Package 'EPLSIM' reference manual

Title:	Partial Linear Single Index Models for Environmental Mixture Analysis
Description:	Collection of ancillary functions and utilities for Partial Linear Single Index Models for Environmental mixture analyses, which currently provides functions for scalar, binary and count outcomes. The outputs of these functions include the single index function, single index coefficients, partial linear coefficients, mixture overall effect, exposure main and interaction effects, and differences of quartile effects. In the future, we will add functions for ordinal, survival, and longitudinal outcomes, as well as models for time-dependent exposures. See Wang et al (2020) <doi:10.1186/s12940-020-00644-4> for an overview.
Authors:	Yuyan Wang [aut, cre] (ORCID: <https://orcid.org/0000-0003-3747-0762>), Mengling Liu [aut, ctb], Myeonggyun Lee [ctb]
Maintainer:	Yuyan Wang <[email protected]>
License:	MIT + file LICENSE
Version:	1.0.1
Built:	2026-07-20 21:00:30 UTC
Source:	https://github.com/cran/EPLSIM

Transformation for confounders vector Z before modeling

Description

Transformation for confounders vector Z before modeling

Usage

confounder.trans(Z_continuous, Z_discrete, data)
confounder.trans(Z_continuous, Z_discrete, data)

Arguments

Z_continuous

A character name vector for continuous confounders

Z_discrete

A character name vector for discrete confounders

data

Orginial data set

Value

Transformed confounder vector and data set ready for further analysis.

Author(s)

Yuyan Wang

Examples

# example to normalize the continuous confounders and
# make dummy variables for categorical confounders
dat.cov <- data.frame(
  age = c(1.5, 2.3, 3.1, 4.8, 5.2),
  sex = c(1, 2, 1, 2, 2),
  race = c(1, 2, 3, 4, 5)
)

# specify the confounder vector
Z.name <- c("age", "sex", "race")

# set levels and make the reference level first for categorical confounders
dat.cov$sex <- factor(dat.cov$sex, 1:2, c('Male', 'Female'))
dat.cov$race <- factor(dat.cov$race,1:5,c("NH-White", "NH-Black",
                                        "MexicanAmerican", "OtherRace", "Hispanic"))

# transform the confounder vector and check
cov_m <- confounder.trans(Z_continuous = c("age"), Z_discrete = c("sex", "race"), data = dat.cov)
Z.name <- cov_m$New.Name
dat.cov <- cov_m$Updated.data
print(Z.name)
# example to normalize the continuous confounders and
# make dummy variables for categorical confounders
dat.cov <- data.frame(
  age = c(1.5, 2.3, 3.1, 4.8, 5.2),
  sex = c(1, 2, 1, 2, 2),
  race = c(1, 2, 3, 4, 5)
)

# specify the confounder vector
Z.name <- c("age", "sex", "race")

# set levels and make the reference level first for categorical confounders
dat.cov$sex <- factor(dat.cov$sex, 1:2, c('Male', 'Female'))
dat.cov$race <- factor(dat.cov$race,1:5,c("NH-White", "NH-Black",
                                        "MexicanAmerican", "OtherRace", "Hispanic"))

# transform the confounder vector and check
cov_m <- confounder.trans(Z_continuous = c("age"), Z_discrete = c("sex", "race"), data = dat.cov)
Z.name <- cov_m$New.Name
dat.cov <- cov_m$Updated.data
print(Z.name)

Plot interaction effect of two exposures from PLSIM

Description

Plot interaction effect of two exposures from PLSIM

Usage

e.interaction.plot(
  fit,
  data,
  exp_1,
  exp_2,
  type = c("linear", "logistic", "log")
)
e.interaction.plot(
  fit,
  data,
  exp_1,
  exp_2,
  type = c("linear", "logistic", "log")
)

Arguments

fit

Fitted model from plsi.lr.auto(), plsi.logistic.auto(), or plsi.log.auto()

data

Original data set

exp_1

Exposure 1 name

exp_2

Exposure 2 name

type

Which outcome scale to plot. "linear" (default) plots the predicted (continuous) outcome, for a fit from plsi.lr.auto(). "logistic" plots the predicted probability, for a fit from plsi.logistic.auto(). "log" plots the predicted count, for a fit from plsi.log.auto().

