ME.fcRegression_MEM: Use UP_MEM or MP_MEM substitution to apply (generalized)...

In MECfda: Scalar-on-Function Regression with Measurement Error Correction

Use UP_MEM or MP_MEM substitution to apply (generalized) linear regression with one functional covariate with measurement error.

Description

The Mixed-effect model (MEM) approach is a two-stage-based method that employs functional mixed-effects models. It allows us to delve into the nonlinear measurement error model, where the relationship between the true and observed measurements is not constrained to be linear, and the distribution assumption on the observed measurement is relaxed to encompass the exponential family rather than being limited to the Gaussian distribution. The MEM approach employs point-wise (UP_MEM) and multi-point-wise (MP_MEM) estimation procedures to avoid potential computational complexities caused by analyses of multi-level functional data and computations of potentially intractable and complex integrals.

Usage

ME.fcRegression_MEM(
  data.Y,
  data.W,
  data.Z,
  method = c("UP_MEM", "MP_MEM", "average"),
  t_interval = c(0, 1),
  t_points = NULL,
  d = 3,
  family.W = c("gaussian", "poisson"),
  family.Y = "gaussian",
  formula.Z,
  basis.type = c("Fourier", "Bspline"),
  basis.order = NULL,
  bs_degree = 3,
  smooth = FALSE,
  silent = TRUE
)

Arguments

data.Y	Response variable, can be an atomic vector, a one-column matrix or data frame, recommended form is a one-column data frame with column name.
data.W	A 3-dimensional array, represents W, the measurement of X. Each row represents a subject. Each column represent a measurement (time) point. Each layer represents an observation.
data.Z	Scalar covariate(s), can be not input or NULL (when there's no scalar covariate), an atomic vector (when only one scalar covariate), a matrix or data frame, recommended form is a data frame with column name(s).
method	The method to construct the substitution X. Available options: 'UP_MEM', 'MP_MEM', 'average'.
t_interval	A 2-element vector, represents an interval, means the domain of the functional covariate. Default is c(0,1), represent interval [0,1].
t_points	Sequence of the measurement (time) points, default is NULL.
d	The number of time points involved for MP_MEM (default and miniumn is 3).
family.W	Distribution of W given X, Available options: "gaussian","poisson".
family.Y	A description of the error distribution and link function to be used in the model, see family.
formula.Z	A formula without the response variable, contains only scalar covariate(s), use the format of lme4 package if random effects exist. e.g. ~ Z_1 + (1|Z_2). If not assigned, include all scalar covariates and intercept term as fixed effects.
basis.type	Type of function basis. Can only be assigned as one type even if there is more than one functional covariates. Available options: 'Fourier' or 'Bspline', represent Fourier basis and b-spline basis respectively. For the detailed form for Fourier and b-splines basis, see fourier_basis_expansion and bspline_basis_expansion.
basis.order	Indicate number of the function basis. When using Fourier basis \frac{1}{2},\sin k t, \cos k t, k = 1,\dots,K, basis.order is the number K. When using b-splines basis \{B_{i,p}(x)\}_{i=-p}^{k}, basis.order is the number of splines, equal to k+p+1. (same as arguement df in bs.) May set a individual number for each functional covariate. When the element of this argument is less than the number of functional covariates, it will be used recursively.
bs_degree	Degree of the piecewise polynomials if use b-splines basis, default is 3. See degree in bs.
smooth	Whether to smooth the substitution of X. Default is FALSE.
silent	Whether not to show the state of the running of the function. Default is TRUE.

Value

Returns a fcRegression object. See fcRegression.

References

Luan, Yuanyuan, et al. "Scalable regression calibration approaches to correcting measurement error in multi-level generalized functional linear regression models with heteroscedastic measurement errors." arXiv preprint arXiv:2305.12624 (2023).

Examples

data(MECfda.data.sim.0.1)
res = ME.fcRegression_MEM(data.Y = MECfda.data.sim.0.1$Y,
                          data.W = MECfda.data.sim.0.1$W,
                          data.Z = MECfda.data.sim.0.1$Z,
                          method = 'UP_MEM',
                          family.W = "gaussian",
                          basis.type = 'Bspline')

MECfda documentation built on April 3, 2025, 10:07 p.m.