hyper_gam {hyper.gam} | R Documentation |
gam with matrix predictor
Description
A generalized additive model gam with one-and-only-one matrix predictor.
Usage
hyper_gam(formula, data, family, nonlinear = FALSE, ...)
Arguments
formula |
formula, e.g., |
data |
|
family |
family object, see function gam for details. Default values are |
nonlinear |
logical scalar,
whether to use nonlinear or linear functional model.
Default |
... |
additional parameters for functions s and ti,
most importantly |
Details
Function hyper_gam()
fits a gam model
of response y
with matrix predictor X
.
This method was originally defined in the context of quantile.
In the following text, the matrix predictor X
is denoted as Q(p)
,
where p
is as.numeric(colnames(X))
.
Linear quantile index, with a linear functional coefficient \beta(p)
,
\text{QI}=\displaystyle\int_0^1\beta(p)\cdot Q(p)\,dp
can be estimated by fitting a functional generalized linear model (FGLM, James, 2002) to exponential-family outcomes, or by fitting a linear functional Cox model (LFCM, Gellar et al., 2015) to survival outcomes.
Non-linear quantile index, with a bivariate twice differentiable function F(\cdot,\cdot)
,
\text{nlQI}=\displaystyle\int_0^1 F\big(p, Q(p)\big)\,dp
can be estimated by fitting a functional generalized additive model (FGAM, McLean et al., 2014) to exponential-family outcomes, or by fitting an additive functional Cox model (AFCM, Cui et al., 2021) to survival outcomes.
Value
Function hyper_gam()
returns a hyper_gam object,
which inherits from class gam.
Author(s)
Tingting Zhan, Erjia Cui
References
James, G. M. (2002). Generalized Linear Models with Functional Predictors, doi:10.1111/1467-9868.00342
Gellar, J. E., et al. (2015). Cox regression models with functional covariates for survival data, doi:10.1177/1471082X14565526
Mathew W. M., et al. (2014) Functional Generalized Additive Models, doi:10.1080/10618600.2012.729985
Cui, E., et al. (2021). Additive Functional Cox Model, doi:10.1080/10618600.2020.1853550