Value

Plot of interaction effect of two exposures with others at average level. Invisibly returns a list with elements panel_1 and panel_2, the data frames underlying the left and right panels respectively (predicted values at each combination of exp_1/ exp_2 value and the other exposure's quantiles).

Author(s)

Yuyan Wang

Examples

## Not run: 
# example to plot interaction effect of two exposures of continuous outcome
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(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)

# plot two exposures' interaction effect of predicted (continuous) outcome
e.interaction.plot(model_lr_auto, data, "X4_a.tocopherol", "X3_g.tocopherol", type = "linear")
e.interaction.plot(model_lr_auto, data, "X4_a.tocopherol", "X10_2.3.4.6.7.8.hxcdf", type = "linear")

# exchange exposures' names
e.interaction.plot(model_lr_auto, data, "X8_3.3.4.4.5.pncb", "X6_PCB156", type = "linear")
e.interaction.plot(model_lr_auto, data, "X6_PCB156", "X8_3.3.4.4.5.pncb", type = "linear")

## End(Not run)
## Not run: 
# example to plot interaction effect of two exposures of continuous outcome
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(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)

# plot two exposures' interaction effect of predicted (continuous) outcome
e.interaction.plot(model_lr_auto, data, "X4_a.tocopherol", "X3_g.tocopherol", type = "linear")
e.interaction.plot(model_lr_auto, data, "X4_a.tocopherol", "X10_2.3.4.6.7.8.hxcdf", type = "linear")

# exchange exposures' names
e.interaction.plot(model_lr_auto, data, "X8_3.3.4.4.5.pncb", "X6_PCB156", type = "linear")
e.interaction.plot(model_lr_auto, data, "X6_PCB156", "X8_3.3.4.4.5.pncb", type = "linear")

## End(Not run)

Plot single exposure's main effect from PLSIM

Description

Plot single exposure's main effect from PLSIM

Usage

e.main.plot(
  fit,
  data,
  exp_name,
  type = c("linear", "logistic", "log"),
  outlier.range = 10
)
e.main.plot(
  fit,
  data,
  exp_name,
  type = c("linear", "logistic", "log"),
  outlier.range = 10
)

Arguments

fit

Fitted model from plsi.lr.auto(), plsi.logistic.auto(), or plsi.log.auto()

data

Original data set

exp_name

Exposure name

type

outlier.range

range argument passed to boxplot() to identify and drop extreme values of the raw exposure before plotting. Default 10 (a permissive threshold; increase to drop fewer points, or set to Inf to keep all points).

Value

Plot of exposure's main effect with other exposures at their confounder-adjusted reference level. Invisibly returns the data frame used to build the plot.

Author(s)

Yuyan Wang

Examples

## Not run: 
# example to plot some exposure's main effect of continuous outcome
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(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)

# plot some exposure's main effect of predicted (continuous) outcome
e.main.plot(model_lr_auto, data, exp_name = c("X4_a.tocopherol"), type = "linear")
e.main.plot(model_lr_auto, data, exp_name = c("X5_PCB99"), type = "linear")
e.main.plot(model_lr_auto, data, exp_name = c("X10_2.3.4.6.7.8.hxcdf"), type = "linear")

## End(Not run)
## Not run: 
# example to plot some exposure's main effect of continuous outcome
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(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)

# plot some exposure's main effect of predicted (continuous) outcome
e.main.plot(model_lr_auto, data, exp_name = c("X4_a.tocopherol"), type = "linear")
e.main.plot(model_lr_auto, data, exp_name = c("X5_PCB99"), type = "linear")
e.main.plot(model_lr_auto, data, exp_name = c("X10_2.3.4.6.7.8.hxcdf"), type = "linear")

## End(Not run)

Plot interquartile effect of specific exposure based on quartile of other exposures

Description

Plot interquartile effect of specific exposure based on quartile of other exposures

Usage

interquartile.quartile.plot(fit, data, type = c("linear", "logistic", "log"))
interquartile.quartile.plot(fit, data, type = c("linear", "logistic", "log"))

Arguments

fit

Fitted model from plsi.lr.auto(), plsi.logistic.auto(), or plsi.log.auto()

data

Original data set

type

Which outcome scale to plot. "linear" (default) plots the difference in predicted (continuous) outcome, for a fit from plsi.lr.auto(). "logistic" plots the difference in predicted probability, for a fit from plsi.logistic.auto(). "log" plots the difference in predicted count, for a fit from plsi.log.auto().

