Locally Sparse Varying Coefficient Mixed Models

Usage

lsvcmm(
  data,
  response,
  subject,
  time,
  vc_covariates = NULL,
  nvc_covariates = NULL,
  offset = NULL,
  weight = NULL,
  add_intercept = T,
  estimated_time = NULL,
  family = DEFAULT_FAMILY_ARGS,
  kernel = DEFAULT_KERNEL_ARGS,
  penalty = DEFAULT_PENALTY_ARGS,
  working_covariance = DEFAULT_WORKING_COVARIANCE_ARGS,
  control = DEFAULT_CONTROL_ARGS,
  return_models = F
)

Arguments

data: A data frame containing the variables in the model.
response: The name of the response variable in data.
subject: The name of the subject variable in data.
time: The name of the time variable in data.
vc_covariates: The names of the varying coefficient covariates in data.
nvc_covariates: The names of the non-varying coefficient covariates in data.
offset: The name of the offset variable in data.
weight: The name of the weight variable in data.
add_intercept: Whether to add an intercept to the model.
estimated_time: The time points at which to estimate the varying coefficients. If missing, all observed time points are used.
family: A list of arguments for the response distribution. See family_args.
kernel: A list of arguments for the kernel. See kernel_args.
penalty: A list of arguments for the penalty. See penalty_args.
working_covariance: A list of arguments for the working covariance. See working_covariance_args.
control: A list of arguments for the control parameters. See control_args.
return_models: Whether to return the fitted models.

Value

A list containing the following elements:

family: A list of arguments for the response distribution. See family_args.
kernel: A list of arguments for the kernel. See kernel_args.
penalty: A list of arguments for the penalty. See penalty_args.
working_covariance: A list of arguments for the working covariance. See working_covariance_args.
control: A list of arguments for the control parameters. See control_args.
results: A data frame containing the results of the optimization. Each row is a model resulting from a particular tuning parameter combination.
nvc_path: A matrix containing the estimated non-varying coefficient path of dimension (p_u, n_models).
vc_path: An array containing the estimated varying coefficient path of dimension (p_x, n_timepoints, n_models).
scaled_time: The time points at which the varying coefficients were estimated.
unscaled_time: The corresponding values in the original scale.
range_time: The range of the time points.
models: A list of the fitted models.

Details

The lsvcmm function fits a locally sparse varying coefficient mixed model (LSVCMM) to longitudinal data.

The LSVCMM is a semiparametric model for longitudinal data that allows the coefficients of the non-varying covariates to vary smoothly over time. The model is defined as $$Y_{ij} = \beta_0(t_{ij}) + \sum_{k=1}^p \beta_k(t_{ij}) X_{ijk} + \epsilon_{ij},$$ where $Y_{ij}$ is the response of the $i$-th subject at time $t_{ij}$, $X_{ijk}$ is the $k$-th non-varying covariate of the $i$-th subject at time $t_{ij}$, $\beta_0(t)$ is the intercept function, $\beta_k(t)$ is the coefficient function of the $k$-th non-varying covariate, and $\epsilon_{ij}$ is the error term.