admm: ADMM algorithm for fitting l1-penalized additive mixed models
In bdsegal/psplinesl1: P-splines with an l_1 penalty for repeated measures

This function obtains point estimates via the ADMM algorithm

1
2
3

admm(y, id, X, rand, lambda, tau, data, rho = 1, lmeUpdate = FALSE,
  epsilonAbs = 1e-04, epsilonRel = 1e-04, iterMax = 1000, warm = NULL,
  forCV = FALSE, centerZ = FALSE, verbose = FALSE, uniUpper = 1000)

`y`	character string denoting output variable
`id`	character string denoting id variable
`X`	list of fixed effect design matrices setup by l1smooth
`lambda`	scalar smoothing parameter for random effects
`tau`	vector of smoothing parameters for fixed effects
`data`	dataset
`rho`	ADMM penalty parameter
`lmeUpdate`	TRUE/FALSE if TRUE, uses lme to estimate random effects. Only available for random intercept models.
`epsilonAbs`	absolute error in ADMM (tolerance for convergence)
`epsilonRel`	relative error in ADMM (tolerance for convergence)
`warm`	list of warm start parameters
`forCV`	TRUE/FALSE If FALSE, returns less information in fitted object
`centerZ`	TRUE/FALSE If TRUE, imposes centering constraints on random effects
`verbose`	TRUE/FALSE If TRUE, prints ADMM iteration
`uniUpper`	upper limit used by uniroot to estimate tau (only used when lmeUpdate = TRUE)
`Z`	random effect design matrix setup by randomEffects
`S`	random effect penalty matrix setup by randomEffects
`iterMAx`	maximum number of ADMM iterations

library(psplinesl1)
data(simData)

# setup p-spline matrices
X <- list(ps(x = "x", data = simData, 
             norder = 2, k = 1, width = 0.05,
             center = TRUE))

# setup random effect matrices
rand <- re(x = "x", id = "id", data = simData,
           randomCurves = FALSE)

# fit model with ADMM
a1 <- admm(y = "y", X, Z = rand$Z, S = rand$S,
            lmeUpdate = TRUE,
            lambda = 0.169,
            rho = 0.169,
            data = simData)

# get and plot fitted model with confidence bands
CI <- ci(model = a1, alpha = 0.05)
plot(CI)

# extract values from ci object for custom plotting
CIpoly <- data.frame(x = c(CI[[1]]$x, rev(CI[[1]]$x)), 
                     y = c(CI[[1]]$lower, rev(CI[[1]]$upper)))

ggplot(aes(x = x, y = y), data = newDat)+
  geom_polygon(data = CIpoly, fill = "grey")+
  geom_line(aes(x = CI[[1]]$x, y = CI[[1]]$smooth))