regmed.fit {regmed}

Regularized Mediation model for a specified lambda penalty value.

Description

Fit regularized mediation model for a specified lambda penalty value. 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.fit(x, mediator, y, lambda, frac.lasso=0.8, x.std=TRUE, med.std=TRUE,
max.outer=5000, max.inner=100, 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

lambda penalty parameter

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).

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.

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.

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 that fitting is more robust

Value

regmed object, with S3 methods available: plot, print, summary

Author(s)

Dan Schaid, Greg Jenkins, Jason Sinnwell

References

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

See Also

regmed.edges summary.regmed

Examples

  data(medsim)
  filter5 <- regmed.prefilter(x[,1], med, y[,1], k=5)
  fit.regmed <- regmed.fit(x[,1], med[,1:5], y[,1], lambda = 0.2, frac.lasso=.8)
  summary(fit.regmed)