Package 'geeVerse'

Compile Results from qpgee()

Description

This function reports correct percentage, TP, FP, MSE and MAD from a (list of) fitted qpgee model comparing to the true betas.

Usage

compile_result(qpgee_results, beta0, threshold = 10^-3)

Arguments

qpgee_results	A (list of) fitted qpgee model.
beta0	True beta used in true data generation process.
threshold	Integer, the threshold to determine whether a estimated beta should be consider as 0.

Value

a vector contains correct percentage, TP, FP, MSE and MAD and its standard error if Monte Carlo simulations.

---

Compile Results from list of qpgee()

Description

This function reports correct percentage, TP, FP, MSE and MAD from a (list of) fitted qpgee model comparing to the true betas.

Usage

## Default S3 method:
compile_result(qpgee_results, beta0, threshold = 0.1)

Arguments

qpgee_results	A (list of) fitted qpgee model.
beta0	True beta used in true data generation process.
threshold	Integer, the threshold to determine whether a estimated beta should be consider as 0.

Value

a vector contains correct percentage, TP, FP, MSE and MAD and its standard error if Monte Carlo simulations.

---

Compile Results from qpgee()

Description

This function reports correct percentage, TP, FP, MSE and MAD from a (list of) fitted qpgee model comparing to the true betas.

Usage

## S3 method for class 'qpgee'
compile_result(qpgee_results, beta0, threshold = 10^-3)

Arguments

qpgee_results	A (list of) fitted qpgee model.
beta0	True beta used in true data generation process.
threshold	Integer, the threshold to determine whether a estimated beta should be consider as 0.

Value

a vector contains correct percentage, TP, FP, MSE and MAD and its standard error if Monte Carlo simulations.

---

Cross-Validation for Generalized Estimating Equations (GEE)

Description

This function performs k-fold cross-validation for model selection in the context of Generalized Estimating Equations (GEE). It is designed to evaluate the performance of different models specified by a range of lambda values, choosing the one that minimizes the cross-validation criterion.

Usage

CVfit(
  formula,
  id,
  data,
  family,
  scale.fix,
  scale.value,
  fold,
  pindex,
  eps,
  maxiter,
  tol,
  lambda.vec = exp(seq(log(10), log(0.1), length.out = 30)),
  corstr = "independence",
  ncore = 1
)

Arguments

formula	an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
id	a vector which identifies the cluster/group for each observation.
data	an optional data frame containing the variables in the model.
family	a description of the error distribution and link function to be used in the model.
scale.fix	logical; if TRUE, the scale parameter is fixed to scale.value.
scale.value	the value of the scale parameter when scale.fix is TRUE.
fold	the number of folds to be used in the cross-validation.
pindex	an optional numeric vector specifying a parameter index.
eps	the threshold for convergence criteria.
maxiter	the maximum number of iterations for the convergence of the algorithm.
tol	the tolerance level for the convergence of the algorithm.
lambda.vec	a vector of lambda values for which the cross-validation error will be calculated.
corstr	the correlation structure used.
ncore	if greater than 1, the function will use parallel computation.

Details

Note that this is a re-implemented version with parallel computing.

Value

An object of class "CVfit", which is a list containing:

fold

The number of folds used in the cross-validation.

lam.vect

The vector of lambda values tested.

cv.vect

The cross-validation error for each lambda.

lam.opt

The lambda value that resulted in the minimum cross-validation error.

cv.min

The minimum cross-validation error.

call

The matched call.

---

GeeVerse: Wrapper for Quantile Penalized Generalized Estimating Equations

Description

This function is a wrapper for qpgee that allows running the model for multiple quantile levels (tau).

Usage

geeVerse(x, y, tau = c(0.25, 0.5, 0.75), ...)

Arguments

x	A matrix of predictors.
y	A numeric vector of response variables.
tau	A vector of quantiles to be estimated (default is c(0.25, 0.5, 0.75)).
...	Additional arguments to be passed to qpgee function.

