Description Usage Arguments Value
Fit a mixed model with lasso, group lasso, or sparsegroup lasso via proximal gradient descent. As this is an iterative algorithm, the step size for each iteration is determined via backtracking line search. A grid search for the regularization parameter λ is performed using warm starts. The mixed model has the form:
y = X b + Z u + residual.
The penalty of the sparsegroup lasso (without additional weights for features) is then:
α λ u_1 + (1  α) λ ∑_l ω^G_l u^{(l)}_2.
If α = 1, this leads to the lasso. If α = 0, this leads to the group lasso. Furthermore, if instead of applying the l_2norm on u^{(l)} but on the fitted values Z^{(l)} u^{(l)} two more algorithms may be called: either the fitted group lasso or the fitted sparsegroup lasso.
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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120  seagull_fitted_group_lasso(
VECTOR_Yc,
Y_MEAN,
MATRIX_Xc,
VECTOR_Xc_MEANS,
VECTOR_Xc_STANDARD_DEVIATIONS,
VECTOR_WEIGHTS_FEATURESc,
VECTOR_WEIGHTS_GROUPSc,
VECTOR_FULL_COLUMN_RANK,
VECTOR_GROUPS,
VECTOR_BETAc,
VECTOR_INDEX_PERMUTATION,
VECTOR_INDEX_EXCLUDE,
EPSILON_CONVERGENCE,
ITERATION_MAX,
GAMMA,
LAMBDA_MAX,
PROPORTION_XI,
DELTA,
NUMBER_INTERVALS,
NUMBER_FIXED_EFFECTS,
NUMBER_VARIABLES,
INTERNAL_STANDARDIZATION,
TRACE_PROGRESS
)
seagull_fitted_sparse_group_lasso(
VECTOR_Yc,
Y_MEAN,
MATRIX_Xc,
VECTOR_Xc_MEANS,
VECTOR_Xc_STANDARD_DEVIATIONS,
VECTOR_WEIGHTS_FEATURESc,
VECTOR_WEIGHTS_GROUPSc,
VECTOR_FULL_COLUMN_RANK,
VECTOR_GROUPS,
VECTOR_BETAc,
VECTOR_INDEX_PERMUTATION,
VECTOR_INDEX_EXCLUDE,
ALPHA,
EPSILON_CONVERGENCE,
ITERATION_MAX,
LAMBDA_MAX,
PROPORTION_XI,
DELTA,
STEP_SIZE,
NUMBER_INTERVALS,
NUMBER_FIXED_EFFECTS,
NUMBER_VARIABLES,
INTERNAL_STANDARDIZATION,
TRACE_PROGRESS
)
seagull_group_lasso(
VECTOR_Yc,
Y_MEAN,
MATRIX_Xc,
VECTOR_Xc_MEANS,
VECTOR_Xc_STANDARD_DEVIATIONS,
VECTOR_WEIGHTS_FEATURESc,
VECTOR_GROUPS,
VECTOR_BETAc,
VECTOR_INDEX_PERMUTATION,
VECTOR_INDEX_EXCLUDE,
EPSILON_CONVERGENCE,
ITERATION_MAX,
GAMMA,
LAMBDA_MAX,
PROPORTION_XI,
NUMBER_INTERVALS,
NUMBER_FIXED_EFFECTS,
NUMBER_VARIABLES,
INTERNAL_STANDARDIZATION,
TRACE_PROGRESS
)
seagull_lasso(
VECTOR_Yc,
Y_MEAN,
MATRIX_Xc,
VECTOR_Xc_MEANS,
VECTOR_Xc_STANDARD_DEVIATIONS,
VECTOR_WEIGHTS_FEATURESc,
VECTOR_BETAc,
VECTOR_INDEX_EXCLUDE,
EPSILON_CONVERGENCE,
ITERATION_MAX,
GAMMA,
LAMBDA_MAX,
PROPORTION_XI,
NUMBER_INTERVALS,
NUMBER_FIXED_EFFECTS,
NUMBER_VARIABLES,
INTERNAL_STANDARDIZATION,
TRACE_PROGRESS
)
seagull_sparse_group_lasso(
VECTOR_Yc,
Y_MEAN,
MATRIX_Xc,
VECTOR_Xc_MEANS,
VECTOR_Xc_STANDARD_DEVIATIONS,
VECTOR_WEIGHTS_FEATURESc,
VECTOR_GROUPS,
VECTOR_BETAc,
VECTOR_INDEX_PERMUTATION,
VECTOR_INDEX_EXCLUDE,
ALPHA,
EPSILON_CONVERGENCE,
ITERATION_MAX,
GAMMA,
LAMBDA_MAX,
PROPORTION_XI,
NUMBER_INTERVALS,
NUMBER_FIXED_EFFECTS,
NUMBER_VARIABLES,
INTERNAL_STANDARDIZATION,
TRACE_PROGRESS
)

VECTOR_Yc 
numeric vector of observations. 
