regmed.grid {regmed}

Regularized mediation models over a vector grid of lambda penalty values.

Description

Fit regularized mediation models over a vector grid of lambda penalty values. Structural equation models for analysis of multiple mediators are extended by creating a sparse group lasso penalized model such that the penalty considers the natural groupings of the pair of parameters that determine mediation, as well as encourages sparseness of the model parameters. The model is x-[alpha] -> mediator-[beta] -> outcome, where alpha and beta are the parameters for the indirect effect of x on y, through the mediator. The model also allows a direct effect of x on y: x-[delta] -> y.

Usage

regmed.grid(x, mediator, y, lambda.vec, frac.lasso=0.8, max.outer=5000,
max.inner=100, x.std=TRUE, med.std=TRUE, step.multiplier = 0.5,
wt.delta = .5, print.iter=FALSE, max.cor=0.99)

Arguments

x

vector representing "exposure" variable (sometimes called instrumental variable)

mediator

matrix of mediators, rows are observations, columns are different mediators

y

vector representing outcome

lambda.vec

vector of lambda penalty parameters

frac.lasso

fraction of penalty (lambda) that is allocated to L1 penalty (lasso). The remaining fraction, (1-frac.lasso) is allocated to group-lasso penalty, where the group is the pair of parameters alpha and beta that determine mediation (x [alpha] -> mediator -> [beta] y).

max.outer

maximum number of outer loop iterations. The outer loop cycles over several inner loops.

max.inner

maximum number of iterations for each inner loop. There is an inner loop for each pair of alpha-beta parameters for each mediator, an inner loop for direct effect (delta), and inner loops for residual variances for x and for y.

x.std

logical (TRUE/FALSE) whether to standardize x by dividing by standard devation of x. Note that x will be centered on its mean.

med.std

logical (TRUE/FALSE) whether to standardize mediators by dividing each mediator by its standard deviation. Note that mediators will be centered on their means.

step.multiplier

a value between 0 and 1 for backtracking, to shrink step size. Value of 0.5 is typical default.

wt.delta

a weight >=0 for how much weight should be given to shrinking delta parameter, by penalaty lambda*wt.delta.

print.iter

print iteration history during fitting routine

max.cor

maximum correlation within mediators, so fitting is more robust

Details

Altough outcome y is not required to be scaled by its standard deviation, it can be beneficial to scale y. This helps with setting range of lambda penalty parameters, because when all x, y, and mediators are scaled, it is reasonable to consider lambda values within the range of 0 to 1. See reference for details of algorithm.

Value

regmed.grid object

Author(s)

Dan Schaid, Jason Sinnwell

References

Schaid, DJ, Sinnwell JP. (2020) Penalized Models for Analysis of Multiple Mediators. Genet Epidemiol 44:408-424.

See Also

plot.regmed.grid regmed.fit

Examples

data(medsim)
fit.grid <- regmed.grid(x[,1], med[,1:5], y[,1],
lambda.vec= c(seq(from=1, to=0, by = -.1)),
frac.lasso=.8)
print(fit.grid)