A generalized additive model gam with one-and-only-one matrix predictor.
hyper_gam(formula, data, family, nonlinear = FALSE, ...)Function hyper_gam() returns a hyper_gam object,
which inherits from class gam.
formula, e.g., y~X, in which
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 \(y\)
logical scalar,
whether to use nonlinear or linear functional model.
Default FALSE
additional parameters for functions s and ti,
most importantly k
Tingting Zhan, Erjia Cui
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.
James, G. M. (2002). Generalized Linear Models with Functional Predictors, tools:::Rd_expr_doi("10.1111/1467-9868.00342")
Gellar, J. E., et al. (2015). Cox regression models with functional covariates for survival data, tools:::Rd_expr_doi("10.1177/1471082X14565526")
Mathew W. M., et al. (2014) Functional Generalized Additive Models, tools:::Rd_expr_doi("10.1080/10618600.2012.729985")
Cui, E., et al. (2021). Additive Functional Cox Model, tools:::Rd_expr_doi("10.1080/10618600.2020.1853550")