R: Fitted gam object

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. (2004) Low rank scale invariant tensor product smooths for generalized additive mixed models. Technical Report 04-13 Department of Statistics, University of Glasgow.

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.