Y_MEAN 
arithmetic mean of VECTOR_Yc. 
MATRIX_Xc 
numeric design matrix relating y to fixed and random effects [X Z]. The columns may be permuted corresponding to their group assignments. 
VECTOR_Xc_MEANS 
numeric vector of arithmetic means of each column of MATRIX_Xc. 
VECTOR_Xc_STANDARD_DEVIATIONS 
numeric vector of estimates of
standard deviations of each column of MATRIX_Xc. Values are calculated via
the function 
VECTOR_WEIGHTS_FEATURESc 
numeric vector of weights for the vectors of fixed and random effects [b^T, u^T]^T. The entries may be permuted corresponding to their group assignments. 
VECTOR_WEIGHTS_GROUPSc 
numeric vector of precalculated weights for each group. 
VECTOR_FULL_COLUMN_RANK 
Boolean vector, which harbors the information of whether or not the groupwise parts of the filtered matrix Z, i.e., Z^{(l)} for each group l, have full column rank. 
VECTOR_GROUPS 
integer vector specifying which effect (fixed and random) belongs to which group. 
VECTOR_BETAc 
numeric vector whose partitions will be returned (partition 1: estimates of fixed effects, partition 2: predictions of random effects). During the computation the entries may be in permuted order. But they will be returned according to the order of the user's input. 
VECTOR_INDEX_PERMUTATION 
integer vector that contains information about the original order of the user's input. 
VECTOR_INDEX_EXCLUDE 
integer vector, which contains the indices of
every column that was filtered due to low standard deviation. This vector
only has an effect, if 
EPSILON_CONVERGENCE 
value for relative accuracy of the solution to stop the algorithm for the current value of λ. The algorithm stops after iteration m, if: sol^{(m)}  sol^{(m1)}_∞ < ε_c * sol1{(m1)}_2. 
ITERATION_MAX 
maximum number of iterations for each value of the
penalty parameter λ. Determines the end of the calculation if
the algorithm didn't converge according to 
GAMMA 
multiplicative parameter to decrease the step size during backtracking line search. Has to satisfy: 0 < γ < 1. 
LAMBDA_MAX 
maximum value for the penalty parameter. This is the start value for the grid search of the penalty parameter λ. 
PROPORTION_XI 
multiplicative parameter to determine the minimum value
of λ for the grid search, i.e. λ_{min} = ξ *
λ_{max}. Has to satisfy: 0 < ξ ≤ 1. If 
DELTA 
numeric value, which is squared and added to the main diagonal of Z^{(l)T} Z^{(l)} for group l, if this matrix is not invertible. 
NUMBER_INTERVALS 
number of lambdas for the grid search between λ_{max} and ξ * λ_{max}. Loops are performed on a logarithmic grid. 
NUMBER_FIXED_EFFECTS 
nonnegative integer to determine the number of fixed effects present in the mixed model. 
NUMBER_VARIABLES 
nonnegative integer which corresponds to the sum of all columns of the initial model matrices X and Z. 
INTERNAL_STANDARDIZATION 
if 
TRACE_PROGRESS 
if 
ALPHA 
mixing parameter of the penalty terms. Satisfies: 0 < α < 1. The penalty term looks as follows: α * "lasso penalty" + (1α) * "group lasso penalty". 
STEP_SIZE 
numeric value which represents the size of the step between consecutive iterations. 
A list of estimates and parameters relevant for the computation:
estimate for the intercept, if present in the model.
estimates for the fixed effects b, if present in the model. Each row corresponds to a particular value of λ.
predictions for the random effects u. Each row corresponds to a particular value of λ.
all values for λ which were used during the grid search.
a sequence of actual iterations for each value of
λ. If an occurring number is equal to max_iter
, then
the algorithm most likely did not converge to rel_acc
during the
corresponding run of the grid search.
The following parameters are also returned. But primarily for the purpose of
comparison and repetition: alpha = ALPHA
(only for the sparsegroup
lasso), max_iter = ITERATION_MAX
, gamma_bls = GAMMA
, xi
= PROPORTION_XI
, and loops_lambda = NUMBER_INTERVALS
.
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