summary: Summary methods for Fit Models

In npreg: Nonparametric Regression via Smoothing Splines

Summary methods for Fit Models

Description

summary methods for object classes "gsm", "sm", and "ss".

Usage

## S3 method for class 'gsm'
summary(object, ...)

## S3 method for class 'sm'
summary(object, ...)

## S3 method for class 'ss'
summary(object, ...)

## S3 method for class 'summary.gsm'
print(x, digits = max(3, getOption("digits") - 3), 
      signif.stars = getOption("show.signif.stars"), ...)

## S3 method for class 'summary.sm'
print(x, digits = max(3, getOption("digits") - 3), 
      signif.stars = getOption("show.signif.stars"), ...)

## S3 method for class 'summary.ss'
print(x, digits = max(3, getOption("digits") - 3), 
      signif.stars = getOption("show.signif.stars"), ...)

Arguments

object	an object of class "gsm" output by the gsm function, "sm" output by the sm function, or "ss" output by the ss function
x	an object of class "summary.gsm" output by the summary.gsm function, "summary.sm" output by the summary.sm function, or "summary.ss" output by the summary.ss function.
digits	the minimum number of significant digits to be printed in values.
signif.stars	logical. If TRUE, ‘significance stars’ are printed for each coefficient.
...	additional arguments affecting the summary produced (currently ignored).

Details

Summary includes information for assessing the statistical and practical significance of the model terms.

Statistical inference is conducted via (approximate) frequentist chi-square tests using the Bayesian interpretation of a smoothing spline (Nychka, 1988; Wahba, 1983).

With multiple smooth terms included in the model, the inferential results may (and likely will) differ slightly depending on the tprk argument (when using the gsm and sm functions).

If significance testing is of interest, the tprk = FALSE option may be desirable, given that this allows for unique basis function coefficients for each model term.

In all cases, the inferential results are based on a (pseudo) F or chi-square statistic which fails to consider the uncertainty of the smoothing parameter estimation.

Value

residuals	the deviance residuals.
fstatistic	the F statistic for testing all effects (parametric and smooth).
dev.expl	the explained deviance.
p.table	the coefficient table for (approximate) inference on the parametric terms.
s.table	the coefficient table for (approximate) inference on the smooth terms.
dispersion	the estimate of the dispersion parameter.
r.squared	the observed coefficient of multiple determination.
adj.r.squared	the adjusted coefficient of multiple determination.
kappa	the collinearity indices, i.e., square-roots of the variance inflation factors (see varinf). A value of 1 indicates no collinearity, and higher values indicate more collinearity of a given term with other model terms.
pi	the importance indices. Larger values indicate more importance, and the values satisfy sum(pi) = 1. Note that elements of pi can be negative.
call	the original function call.
family	the specified family (for gsm objects).

Author(s)

Nathaniel E. Helwig <[e-mail]>

References

Helwig, N. E. (2020). Multiple and Generalized Nonparametric Regression. In P. Atkinson, S. Delamont, A. Cernat, J. W. Sakshaug, & R. A. Williams (Eds.), SAGE Research Methods Foundations. doi: 10.4135/9781526421036885885

Nychka, D. (1988). Bayesian confience intervals for smoothing splines. Journal of the American Statistical Association, 83(404), 1134-1143. doi: 10.2307/2290146

Wahba, G. (1983). Bayesian "confidence intervals" for the cross-validated smoothing spline. Journal of the Royal Statistical Society. Series B, 45(1), 133-150. doi: 10.1111/j.2517-6161.1983.tb01239.x

See Also

gsm, sm, and ss

Examples

### Example 1: gsm

# generate data
set.seed(1)
n <- 1000
x <- seq(0, 1, length.out = n)
z <- factor(sample(letters[1:3], size = n, replace = TRUE))
fun <- function(x, z){
  mu <- c(-2, 0, 2)
  zi <- as.integer(z)
  fx <- mu[zi] + 3 * x + sin(2 * pi * x + mu[zi]*pi/4)
}
fx <- fun(x, z)
y <- rbinom(n = n, size = 1, p = 1 / (1 + exp(-fx)))

# define marginal knots
probs <- seq(0, 0.9, by = 0.1)
knots <- list(x = quantile(x, probs = probs),
              z = letters[1:3])

# fit sm with specified knots (tprk = TRUE)
gsm.ssa <- gsm(y ~ x * z, family = binomial, knots = knots)
summary(gsm.ssa)

# fit sm with specified knots (tprk = FALSE)
gsm.gam <- gsm(y ~ x * z, family = binomial, knots = knots, tprk = FALSE)
summary(gsm.gam)


### Example 2: sm

# generate data
set.seed(1)
n <- 100
x <- seq(0, 1, length.out = n)
z <- factor(sample(letters[1:3], size = n, replace = TRUE))
fun <- function(x, z){
  mu <- c(-2, 0, 2)
  zi <- as.integer(z)
  fx <- mu[zi] + 3 * x + sin(2 * pi * x + mu[zi]*pi/4)
}
fx <- fun(x, z)
y <- fx + rnorm(n, sd = 0.5)

# define marginal knots
probs <- seq(0, 0.9, by = 0.1)
knots <- list(x = quantile(x, probs = probs),
              z = letters[1:3])

# fit sm with specified knots (tprk = TRUE)
sm.ssa <- sm(y ~ x * z, knots = knots)
summary(sm.ssa)

# fit sm with specified knots (tprk = FALSE)
sm.gam <- sm(y ~ x * z, knots = knots, tprk = FALSE)
summary(sm.gam)


### Example 3: ss

# generate data
set.seed(1)
n <- 100
x <- seq(0, 1, length.out = n)
fx <- 2 + 3 * x + sin(2 * pi * x)
y <- fx + rnorm(n, sd = 0.5)

# regular smoothing spline
ss.reg <- ss(x, y, nknots = 10)
summary(ss.reg)

npreg documentation built on July 21, 2022, 1:06 a.m.