Value

Plot of main interquartile effect of exposure based on quartile of other exposures

Author(s)

Yuyan Wang

Examples

## Not run: 
# example to interquartile effect based on quartile of other exposures of continuous outcome
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(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)

# plot interquartile quartile of difference in predicted (continuous) outcome
interquartile.quartile.plot(model_lr_auto, data, type = "linear")

## End(Not run)
## Not run: 
# example to interquartile effect based on quartile of other exposures of continuous outcome
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(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)

# plot interquartile quartile of difference in predicted (continuous) outcome
interquartile.quartile.plot(model_lr_auto, data, type = "linear")

## End(Not run)

Plot mixture's overall effect based on quantile of exposures from PLSIM

Description

Plot mixture's overall effect based on quantile of exposures from PLSIM

Usage

mixture.overall.plot(fit, data, type = c("linear", "logistic", "log"))
mixture.overall.plot(fit, data, type = c("linear", "logistic", "log"))

Arguments

fit

Fitted model from plsi.lr.auto(), plsi.logistic.auto(), or plsi.log.auto()

data

Original data set

type

Value

Plot of predicted outcomes based on quantile of exposures

Author(s)

Yuyan Wang

Examples

## Not run: 
# example to plot mixture's overall effect of continuous outcome
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(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)

# plot mixture overall effect of predicted (continuous) outcome
mixture.overall.plot(model_lr_auto, data, type = "linear")

## End(Not run)
## Not run: 
# example to plot mixture's overall effect of continuous outcome
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(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)

# plot mixture overall effect of predicted (continuous) outcome
mixture.overall.plot(model_lr_auto, data, type = "linear")

## End(Not run)

This is data from NHANES 2003–2004

Description

A data set containing outcome triglyceride, ten exposures, and three confounders.

Usage

nhanes
nhanes

Format

An object of class data.frame with 800 rows and 14 columns.

Details

triglyceride: outcome triglyceride level, unite mg/dl
a1.trans.b.carotene: exposure: trans-b-carotene (ug/dL)
a5.Retinol: exposure: retinol (ug/dL)
a6.g.tocopherol: exposure: g-tocopherol (ug/dL)
a7.a.Tocopherol: exposure: a-tocopherol (ug/dL)
a10.PCB99: exposure: Polychlorinated Biphenyl (PCB) 99 Lipid Adj (ng/g)
a13.PCB156: exposure: Polychlorinated Biphenyl (PCB) 156 Lipid Adj (ng/g)
a19.PCB206: exposure: Polychlorinated Biphenyl (PCB) 206 Lipid Adj (ng/g)
a20.3.3.4.4.5.pncb: exposure: 3,3,4,4,5-Pentachlorobiphenyl (pncb) Lipid Adj (pg/g)
a21.1.2.3.4.7.8.hxcdf: exposure: 1,2,3,4,7,8-hxcdf Lipid Adj (pg/g)
a22.2.3.4.6.7.8.hxcdf: exposure: 2,3,4,6,7,8-hxcdf Lipid Adj (pg/g)
age: subject age at measurement
sex: subject sex
race: subject race

Author(s)

Yuyan Wang [email protected]

This is an updated data from original data based on NHANES 2003–2004 survey

Description

A data set containing outcome triglyceride, re-named ten exposures, and transformed confounders.

Usage

nhanes.new
nhanes.new

Format

An object of class data.frame with 789 rows and 17 columns.

Details

triglyceride: outcome triglyceride level, unite mg/dl
X1_trans.b.carotene: renamed exposure: trans-b-carotene (ug/dL)
X2_retinol: renamed exposure: retinol (ug/dL)
X3_g.tocopherol: renamed exposure: g-tocopherol (ug/dL)
X4_a.tocopherol: renamed exposure: a-tocopherol (ug/dL)
X5_PCB99: renamed exposure: Polychlorinated Biphenyl (PCB) 99 Lipid Adj (ng/g)
X6_PCB156: renamed exposure: Polychlorinated Biphenyl (PCB) 156 Lipid Adj (ng/g)
X7_PCB206: renamed exposure: Polychlorinated Biphenyl (PCB) 206 Lipid Adj (ng/g)
X8_3.3.4.4.5.pncb: renamed exposure: 3,3,4,4,5-Pentachlorobiphenyl (pncb) Lipid Adj (pg/g)
X9_1.2.3.4.7.8.hxcdf: renamed exposure: 1,2,3,4,7,8-hxcdf Lipid Adj (pg/g)
X10_2.3.4.6.7.8.hxcdf: renamed exposure: 2,3,4,6,7,8-hxcdf Lipid Adj (pg/g)
AGE.c: rescaled continuous confounder: subject age at measurement
SEX.Female: categorical confounder dummy variable: subject sex as Female
RACE.NH.Black: categorical dummy variable: subject race as Non-Hispanic Black
RACE.MexicanAmerican: categorical dummy variable: subject race as Mexican American
RACE.OtherRace: categorical dummy variable: subject race as Other Races
RACE.Hispanic: categorical dummy variable: subject race as Hispanic

