Description Usage Arguments Value Examples

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

1 2 3 4 5 6 7 8 | ```
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())
## Default S3 method:
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())
``` |

`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 |

`control` |
control parameters for the algorithm and the Armijo Rule, see |

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 |

`D` |
The estimates of the random effects covariance matrix |

`Lvec` |
Vectorized |

`coefficients` |
estimated fixed-effects coefficients |

`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 |

`fitted.values` |
The fitted values |

`residuals` |
raw residuals |

`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 |

`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` |
The number of iterations used. |

`stopped` |
logical indicating whether the algorithm stopped due to too many parameters, if yes need to increase |

`CovOpt` |
optimization routine |

`control` |
see |

`objective` |
Value of the objective function at the final estimates |

`call` |
call |

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
### 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)
## 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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