splmm: Function to fit linear mixed-effects model with double penalty for fixed effects and random effects

Description

All the details of the algorithm can be found in the manuscript.

Usage

splmm(x, y, z, grp, lam1, lam2, nonpen.b=1,nonpen.L=1,penalty.b=c("lasso","scad"),
      penalty.L=c("lasso","scad"),CovOpt=c("nlminb","optimize"),
      standardize=TRUE,control=splmmControl())
# S3 method for default
splmm(x, y, z, grp, lam1, lam2, nonpen.b=1,nonpen.L=1,penalty.b=c("lasso","scad"),
      penalty.L=c("lasso","scad"),CovOpt=c("nlminb","optimize"),
      standardize=TRUE,control=splmmControl())

Value

A 'splmm' object is returned, for which

coef,resid, fitted,

print, summary methods exist.

data: data set used for fitting the model, as a list with four components: x, y, z, grp (see above)
coefInit: list of the starting values for beta, random effects covariance structure, and variance structure
penalty.b: The penalty method for fixed effects penalization.
penalty.L: The penalty method for random effects penalization.
nonpen.b: Index of indices of fixed effects not penalized.
nonpen.L: Index of indices of random effects not penalized.
lambda1: regularization parameter for fixed effects penalization scaled by the number of subjects.
lambda2: regularization parameter for random effects penalization the number of subjects.
sigma: standard deviation \(\hat{\sigma}\) of the errors
D: The estimates of the random effects covariance matrix \(\hat{D}\).
Lvec: Vectorized \(\hat{L}\), the lower triangular matrix of \(\hat{D}\) from Cholesky Decomposition.
coefficients: estimated fixed-effects coefficients \(\hat{\beta}\)
random: vector with random effects, sorted by groups
ranef: vector with random effects, sorted by effect
u: vector with the standardized random effects, sorted by effect
fixef: estimated fixed-effects coeffidients \(\hat{\beta}\)
fitted.values: The fitted values \(\hat{y} = \hat{X} \beta + Z \hat{b}_i\)
residuals: raw residuals \(y-\hat{y}\)
corD: Correlation matrix of the random effects
logLik: value of the log-likelihood function
deviance: deviance=-2*logLik
npar: Number of parameters. Corresponds to the cardinality of the set of nonzero coefficients plus the number of nonzero variance in D
aic: AIC
bic: BIC
bicc: Modified BIC defined by Wang et al (2009)
ebic: Extended BIC defined by Chen and Chen (2008)
converged: Does the algorithm converge? 0: correct convergence ; an odd number means that maxIter was reached ; an even number means that the Armijo step was not succesful. For each unsuccessfull Armijo step, 2 is added to converged. If converged is large compared to the number of iterations counter, you may increase maxArmijo.
counter: The number of iterations used.
stopped: logical indicating whether the algorithm stopped due to too many parameters, if yes need to increase lam1 or lam2
CovOpt: optimization routine
control: see splmmControl
objective: Value of the objective function at the final estimates
call: call

Arguments

x: matrix of dimension N x p including the fixed-effects covariables. An intercept has to be included in the first column as (1,...,1).
y: response variable of length N.
z: random effects matrix of dimension N x q. It has to be a matrix, even if q=1.
grp: grouping variable of length N
lam1: regularization parameter for fixed effects penalization.
lam2: regularization parameter for random effects penalization.
nonpen.b: Index of indices of fixed effects not penalized. The default value is 1, which means the fixed intercept is not penalized
nonpen.L: Index of indices of random effects not penalized. The default value is 1, which means the random intercept is not penalized
penalty.b: The penalty method for fixed effects penalization. Currently available options include LASSO penalty and SCAD penalty.
penalty.L: The penalty method for fixed effects penalization. Currently available options include LASSO penalty and SCAD penalty.
CovOpt: which optimization routine should be used for updating the variance parameter. The available options include optimize and nlminb. nlminb uses the estimate of the last iteration as a starting value. nlminb is faster if there are many Gauss-Seidel iterations.
standardize: A logical parameter specifying whether the fixed effects matrix x and random effects matrix z should be standardized such that each column has mean 0 and standard deviation 1. The default value is TRUE
control: control parameters for the algorithm and the Armijo Rule, see 'splmmControl' for the details

Examples

Run this code


### Use splmm for a toy dataset.

data(simulated_data)

set.seed(144)
fit = splmm(x=simulated_data$x,y=simulated_data$y,
z=simulated_data$z,grp=simulated_data$grp,
lam1=0.1,lam2=0.01, penalty.b="scad", penalty.L="scad")
summary(fit)

# \donttest{

## Use splmm on the Kenya school cognitive data set


data(cognitive)

x <- model.matrix(ravens ~schoolid+treatment+year+sex+age_at_time0
                  +height+weight+head_circ+ses+mom_read+mom_write
                  +mom_edu, cognitive)
z <- x

fit <- splmm(x=x,y=cognitive$ravens,z=z,grp=cognitive$id,lam1=0.1,
lam2=0.1,penalty.b="lasso", penalty.L="lasso")
summary(fit)
# }

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