Author(s)

Yuyan Wang [email protected]

Partial linear single index log-linear regression with automatic smoothness selection

Description

Count-outcome analog of plsi.lr.auto() / plsi.logistic.auto(): same partial linear single index model, but for non-negative count data via a log link. The link function is estimated with a penalized regression spline (mgcv::gam, REML smoothing-parameter selection), so there is no spline.num to hand-tune, only an upper bound k on basis complexity, with REML shrinking unneeded wiggliness toward a straight line on the log scale.

Usage

plsi.log.auto(
  data,
  Y.name,
  X.name,
  Z.name,
  family = c("nb", "poisson"),
  k = 10,
  bs = "cr",
  initial.random.num = 5,
  seed = 2026
)
plsi.log.auto(
  data,
  Y.name,
  X.name,
  Z.name,
  family = c("nb", "poisson"),
  k = 10,
  bs = "cr",
  initial.random.num = 5,
  seed = 2026
)

Arguments

data

A data set including all needed variables

Y.name

Variable name for the count outcome. Must be non-negative integers (0, 1, 2, ...).

X.name

Variable name vector for exposures

Z.name

Variable name vector for confounders

family

Count distribution to use. "nb" (default) fits a negative binomial GAM (mgcv::nb()), which estimates its own dispersion parameter and is the safer default for real count data, which is usually overdispersed (variance > mean) relative to Poisson. "poisson" fits a Poisson GAM, valid only if the mean-equals- variance assumption actually holds; if unsure, leave the default.

k

Upper bound on basis dimension for the smooth link function. 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

As with plsi.logistic.auto(), the "confounder-free" single-index model cannot be built by subtracting confounder effects from y on the response scale (counts aren't additive that way either), and it cannot be built by residualizing the full model's own fitted linear predictor, that would leave a value that is already an exact smooth function of the single index, so refitting a smooth to it would just retrace the same curve with near-zero (and spuriously tiny) standard errors. Instead, the confounder contribution from the full model is fixed as a known offset() and a second, confounder-free count GAM (same family as the full model) is refit directly against the actual observed y, preserving real count sampling variability. Predictions from this model are made at offset = 0, consistent with how the offset was netted out of every training point.

Value

A list of model estimation and prediction results, structured analogously to plsi.logistic.auto()'s output:

si.coefficient: Single-index direction estimates and inference.
confounder.coefficient: Confounder log-rate coefficients, plus rate ratios and their 95% CIs.
si.fun: The estimated single-index link function, on both the log scale (fit/se/lwr/upr) and the count scale (count.fit/count.lwr/count.upr), obtained by exponentiating the log-scale CI so it stays non-negative.
si.fun.model: A confounder-free gam of the count outcome on the single index alone (via a fixed offset for confounder contribution), predict() from this needs only single_index_estimated, not the original confounders. See Details.
full.model: The full fitted gam (smooth + confounders), kept for reference/diagnostics.

Author(s)

Yuyan Wang

Examples

## Not run: 
data(nhanes.new)
data <- nhanes.new

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" )

# demo count outcome (illustrative only as nhanes.new has no native count variable).
Simulated from a *true* single-index combination of the exposures, run through a
nonlinear log-rate link, plus a confounder effect, so the example actually has an
exposure-outcome relationship for plsi.log.auto() to recover, rather than
depending on the confounder alone.

