confint.cgaim {cgaim}

Confidence intervals

Description

Computes confidence intervals for the CGAIM components.

Usage

## S3 method for class 'cgaim'
confint(object, parm, level = 0.95, type = c("normal",
  "bootstrap"), B = 100, ...)

## S3 method for class 'boot.cgaim'
confint(object, parm, level = 0.95, ...)

Arguments

object

A cgaim or boot.cgaim object.

parm

The model components for which to get confidence intervals. One or several of: "alpha" for index weights, "beta" for scaling coefficients and "g" for ridge function. By default, returns confidence intervals for all components.

level

The level of confidence intervals. Default to 0.95.

type

The type of confidence intervals. Either "normal" (the default) or "bootstrap". See details.

B

The number of samples to be simulated.

...

Additional parameters to be passed to boot.cgaim for bootstrap confidence intervals.

Details

Two types of confidence intervals are currently implemented in the function. When type = "normal", confidence intervals are computed assuming components are normally distributed. Beta coefficients are treated as regular linear regression coefficients and g as regular smooth functions estimated by (shape-constrained) generalized additive models. For alpha coefficients, we consider a linear transformation mapping them to a Truncated Multivariate Normal distribution (i.e. with only bound constraints). Simulation from the TMVN are performed (see tmvnorm) and transformed back into the original coefficient space (i.e. with linear constraints). The parameter B controls the number of simulations from the TMVN. Confidence intervals are computed as the percentiles of these simulated coefficients, ensuring the confidence region is entirely within the feasible region defined by the constraints.

When type = "bootstrap", confidence intervals are estimated by percentile bootstrap. boot.cgaim is called internally to create B samples of model components, and confidence intervals are then computed as the percentiles of bootstrap samples. Alternatively, the user can directly call boot.cgaim and feed the result into confint.boot.cgaim.

Value

A list of confidence intervals. Contains one element per model component in the parm argument.

Note

Confidence intervals for the g functions are evaluated on the same n index values as the functions in object.

References

Masselot, P. and others, 2022. Constrained groupwise additive index models. Biostatistics.

Pya, N., Wood, S.N., 2015. Shape constrained additive models. Stat. Comput. 25, 543–559.

Wood, S.N., 2017. Generalized Additive Models: An Introduction with R, 2nd ed, Texts in Statistical Science. Chapman and Hall/CRC.

DiCiccio, T.J., Efron, B., 1996. Bootstrap Confidence Intervals. Statistical Science 11, 189–212.

Carpenter, J., Bithell, J., 2000. Bootstrap confidence intervals: when, which, what? A practical guide for medical statisticians. Statistics in Medicine 19, 1141–1164.

See Also

boot.cgaim for bootstrapping.

Examples

# A simple CGAIM
n <- 200
x1 <- rnorm(n)
x2 <- x1 + rnorm(n)
z <- x1 + x2
y <- z + rnorm(n)
df1 <- data.frame(y, x1, x2) 
ans <- cgaim(y ~ g(x1, x2, acons = list(monotone = 1)), data = df1)

# Normal confidence intervals
set.seed(1)
ci1 <- confint(ans, B = 1000)
ci1$alpha
ci1$beta

# Select only alphas: identical to above result
set.seed(1)
confint(ans, B = 1000, parm = "alpha")

# Select only betas: identical to above result
set.seed(1)
confint(ans, B = 1000, parm = "beta")

# Confidence intervals by bootstrap (more computationally intensive, B should be increased)
set.seed(2)
ci2 <- confint(ans, type = "boot", B = 10)

# Alternatively, bootstrap samples can be performed beforehand
set.seed(2) 
boot1 <- boot.cgaim(ans, B = 10)
ci3 <- confint(boot1)