providing a \(n
\times n\) weight matrix in the weights argument,
where \(n\) is the number of
observations. Note that cross-validation is NOT
IMPLEMENTED for loss='wls'.
# generate weight matrix
times <- seq_along(bardet$y)
rho <- 0.5
sigma <- 1
H <- abs(outer(times, times, "-"))
V <- sigma * rho^H
p <- nrow(V)
V[cbind(1:p, 1:p)] <- V[cbind(1:p, 1:p)] * sigma
# reduce eps to speed up convergence for vignette build
fit_wls <- gglasso(x = bardet$x, y = bardet$y, group = group1, loss = "wls",
weight = V, eps = 1e-4)
plot(fit_wls)
## s89 s90 s91 s92 s93
## (Intercept) 8.09429262 8.09340481 8.09254573 8.09170743 8.09089247
## V1 -0.13922372 -0.14077803 -0.14222609 -0.14359110 -0.14487482
## V2 -0.15966042 -0.16117772 -0.16261019 -0.16397683 -0.16527730
## V3 0.03917529 0.03880296 0.03847035 0.03816594 0.03788642
## V4 -0.16548208 -0.17057112 -0.17546237 -0.18021267 -0.18481370
## s94 s95 s96 s97 s98
## (Intercept) 8.09011527 8.08935394 8.08862146 8.08793054 8.08727098
## V1 -0.14606257 -0.14719352 -0.14824987 -0.14921624 -0.15011520
## V2 -0.16649386 -0.16766459 -0.16877053 -0.16979410 -0.17075592
## V3 0.03763241 0.03739356 0.03717453 0.03697953 0.03680099
## V4 -0.18919074 -0.19347289 -0.19758499 -0.20145156 -0.20513769
## s99
## (Intercept) 8.08664325
## V1 -0.15094837
## V2 -0.17165664
## V3 0.03663899
## V4 -0.20863833