predict.gammi: Predict Method for gammi Fits

In gammi: Generalized Additive Mixed Model Interface

Predict Method for gammi Fits

Description

Obtain predictions from a fit generalized additive mixed model (gammi) object.

Usage

## S3 method for class 'gammi'
predict(object, 
        newx,
        newdata, 
        se.fit = FALSE,
        type = c("link", "response", "terms"),
        conf.int = FALSE, 
        conf.level = 0.95,
        ...)

Arguments

object	Object of class "gammi"
newx	Matrix of new x scores for prediction (default S3 method). Must have p columns arranged in the same order as the x matrix used to fit the model.
newdata	Data frame of new data scores for prediction (S3 "formula" method). Must contain all variables in the formula (and fixed formula if applicable) used to fit the model.
se.fit	Logical indicating whether standard errors of predictions should be returned.
type	Type of prediction to return: link = linear prediction, response = fitted value, and terms = matrix where each columns contains each term's linear predictor contribution.
conf.int	Logical indicating whether confidence intervals for predictions should be returned.
conf.level	Scalar between 0 and 1 controlling the confidence level for the interval. Ignored if conf.int = FALSE.
...	Additional arugments (ignored).

Details

The default of type = "link" returns the model implied linear predictor corresponding to newx or newdata, i.e.,

g(\hat{\boldsymbol\mu}_{\theta (\mathrm{new}) }) = \hat{f}_\theta(\mathbf{X}_\mathrm{new}, \mathbf{Z}_\mathrm{new}) + \mathbf{X}_\mathrm{new}^\top \hat{\boldsymbol\beta}_\theta

where \hat{f}_\theta(\cdot) is the estimated smooth function (with the subscript of \theta denoting the dependence on the variance parameters), and \hat{\boldsymbol\beta}_\theta are the fixed effect estimates (if applicable). Note that \mathbf{X}_\mathrm{new} and \mathbf{Z}_\mathrm{new} denote the new data at which the predictions will be formed.

Using type = "response" returns the predictions on the fitted value scale, i.e.,

\hat{\boldsymbol\mu}_{\theta (\mathrm{new})} = g^{-1} \left( \hat{f}_\theta(\mathbf{X}_\mathrm{new}, \mathbf{Z}_\mathrm{new}) + \mathbf{X}_\mathrm{new}^\top \hat{\boldsymbol\beta}_\theta \right)

where g^{-1}(\cdot) denotes the inverse of the chosen link function.

Using type = "terms" returns a matrix where each column contains the linear predictor contribution for a different model term, i.e., the k-th column contains

\hat{f}_{\theta k}(\mathbf{X}_\mathrm{new}, \mathbf{Z}_\mathrm{new}) + \mathbf{X}_{\mathrm{new} k }^\top \hat{\boldsymbol\beta}_{\theta k}

where \hat{f}_{\theta k} is the k-th additive function, i.e., \hat{f}_\theta(\mathbf{X}_\mathrm{new}, \mathbf{Z}_\mathrm{new}) = \sum_{k=1}^K \hat{f}_{\theta k}(\mathbf{X}_\mathrm{new}, \mathbf{Z}_\mathrm{new}) and the second term denotes the (optional) fixed-effect contribution for the k-th term, i.e., \mathbf{X}_\mathrm{new}^\top \hat{\boldsymbol\beta}_\theta = \sum_{k=1}^K \mathbf{X}_{\mathrm{new} k }^\top \hat{\boldsymbol\beta}_{\theta k}

Value

If type = "link" or type = "response", returns either a vector (of predictions corresponding to the new data) or a data frame that contains the predictions, along with their standard errors and/or confidence interval endpoints (as controlled by se.fit and conf.int arguments).

If type = "terms", returns either a matrix (with columns containing predictions for each term) or a list that contains the term-wise predictions, along with their standard errors and/or confidence interval endpoints (as controlled by se.fit and conf.int arguments).

Note

Terms entered through the random argument of the gammi function are not included as a part of predictions.

Author(s)

Nathaniel E. Helwig <[e-mail]>

References

Helwig, N. E. (2024). Precise tensor product smoothing via spectral splines. Stats, 7(1), 34-53, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3390/stats7010003")}

See Also

gammi for fitting generalized additive mixed models

plot.gammi for plotting effects from gammi objects

summary.gammi for summarizing results from gammi objects

Examples

# load 'gammi' package
library(gammi)

# mean function
eta <- function(x, z, additive = TRUE){
  mx1 <- cos(2 * pi * (x - pi))
  mx2 <- 30 * (z - 0.6)^5
  mx12 <- 0
  if(!additive) mx12 <- sin(pi * (x - z))
  mx1 + mx2 + mx12
}

# generate mean function
set.seed(1)
n <- 1000
nsub <- 50
x <- runif(n)
z <- runif(n)
fx <- eta(x, z)

# generate random intercepts
subid <- factor(rep(paste0("sub", 1:nsub), n / nsub),
                levels = paste0("sub", 1:nsub))
u <- rnorm(nsub, sd = sqrt(1/2))

# generate responses
y <- fx + u[subid] + rnorm(n, sd = sqrt(1/2))

# fit model via formula method
mod <- gammi(y ~ x + z, random = ~ (1 | subid))
mod

# get fitted values via predict
fit <- predict(mod, newdata = data.frame(x = x, z = z))
max(abs(fit - mod$fitted.values))

# get fitted values with SE and CI
fit <- predict(mod, newdata = data.frame(x = x, z = z), conf.int = TRUE)
head(fit)

# get fitted values with SE and CI for each term
fit <- predict(mod, newdata = data.frame(x = x, z = z), 
               type = "terms", conf.int = TRUE)
str(fit)                                  # list with 4 components
head(sapply(fit, function(x) x[,1]))      # for x effect
head(sapply(fit, function(x) x[,2]))      # for z effect

gammi documentation built on April 4, 2025, 4:48 a.m.