hyper_gam: gam with matrix predictor

In hyper.gam: Generalized Additive Models with Hyper Column

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., y~X, in which Response y may be double, logical and Surv Predictor X is a double matrix, the colnames of which must be convertible to numeric vector, indicating a common tabulating grid shared by all subjects.
data	data.frame
family	family object, see function gam for details. Default values are mgcv::cox.ph() for Surv response y; stats::binomial(link = 'logit') for logical response y; stats::gaussian(link = 'identity') for double response y
nonlinear	logical scalar, whether to use nonlinear or linear functional model. Default FALSE
...	additional parameters for functions s and ti, most importantly k

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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/1467-9868.00342")}

Gellar, J. E., et al. (2015). Cox regression models with functional covariates for survival data, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/1471082X14565526")}

Mathew W. M., et al. (2014) Functional Generalized Additive Models, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10618600.2012.729985")}

Cui, E., et al. (2021). Additive Functional Cox Model, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10618600.2020.1853550")}

hyper.gam documentation built on June 8, 2025, 10:41 a.m.