lmmen (version 1.0)

lmmen: linear mixed model Elastic Net

Description

Regularize a linear mixed model with the linear mixed model Elastic Net penalty.

Usage

lmmen(data, init.beta, frac, eps = 10^(-4), verbose = FALSE)

Arguments

data

matrix, data

init.beta

numeric, initial values for fixed effects coefficients

frac

numeric, penalty levels for fixed and random effects expressed in ratios. c(L1.fixed,L2.fixed,L1.random,L2.random)

eps

numeric, tolerance level to pass to solve.QP, Default: 10^(-4)

verbose

boolean, show output during optimization Default: FALSE

Value

lmmen fit object including

fixed: estimated fixed effects coefficients

stddev: estimated random effects covariance matrix standard deviations

sigma.2: standard error of the model residual effect

lambda: estimated lower triangle of \(\Lambda\) (correlation of random effects)

Mean.est: model prediction \(X^{t}\beta\)

loglike: log likelihood

df: degrees of freedom

BIC: Minimum BIC penalty value

frac: ratio placed on the penalties corresponding to BIC

Gamma.Mat.RE: estimated \(\Gamma\)

Cov.Mat.RE: estimated random effect covariance matrix

Corr.Mat.RE: estimate random effects correlation matrix

solveQP: output of the call to solveQP corresponding to min BIC

Details

\(y_i=x^{t}_{ij}\beta+z^{t}_{ij}b_i+\epsilon_i,\)

\(\epsilon_i\sim N(0,\sigma^2I_{n_i})\)

The lmmen function solves for the folloing problem.

\(Q(\phi|y,b)=||y-Z\Lambda\Gamma b-X\beta||^2+\tilde{P}(\beta,d)\)

\(\tilde{P}(\beta,d)=\)

\(\lambda_2^f\sum\limits_{i\in P}\beta_i^2+\lambda_2^r\sum\limits_{j\in Q}d_j^2+\)

\(\lambda_1^f\sum\limits_{i \in P}|\beta_i|+\lambda_1^r\sum\limits_{j \in Q}|d_j|\)

Where \(\tilde{P}\) and \(Q(\phi)\) denote the penalty applied to the likelihood and the penalized log-likelihood.

When the final model is not a mixed effects model, but either a fixed effects or random effects model then the original form of the Elastic Net penalty is applied.

References

Prepublished version of the lmmen paper.

See Also

solve.QP

Examples

# NOT RUN {
 dat <- initialize_example(n.i = 5,n = 30,q=4,seed=1)
 init <- init.beta(dat,method='glmnet')
 lmmen(data=dat,init.beta=init,frac=c(0.8,1,1,1))
# }