Value

A list containing the results for each tau value and a combined beta matrix.

---

Generate Data for Simulation

Description

This function generates simulated data including the predictor matrix 'X' and the response vector 'y', based on the specified parameters. The function allows for the simulation of data under different settings of correlation, distribution, and the number of observations and subjects.

Usage

generate_data(
  nsub,
  nobs,
  p,
  beta0,
  rho,
  corstr = "AR1",
  dis = "normal",
  ka = 0,
  SNPs = NULL
)

Arguments

nsub	Integer, the number of subjects.
nobs	Integer or numeric vector, the number of observations per subject.
p	Integer, the number of predictors.
beta0	Numeric vector, initial coefficients for the first few predictors.
rho	Numeric, the correlation coefficient used in generating correlated errors.
corstr	Character, specifies the correlation of correlation structure for the covariance matrix. Options are "cs" or "exchangeable" for compound symmetry, "AR1" for autoregressive, and any other input will result in an identity matrix.
dis	Character, the distribution of errors ("normal" or "t").
ka	1 for heterogeneous errors and 0 for homogeneous errors.
SNPs	User can provide simulated or real SNPs for genetic data simulation.

Value

A list containing two elements: 'X', the matrix of predictors, and 'y', the response vector.

Examples

set.seed(123)
sim_data <- generate_data(
  nsub = 50, nobs = rep(5, 50), p = 10,
  beta0 = c(rep(1, 5), rep(0, 5)), rho = 0.3
)

---

PGEE accelerated with RCpp

Description

A function to fit penalized generalized estimating equation model. This function was re-wrote partly with RCPP and RCPPEigen for better computation efficiency.

Usage

PGEE(
  formula,
  id,
  data,
  na.action = NULL,
  family = gaussian(link = "identity"),
  corstr = "independence",
  Mv = NULL,
  beta_int = NULL,
  R = NULL,
  scale.fix = TRUE,
  scale.value = 1,
  lambda,
  pindex = NULL,
  eps = 10^-6,
  maxiter = 30,
  tol = 10^-3,
  silent = TRUE,
  fastginv = TRUE
)

Arguments

formula	A formula expression response ~ predictors;
id	A vector for identifying subjects/clusters.
data	A data frame which stores the variables in formula with id variable.
na.action	A function to remove missing values from the data. Only na.omit is allowed here.
family	A family object: a list of functions and expressions for defining link and variance functions. Families supported in PGEE are binomial, gaussian, gamma and poisson. The links, which are not available in gee, is not available here. The default family is gaussian.
corstr	A character string, which specifies the correlation of correlation structure. Structures supported in PGEE are "AR-1","exchangeable", "fixed", "independence", "stat_M_dep","non_stat_M_dep", and "unstructured". The default corstr correlation is "independence".
Mv	If either "stat_M_dep", or "non_stat_M_dep" is specified in corstr, then this assigns a numeric value for Mv. Otherwise, the default value is NULL.
beta_int	User specified initial values for regression parameters. The default value is NULL.
R	If corstr = "fixed" is specified, then R is a square matrix of dimension maximum cluster size containing the user specified correlation. Otherwise, the default value is NULL.
scale.fix	A logical variable; if true, the scale parameter is fixed at the value of scale.value. The default value is TRUE.
scale.value	If scale.fix = TRUE, this assigns a numeric value to which the scale parameter should be fixed. The default value is 1.
lambda	A numerical value for the penalization parameter of the scad function, which is estimated via cross-validation.
pindex	An index vector showing the parameters which are not subject to penalization. The default value is NULL. However, in case of a model with intercept, the intercept parameter should be never penalized.
eps	A numerical value for the epsilon used in minorization-maximization algorithm. The default value is 10^-6.
maxiter	The number of iterations that is used in the estimation algorithm. The default value is 25.
tol	The tolerance level that is used in the estimation algorithm. The default value is 10^-3.
silent	A logical variable; if false, the regression parameter estimates at each iteration are printed. The default value is TRUE.
fastginv	A logical variable for usage of fast implementation of generalized matrix inverse.

