plsi.lr.auto.constraint: Partial linear single index regression with automatic...

In EPLSIM: Partial Linear Single Index Models for Environmental Mixture Analysis

Partial linear single index regression with automatic smoothness selection

Description

Same model as plsi.lr.v2(), but the link function is estimated with a penalized regression spline (mgcv::gam, REML smoothing-parameter selection) instead of a fixed-df natural spline. This removes the need to hand-tune spline.num: you supply an upper bound on basis complexity (k), and REML shrinks unneeded wiggliness toward a straight line automatically. Effective degrees of freedom actually used by the fitted link function are reported in si.fun.edf.

Usage

plsi.lr.auto.constraint(
  data,
  Y.name,
  X.name,
  Z.name,
  k = 10,
  bs = "cr",
  initial.random.num = 5,
  seed = 2026
)

Arguments

data	A data set including all needed variables
Y.name	Variable name for scalar outcome
X.name	Variable name vector for exposures
Z.name	Variable name vector for confounders
k	Upper bound on basis dimension for the smooth link function (analogous to spline.num in plsi.lr.v2, but not a fixed df, REML penalizes down from this ceiling). Default 10.
bs	Smooth basis type passed to mgcv::s(); default "cr" (cubic regression spline).
initial.random.num	Number of random initials for the single-index direction search
seed	A single integer used to seed the RNG so results (random initials and downstream optim() convergence) are reproducible. Set to NULL to skip seeding and use whatever RNG state is already active in the calling environment. Default is 2026.

Details

The single-index coefficient \beta is constrained to \|\beta\| = 1 and \beta_1 > 0 for identifiability. Rather than optimizing over \beta directly and projecting/normalizing after the fact, the search is reparameterized in terms of \sigma = (\sigma_1, \dots, \sigma_{p-1}) via \beta(\sigma) = \{(1 - \|\sigma\|^2)^{1/2}, \sigma_1, \dots, \sigma_{p-1}\}^T. Both constraints hold automatically for any \sigma with \|\sigma\| < 1, so optim() runs unconstrained over \sigma and \beta_1 > 0, \|\beta\| = 1 never need to be imposed after the fact. Standard errors for \beta are obtained from the Hessian in \sigma-space via the delta method.

The anchor exposure – the one assigned \beta_1, the coordinate constrained > 0 – is chosen as the candidate exposure with the largest absolute correlation with Y.name (not the largest signed/positive correlation), so an exposure strongly but negatively associated with the outcome can still be selected as the anchor. Which exposure was selected, and its correlation with Y.name, is reported in attr(si.coefficient, "note") and in anchor.note of the returned list.

Value

A list of model estimation and prediction results, structured analogously to plsi.lr.v2()'s output.

Author(s)

Yuyan Wang

Examples

## Not run: 
# example to run plsi.lr.auto.constraint
data(nhanes.new)
data <- nhanes.new

Y.name <- "log.triglyceride"
X.name <- c("X1_trans.b.carotene", "X2_retinol", "X3_g.tocopherol", "X4_a.tocopherol",
            "X5_PCB99", "X6_PCB156", "X7_PCB206",
            "X8_3.3.4.4.5.pncb", "X9_1.2.3.4.7.8.hxcdf", "X10_2.3.4.6.7.8.hxcdf")
Z.name <- c("AGE.c", "SEX.Female", "RACE.NH.Black",
           "RACE.MexicanAmerican", "RACE.OtherRace", "RACE.Hispanic" )

k <- 10
bs <- "cr"
initial.random.num <- 1
seed = 2026

model_lr_auto <- plsi.lr.auto.constraint(data = data,
                      Y.name = Y.name, X.name = X.name, Z.name = Z.name,
                      k = k, bs = bs, initial.random.num = initial.random.num, seed = seed)

## End(Not run)

EPLSIM documentation built on Nov. 5, 2026, 1:08 a.m.