Description Usage Arguments Details Value References See Also Examples
Regularize a linear mixed model with the linear mixed model Elastic Net penalty.
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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 |
y_i=x^{t}_{ij}β+z^{t}_{ij}b_i+ε_i,
ε_i\sim N(0,σ^2I_{n_i})
The lmmen function solves for the folloing problem.
Q(φ|y,b)=||y-ZΛΓ b-Xβ||^2+\tilde{P}(β,d)
\tilde{P}(β,d)=
λ_2^f∑\limits_{i\in P}β_i^2+λ_2^r∑\limits_{j\in Q}d_j^2+
λ_1^f∑\limits_{i \in P}|β_i|+λ_1^r∑\limits_{j \in Q}|d_j|
Where \tilde{P} and Q(φ) 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.
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 Λ (correlation of random effects)
Mean.est: model prediction X^{t}β
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 Γ
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
Prepublished version of the lmmen paper.
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Loading required package: lmmlasso
Loading required package: emulator
Loading required package: mvtnorm
Loading required package: miscTools
Loading required package: penalized
Loading required package: survival
Welcome to penalized. For extended examples, see vignette("penalized").
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This is a test release of the package 'lmmlasso'. If you have any questions or problems, do not hesitate to contact the author.
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$fixed
[1] 0.359625 0.542706 0.570917 0.000000 0.000000 0.000000 0.000000 0.000000
[9] 0.000000
$stddev
[1] 2.2696830 1.5295087 0.7474349 0.2157175
$BIC
[1] 754.7452
$sigma.2
[1] 2.759154
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