set.seed(2026)
beta_true <- c(0.30, -0.20, 0.10, 0.40, -0.30, 0.20, -0.10, 0.25, -0.15, 0.35)
beta_true <- beta_true / sqrt(sum(beta_true^2)) # unit norm, matching the model's
# own identifiability constraint
x_std <- scale(data[, X.name]) # standardize so the demo index is on a sane, comparable scale
single_index_true <- as.vector(x_std %*% beta_true)
log_rate <- 0.3 + 0.4 * sin(single_index_true) + 0.05 * data$AGE.c
data$n.events <- stats::rpois(nrow(data), lambda = exp(log_rate))

Y.name <- "n.events"

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

model_log_auto <- plsi.log.auto(data = data, Y.name = Y.name, X.name = X.name,
                      Z.name = Z.name, family = "nb", k = k, bs = bs,
                      initial.random.num = initial.random.num, seed = seed)

## End(Not run)
## Not run: 
data(nhanes.new)
data <- nhanes.new

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" )

# demo count outcome (illustrative only as nhanes.new has no native count variable).
Simulated from a *true* single-index combination of the exposures, run through a
nonlinear log-rate link, plus a confounder effect, so the example actually has an
exposure-outcome relationship for plsi.log.auto() to recover, rather than
depending on the confounder alone.

set.seed(2026)
beta_true <- c(0.30, -0.20, 0.10, 0.40, -0.30, 0.20, -0.10, 0.25, -0.15, 0.35)
beta_true <- beta_true / sqrt(sum(beta_true^2)) # unit norm, matching the model's
# own identifiability constraint
x_std <- scale(data[, X.name]) # standardize so the demo index is on a sane, comparable scale
single_index_true <- as.vector(x_std %*% beta_true)
log_rate <- 0.3 + 0.4 * sin(single_index_true) + 0.05 * data$AGE.c
data$n.events <- stats::rpois(nrow(data), lambda = exp(log_rate))

Y.name <- "n.events"

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

model_log_auto <- plsi.log.auto(data = data, Y.name = Y.name, X.name = X.name,
                      Z.name = Z.name, family = "nb", k = k, bs = bs,
                      initial.random.num = initial.random.num, seed = seed)

## End(Not run)

Partial linear single index logistic regression with automatic smoothness selection

Description

Binary-outcome analog of plsi.lr.auto(): same partial linear single index model, but with a logistic link. The link function is estimated with a penalized regression spline (mgcv::gam, family = binomial(), REML smoothing-parameter selection), so there is no spline.num to hand-tune, only an upper bound k on basis complexity, with REML shrinking unneeded wiggliness toward a straight line on the logit scale.

Usage

plsi.logistic.auto(
  data,
  Y.name,
  X.name,
  Z.name,
  k = 10,
  bs = "cr",
  initial.random.num = 5,
  seed = 2026
)
plsi.logistic.auto(
  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 the binary outcome. Must be coded 0/1, or a 2-level factor (which will be coerced to 0/1 by level order, with a message reporting which level became 0 and which became 1).

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. 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

Details

Because the outcome is binary, the "confounder-free" single-index model cannot be built by subtracting confounder effects from y on the response scale the way plsi.lr.auto() does (probabilities aren't additive), and it cannot be built by residualizing the full model's own fitted linear predictor either, that would leave a value that is already an exact smooth function of the single index, so refitting a smooth to it would just retrace the same curve with near-zero (and spuriously tiny) standard errors. Instead, the confounder contribution from the full model is fixed as a known offset() and a second, confounder-free binomial gam is refit directly against the actual observed y, preserving real binomial sampling variability. Predictions from this model are made at offset = 0, consistent with how the offset was netted out of every training point.

Value

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

si.coefficient: Single-index direction estimates and inference.
confounder.coefficient: Confounder log-odds coefficients, plus odds ratios and their 95% CIs.
si.fun: The estimated single-index link function, on both the logit scale (fit/se/lwr/upr) and the probability scale (prob.fit/prob.lwr/prob.upr), obtained by back-transforming the logit-scale CI so it stays between 0 and 1.
si.fun.model: A confounder-free gam of the logit-scale residual on the single index alone, predict() from this needs only single_index_estimated, not the original confounders. See Details.
full.model: The full fitted gam (smooth + confounders), kept for reference/diagnostics.