Value

a PGEE object, which includes: fitted coefficients - the fitted single index coefficients with unit norm and first component being non negative

Examples

# generate data
set.seed(2021)
sim_data <- generate_data(
  nsub = 100, nobs = rep(10, 100), p = 100,
  beta0 = c(rep(1, 7), rep(0, 93)), rho = 0.6, corstr = "AR1",
  dis = "normal", ka = 1
)


PGEE_fit <- PGEE("y ~.-id-1", id = id, data = sim_data,
 corstr = "exchangeable", lambda = 0.01)
PGEE_fit$coefficients

---

Print summary method for qpgee model objects

Description

Print summary method for qpgee model objects

Usage

## S3 method for class 'summary.qpgee'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

x	A 'qpgee' model object.
digits	Default digits.
...	Additional arguments (not used).

Value

Prints a summary of the qpgee model.

---

Quantile Penalized Generalized Estimating Equations (QPGEE)

Description

Fits a quantile penalized generalized estimating equation (QPGEE) model for longitudinal data using penalized quantile regression with different working correlation structures.

Usage

qpgee(x, ...)

## S3 method for class 'formula'
qpgee(x, id, data = parent.frame(), ...)

## Default S3 method:
qpgee(
  x,
  y,
  nobs,
  tau = 0.5,
  corstr = "exchangeable",
  lambda = NULL,
  method = "HBIC",
  intercept = TRUE,
  betaint = NULL,
  nfold = 5,
  ncore = 1,
  control = qpgeeControl(),
  ...
)

Arguments

x	A matrix of predictors.
...	Other arguments passed to methods.
id	A vector identifying the clusters (subjects).
data	An optional data frame.
y	A numeric vector of response variables.
nobs	A numeric vector of observations per subject.
tau	The quantile to be estimated (default is 0.5).
corstr	A string specifying the working correlation structure. Options include "exchangeable" (Exchangeable), "AR1" (Autoregressive), "Tri" (Tri-diagonal), "independence" (Independent), and "unstructured".
lambda	A vector of penalty parameters. If NULL, auto-selection is performed.
method	Criterion for penalty selection ("HBIC" or "CV").
intercept	Logical; if TRUE, an intercept is added.
betaint	Initial values for the beta coefficients. If NULL, non-longitudinal quantile regression is used for initialization.
nfold	The number of folds used in cross-validation.
ncore	Number of cores for parallel processing.
control	A list of control parameters from 'qpgeeControl()', such as max_it, epsilon, shrinkCutoff, standardize and trace.

Value

An object of class 'qpgee'.

Examples

# Quick Example:
# 1. Generate some data
set.seed(123)
sim_data <- generate_data(
  nsub = 50, nobs = rep(5, 50), p = 10,
  beta0 = c(rep(1, 5), rep(0, 5)), rho = 0.3
)

# 2. Fit the model using the formula interface
fit <- qpgee(
  y ~ . - id,
  data = sim_data,
  id = sim_data$id,
  tau = 0.5,
  method = "HBIC"
)

# 3. View the summary of the results
summary(fit)

---

Control Parameters for qpgee

Description

Provides control parameters for the Quantile Penalized Generalized Estimating Equations (QPGEE) fitting procedure. Similar in spirit to 'geese.control()' in the geepack package.

Usage

qpgeeControl(
  epsilon = 1e-04,
  decay = 1,
  maxit = 100,
  trace = FALSE,
  standardize = FALSE,
  shrinkCutoff = 1e-04
)

Arguments

epsilon	Convergence tolerance for the parameter estimates. Iteration stops when the maximum change in coefficients is below this value.
decay	Decay rate of learning step.
maxit	Maximum number of iterations.
trace	Logical indicating if output should be produced for each iteration. (You can decide how much information to show inside the C++/R loop.)
standardize	Logical indicating whether to scale X.
shrinkCutoff	Threshold below which coefficients are shrunk to zero (removal of “small” coefficients).

