gamObject {mgcv}R Documentation

Fitted gam object

Description

A fitted GAM object returned by function gam and of class "gam" inheriting from classes "glm" and "lm". Method functions anova, logLik, influence, plot, predict, print, residuals and summary exist for this class.

All compulsory elements of "glm" and "lm" objects are present, but the fitting method for a GAM is different to a linear model or GLM, so that the elements relating to the QR decomposition of the model matrix are absent.

Value

A gam object has the following elements:

aic AIC of the fitted model: bear in mind that the degrees of freedom used to calculate this are the effective degrees of freedom of the model, and the likelihood is evaluated at the maximum of the penalized likelihood in most cases, not at the MLE.
assign Array whose elements indicate which model term (listed in pterms) each parameter relates to: applies only to non-smooth terms.
boundary did parameters end up at boundary of parameter space?
call the matched call (allows update to be used with gam objects, for example).
coefficients the coefficients of the fitted model. Parametric coefficients are first, followed by coefficients for each spline term in turn.
control the gam control list used in the fit.
converged indicates whether or not the iterative fitting method converged.
data the original supplied data argument (for class "glm" compatibility).
deviance model deviance (not penalized deviance).
df.null null degrees of freedom.
df.residual effective residual degrees of freedom of the model.
edf estimated degrees of freedom for each model parameter. Penalization means that many of these are less than 1.
family family object specifying distribution and link used.
fit.method Character string describing the multiple GCV/UBRE smoothing parameter estimation method used.
fitted.values fitted model predictions of expected value for each datum.
formula the model formula.
full.formula the model formula with each smooth term fully expanded and with option arguments given explicitly (i.e. not with reference to other variables) - useful for later prediction from the model.
gcv.ubre The minimized GCV or UBRE score.
hat array of elements from the leading diagonal of the `hat' (or `influence') matrix. Same length as response data vector.
iter number of iterations of P-IRLS taken to get convergence.
linear.predictors fitted model prediction of link function of expected value for each datum.
method One of "GCV" or "UBRE", depending on the fitting criterion used.
mgcv.conv A list of convergence diagnostics relating to the "mgcv" or "magic" parts of smoothing parameter estimation - this will not be very meaningful for pure "outer" estimation of smoothing parameters. mgcv.conv differs for method "magic" and "mgcv". Here is the "mgcv" version:
score
corresponding to edf, an array of GCV or UBRE scores for the model given the final estimated relative smoothing parameters.

g
the gradient of the GCV/UBRE score w.r.t. the relative smoothing parameters at termination.

h
the second derivatives corresponding to g above - i.e. the leading diagonal of the Hessian.

e
the eigen-values of the Hessian. All non-negative indicates a positive definite Hessian.

iter
the number of iterations taken.

in.ok
TRUE if the second smoothing parameter guess improved the GCV/UBRE score.

step.fail
TRUE if the algorithm terminated by failing to improve the GCV/UBRE score rather than by `converging'. Not necessarily a problem, but check the above derivative information quite carefully.

In the case of "magic" the items are:
full.rank
The apparent rank of the problem given the model matrix and constraints.

rank
The numerical rank of the problem.

fully.converged
TRUE is multiple GCV/UBRE converged by meeting convergence criteria. FALSE if method stopped with a steepest descent step failure.

hess.pos.def
Was the hessian of the GCV/UBRE score positive definite at smoothing parameter estimation convergence?

iter
How many iterations were required to find the smoothing parameters?

score.calls
and how many times did the GCV/UBRE score have to be evaluated?

rms.grad
root mean square of the gradient of the GCV/UBRE score at convergence.

min.edf Minimum possible degrees of freedom for whole model.
model model frame containing all variables needed in original model fit.
na.action The na.action used in fitting.
nsdf number of parametric, non-smooth, model terms including the intercept.
null.deviance deviance for single parameter model.
offset model offset.
outer.info If `outer' iteration has been used to fit the model (see gam.method) then this is present and contains whatever was returned by the optimization routine used (currently nlm or optim).
prior.weights prior weights on observations.
pterms terms object for strictly parametric part of model.
rank apparent rank of fitted model.
residuals the working residuals for the fitted model.
sig2 estimated or supplied variance/scale parameter.
smooth list of smooth objects, containing the basis information for each term in the model formula in the order in which they appear. These smooth objects are what gets returned by the smooth.construct objects.
sp smoothing parameter for each smooth.
terms terms object of model model frame.
Vp estimated covariance matrix for the parameters. This is a Bayesian posterior covariance matrix that results from adopting a particular Bayesian model of the smoothing process. Paricularly useful for creating credible/confidence intervals.
Ve frequentist estimated covariance matrix for the parameter estimators. Particularly useful for testing whether terms are zero. Not so useful for CI's as smooths are usually biased.
weights final weights used in IRLS iteration.
y response data.

WARNINGS

This model object is different to that described in Chambers and Hastie (1993) in order to allow smoothing parameter estimation etc.

Author(s)

Simon N. Wood simon.wood@r-project.org

References

Key References on this implementation:

Wood, S.N. (2000) Modelling and Smoothing Parameter Estimation with Multiple Quadratic Penalties. J.R.Statist.Soc.B 62(2):413-428

Wood, S.N. (2003) Thin plate regression splines. J.R.Statist.Soc.B 65(1):95-114

Wood, S.N. (in press) Stable and efficient multiple smoothing parameter estimation for generalized additive models. J. Amer. Statist. Ass.

Wood, S.N. (2004) On confidence intervals for GAMs based on penalized regression splines. Technical Report 04-12 Department of Statistics, University of Glasgow.

Wood, S.N. (2006) Low rank scale invariant tensor product smooths for generalized additive mixed models. Biometrics.

Key Reference on GAMs and related models:

Hastie (1993) in Chambers and Hastie (1993) Statistical Models in S. Chapman and Hall.

Hastie and Tibshirani (1990) Generalized Additive Models. Chapman and Hall.

Wahba (1990) Spline Models of Observational Data. SIAM

See Also

gam


[Package mgcv version 1.3-23 Index]