Author(s)

Yuyan Wang

Examples

## Not run: 
data(nhanes.new)
data <- nhanes.new

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" )

# demo binary outcome (illustrative only as nhanes.new has no native binary variable).
 Simulated from a *true* single-index combination of the exposures, run through a
 nonlinear logit link, plus a confounder effect, and drawn as genuine Bernoulli noise
 (not a hard threshold on an existing variable), a hard threshold produces near-perfect
 separation and destabilizes the fit, whereas real classification uncertainty is both
 more realistic and numerically well-behaved.

set.seed(2026)
beta_true <- c(0.30, -0.20, 0.10, 0.40, -0.30, 0.20, -0.10, 0.25, -0.15, 0.35)
beta_true <- beta_true / sqrt(sum(beta_true^2))
x_std <- scale(data[, X.name])
single_index_true <- as.vector(x_std %*% beta_true)
log_odds <- -0.2 + 0.5 * sin(single_index_true) + 0.05 * data$AGE.c
data$high.triglyceride <- stats::rbinom(nrow(data), size = 1, prob = stats::plogis(log_odds))

Y.name <- "high.triglyceride"

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

model_logistic_auto <- plsi.logistic.auto(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)

## Not run: 
data(nhanes.new)
data <- nhanes.new

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" )

# demo binary outcome (illustrative only as nhanes.new has no native binary variable).
 Simulated from a *true* single-index combination of the exposures, run through a
 nonlinear logit link, plus a confounder effect, and drawn as genuine Bernoulli noise
 (not a hard threshold on an existing variable), a hard threshold produces near-perfect
 separation and destabilizes the fit, whereas real classification uncertainty is both
 more realistic and numerically well-behaved.

set.seed(2026)
beta_true <- c(0.30, -0.20, 0.10, 0.40, -0.30, 0.20, -0.10, 0.25, -0.15, 0.35)
beta_true <- beta_true / sqrt(sum(beta_true^2))
x_std <- scale(data[, X.name])
single_index_true <- as.vector(x_std %*% beta_true)
log_odds <- -0.2 + 0.5 * sin(single_index_true) + 0.05 * data$AGE.c
data$high.triglyceride <- stats::rbinom(nrow(data), size = 1, prob = stats::plogis(log_odds))

Y.name <- "high.triglyceride"

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

model_logistic_auto <- plsi.logistic.auto(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)

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

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
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(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)
## Not run: 
# example to run plsi.lr.auto
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(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)

Partial linear single index linear regression for scalar outcome, earliest version

Description

Partial linear single index linear regression for scalar outcome, earliest version

Usage

plsi.lr.v1(
  data,
  Y.name,
  X.name,
  Z.name,
  spline.num,
  spline.degree,
  initial.random.num
)
plsi.lr.v1(
  data,
  Y.name,
  X.name,
  Z.name,
  spline.num,
  spline.degree,
  initial.random.num
)

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

spline.num

A number representing the degree of freedom of B-spline basis for link function

spline.degree

A number representing the degree of the piece-wise polynomial of B-spline basis for link function

initial.random.num

A number representing the number of random initials used in the function

Value

A list of model estimation and prediction results

Author(s)

Yuyan Wang

Examples

## Not run: 
# example to run the function
data(nhanes.new)
dat <- nhanes.new

# specify variable names
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" )

# specify spline degree of freedom
spline.num = 5
# specify spline degree
spline.degree = 3
# specify number of random initials for estimation
initial.random.num = 1

# run the model
set.seed(2023)
model_1 <- plsi.lr.v1(data = dat, Y.name = Y.name, X.name = X.name, Z.name = Z.name,
                      spline.num, spline.degree, initial.random.num)

## End(Not run)
## Not run: 
# example to run the function
data(nhanes.new)
dat <- nhanes.new

# specify variable names
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" )

# specify spline degree of freedom
spline.num = 5
# specify spline degree
spline.degree = 3
# specify number of random initials for estimation
initial.random.num = 1

# run the model
set.seed(2023)
model_1 <- plsi.lr.v1(data = dat, Y.name = Y.name, X.name = X.name, Z.name = Z.name,
                      spline.num, spline.degree, initial.random.num)

## End(Not run)

Partial linear single index linear regression for scalar outcome, second version

Description

Partial linear single index linear regression for scalar outcome, second version

Usage

plsi.lr.v2(
  data,
  Y.name,
  X.name,
  Z.name,
  spline.num,
  spline.degree,
  initial.random.num,
  seed = 2026
)
plsi.lr.v2(
  data,
  Y.name,
  X.name,
  Z.name,
  spline.num,
  spline.degree,
  initial.random.num,
  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

spline.num

A number representing the degree of freedom of B-spline basis for link function

spline.degree

A number representing the degree of the piece-wise polynomial of B-spline basis for link function

initial.random.num

A number representing the number of random initials used in the function

seed

Value

A list of model estimation and prediction results

Author(s)

