Fits a generalized additive model with penalized regression spline
smooths and automatic smoothness selection, reproducing the default fits
of mgcv::gam: the same thin plate regression spline and cubic
regression spline bases, the same identifiability constraints and penalty
scaling, and smoothing parameters chosen by GCV/UBRE ("GCV.Cp") or
by Laplace-approximate REML ("REML") with Newton's method on the
log smoothing parameters. Binomial (logit) and Poisson (log) responses
are fitted by penalized iteratively re-weighted least squares (P-IRLS).
Arguments
- formula
A model formula such as
y ~ s(x) + s(z, bs = "cr") + w.- data
A data frame containing the variables in the formula.
- family
One of
"gaussian"(identity link),"binomial"(logit link, 0/1 or logical or two-level factor response) or"poisson"(log link).- method
Smoothness selection criterion:
"GCV.Cp"(GCV when the scale is unknown, UBRE/Mallows' Cp for binomial and Poisson) or"REML".- weights
Optional non-negative prior weights, one per row of
data.- sp
Optional fixed smoothing parameters, one per penalized smooth in formula order (as
mgcv::gam'ssp);NULL(default) estimates them. Withmethod = "REML"and a Gaussian response the scale is still estimated.- ...
Unused; present for compatibility with the bridge calling convention.
Value
An object of class "morie_gam": a list with
coefficients, Vp (Bayesian posterior covariance),
Ve (frequentist covariance), edf (per coefficient),
edf_smooth, edf_total, sp (smoothing parameters),
score (the minimised GCV/UBRE or REML criterion), scale,
fitted.values, linear.predictors, residuals,
deviance, null.deviance, dev.expl, r.sq,
aic, smooths (basis information used by predict)
and optimiser diagnostics.
Details
The right-hand side may contain ordinary parametric terms (anything
model.matrix understands) and smooth terms written s(x),
s(x, k = 20), s(x, bs = "cr") or the two-dimensional
isotropic thin plate smooth s(x, z). The s() terms are read
from the formula as data; no function s is called. For more than
2000 unique covariate values a thin plate basis is built from 2000 knots
sampled with the fixed seed 1, as mgcv does, without disturbing the
caller's random number stream.
References
Wood, S. N. (2017) Generalized Additive Models: An Introduction with R, 2nd ed., CRC Press. Wood, S. N. (2003) Thin plate regression splines, JRSS B 65, 95-114. Wood, S. N. (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models, JRSS B 73, 3-36. Wood, S. N. (2013) On p-values for smooth components of an extended generalized additive model, Biometrika 100, 221-228.
Examples
set.seed(1)
d <- data.frame(x = runif(200), z = runif(200))
d$y <- sin(2 * pi * d$x) + d$z + rnorm(200, 0, 0.3)
fit <- morie_gam(y ~ s(x) + z, data = d)
fit
#>
#> Family: gaussian
#> Link function: identity
#>
#> Formula:
#> y ~ s(x) + z
#> <environment: 0x562176affb88>
#>
#> Estimated degrees of freedom:
#> s(x)
#> 5.9288
#> total = 7.9288
#>
#> GCV score: 0.097038062 scale est. = 0.0931911
#> n = 200
summary(fit)
#>
#> Family: gaussian
#> Link function: identity
#>
#> Formula:
#> y ~ s(x) + z
#> <environment: 0x562176affb88>
#>
#> Parametric coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.054121 0.041983 -1.2891 0.1989
#> z 1.082555 0.076775 14.1003 <2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Approximate significance of smooth terms:
#> edf Ref.df F p-value
#> s(x) 5.9288 7.1039 150.87 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> R-sq.(adj) = 0.86 Deviance explained = 86.4%
#> GCV = 0.0970381 Scale est. = 0.0931911 n = 200
head(predict(fit, newdata = data.frame(x = c(0.1, 0.5), z = 0.5)))
#> 1 2
#> 1.152791 0.528741