Value

A list with the components epsilon, maxit, trace, and shrinkCutoff.

Examples

ctrl <- qpgeeControl(epsilon = 1e-5, maxit = 200, trace = TRUE)

---

Generate Covariance Matrix

Description

This function generates a covariance matrix based on the specified correlation structure. The function supports "compound symmetry" (cs) and "autoregressive" (ar) correlation structures, as well as an identity matrix as the default option when neither "cs" nor "AR1" is specified.

Usage

Siga_cov(rho, corstr, nt)

Arguments

rho	Numeric, the correlation coefficient used for generating the covariance matrix. For "cs" or "exchangeable", it represents the common correlation between any two observations. For "AR1", it represents the correlation between two consecutive observations, with the correlation decreasing for observations further apart.
corstr	Character, specifies the correlation of correlation structure for the covariance matrix. Options are "cs" or "exchangeable" for compound symmetry, "AR1" for autoregressive, and any other input will result in an identity matrix.
nt	Integer, the dimension of the square covariance matrix (number of time points or observations).

Value

A square matrix of dimension 'nt' representing the specified covariance structure.

---

A Simulated Genetic Data from HapGen2

Description

The 'simuGene' dataset contains 500 SNPs simulated data from a commonly used tool for genetic data, HapGen2. We re-sampled existing genotype data to create this simulated data. The genotype data we resample from is the publicly available 1000 Genomes Project data. More specifically, we use resampled from chromosome 14.

Usage

simuGene

Format

A data frame with 1000 rows (subjects) and 500 columns (SNPs).

Examples

data(simuGene)
head(simuGene)

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A Subset of Yeast Cell Cycle Gene Expression Data (G1 Phase)

Description

The 'yeastG1' dataset contains gene expression data from the yeast cell cycle during the G1 phase. The original dataset (Spellman et al. 1998) includes expression levels for 6178 genes measured at 18 time points. And this is a subset of 283 cell-cycled-regularized genes observed over 4 time points at G1 stage and the standardized binding probabilities of a total of 96 TFs obtained from

Usage

yeastG1

Format

A data frame with 1132 rows and 99 columns.

The dataset contains gene expression levels for the following transcription factors: ABF1, ACE2, ADR1, ARG80, ARG81, ARO80, ASH1, BAS1, CAD1, CBF1, CIN5, CRZ1, CUP9, DAL81, DAL82, DIG1, DOT6, FHL1, FKH1, FKH2, FZF1, GAL4, GAT1, GAT3, GCN4, GCR1, GCR2, GLN3, GRF10.Pho2., GTS1, HAL9, HAP2, HAP3, HAP4, HAP5, HIR1, HIR2, HMS1, HSF1, IME4, INO2, INO4, IXR1, LEU3, MAC1, MAL13, MATa1, MBP1, MCM1, MET31, MET4, MIG1, MOT3, MSN1, MSN4, MSS11, MTH1, NDD1, NRG1, PDR1, PHD1, PHO4, PUT3, RAP1, RCS1, REB1, RFX1, RGM1, RLM1, RME1, ROX1, RPH1, RTG1, RTG3, SFP1, SIG1, SIP4, SKN7, SMP1, SOK2, SRD1, STB1, STE12, STP1, STP2, SUM1, SWI4, SWI5, SWI6, YAP1, YAP5, YAP6, YFL044C, YJL206C, ZAP1, ZMS1

Source

Spellman, P. T., Sherlock, G., Zhang, M. Q., Iyer, V. R., Anders, K., Eisen, M. B., ... & Futcher, B. (1998). Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Molecular biology of the cell, 9(12), 3273-3297.

Wang, L., Zhou, J., and Qu, A. (2012). Penalized generalized estimating equations for high-dimensional longitudinal data analysis. Biometrics, 68, 353–360.

Examples

data(yeastG1)
head(yeastG1)

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