Yuyan Wang

Examples

## Not run: 
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" )

spline.num <- 5
spline.degree <- 3
initial.random.num <- 1
seed = 2026

model_lr_v2 <- plsi.lr.v2(data = data, Y.name = Y.name, X.name = X.name, Z.name = Z.name,
                      spline.num, spline.degree, initial.random.num, seed = seed)

## End(Not run)
## Not run: 
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" )

spline.num <- 5
spline.degree <- 3
initial.random.num <- 1
seed = 2026

model_lr_v2 <- plsi.lr.v2(data = data, Y.name = Y.name, X.name = X.name, Z.name = Z.name,
                      spline.num, spline.degree, initial.random.num, seed = seed)

## End(Not run)

Plot estimated single index coefficients frpm PLSIM

Description

Plot estimated single index coefficients frpm PLSIM

Usage

si.coef.plot(si.coef.est)
si.coef.plot(si.coef.est)

Arguments

si.coef.est

A data set of estimated single index coefficients

Value

Single index coefficient plot

Author(s)

Yuyan Wang

Examples

## Not run: 
# example to plot estimated single index function of continuous outcome
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(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)

# plot estimated single index coefficients
si.coef.plot(model_lr_auto$si.coefficient)

# check estimated single index coefficients
model_lr_auto$si.coefficient

## End(Not run)
## Not run: 
# example to plot estimated single index function of continuous outcome
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(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)

# plot estimated single index coefficients
si.coef.plot(model_lr_auto$si.coefficient)

# check estimated single index coefficients
model_lr_auto$si.coefficient

## End(Not run)

Plot estimated single index function

Description

Plot estimated single index function

Usage

si.fun.plot(
  si.ci,
  type = c("linear", "logistic", "log"),
  xlab = "Single index: u",
  ylab = NULL
)
si.fun.plot(
  si.ci,
  type = c("linear", "logistic", "log"),
  xlab = "Single index: u",
  ylab = NULL
)

Arguments

si.ci

A data set of estimated index and corresponding single index values, typically the si.fun element returned by plsi.lr.auto(), plsi.logistic.auto(), or plsi.log.auto() (or the analogous plsi.lr.v2() output for the linear case).

type

Which outcome scale to plot. "linear" (default) plots the predicted outcome g(u) using the fit/lwr/upr columns, as returned for a continuous outcome. "logistic" plots the predicted probability using the prob.fit/prob.lwr/ prob.upr columns returned by plsi.logistic.auto(), with the y-axis bounded between 0 and 1. "log" plots the predicted count using the count.fit/count.lwr/count.upr columns returned by plsi.log.auto(), with the y-axis bounded below at 0.

xlab

X-axis label. Default "Single index: u".

ylab

Y-axis label. If NULL (default), a label appropriate to type is used automatically.

Value

Single index function plot

Author(s)

Yuyan Wang

Examples

## Not run: 
# example to plot estimated single index function of continuous outcome
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(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)
# plot single index function of predicted (continuous) outcome
si.fun.plot(model_lr_auto$si.fun, type = "linear")

## End(Not run)
## Not run: 
# example to plot estimated single index function of continuous outcome
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(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)
# plot single index function of predicted (continuous) outcome
si.fun.plot(model_lr_auto$si.fun, type = "linear")

## End(Not run)

Package 'EPLSIM'

Help Index

Transformation for confounders vector Z before modeling

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Plot interaction effect of two exposures from PLSIM

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Plot single exposure's main effect from PLSIM

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Plot interquartile effect of specific exposure based on quartile of other exposures

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Plot mixture's overall effect based on quantile of exposures from PLSIM

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This is data from NHANES 2003–2004

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This is an updated data from original data based on NHANES 2003–2004 survey

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Partial linear single index log-linear regression with automatic smoothness selection

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Partial linear single index logistic regression with automatic smoothness selection

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Partial linear single index regression with automatic smoothness selection

Description

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Partial linear single index linear regression for scalar outcome, earliest version

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Partial linear single index linear regression for scalar outcome, second version