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

boundary 
did parameters end up at boundary of parameter space? 
call 
the matched call (allows 
cmX 
column means of the model matrix (with elements corresponding to smooths set to zero ) — useful for componentwise CI calculation. 
coefficients 
the coefficients of the fitted model. Parametric coefficients are first, followed by coefficients for each spline term in turn. 
control 
the 
converged 
indicates whether or not the iterative fitting method converged. 
data 
the original supplied data argument (for class 
db.drho 
matrix of first derivatives of model coefficients w.r.t. log smoothing parameters. 
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. 
edf1 
similar, but using alternative estimate of EDF. Useful for testing. 
edf2 
if estimation is by ML or REML then an edf that accounts for smoothing parameter
uncertainty can be computed, this is it. 
family 
family object specifying distribution and link used. 
fitted.values 
fitted model predictions of expected value for each datum. 
formula 
the model formula. 
full.sp 
full array of smoothing parameters multiplying penalties (excluding any contribution
from 
F 
Degrees of freedom matrix. This may be removed at some point, and should probably not be used. 
gcv.ubre 
The minimized smoothing parameter selection score: GCV, UBRE(AIC), GACV, negative log marginal likelihood or negative log restricted likelihood. 
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 PIRLS taken to get convergence. 
linear.predictors 
fitted model prediction of link function of expected value for each datum. 
method 
One of 
mgcv.conv 
A list of convergence diagnostics relating to the

min.edf 
Minimum possible degrees of freedom for whole model. 
model 
model frame containing all variables needed in original model fit. 
na.action 
The 
nsdf 
number of parametric, nonsmooth, model terms including the intercept. 
null.deviance 
deviance for single parameter model. 
offset 
model offset. 
optimizer 

outer.info 
If ‘outer’ iteration has been used to fit the model (see

paraPen 
If the 
pred.formula 
one sided formula containing variables needed for prediction, used by 
prior.weights 
prior weights on observations. 
pterms 

R 
Factor R from QR decomposition of weighted model matrix, unpivoted to be in same column order as model matrix (so need not be upper triangular). 
rank 
apparent rank of fitted model. 
reml.scale 
The scale (RE)ML scale parameter estimate, if (P)(RE)ML used for smoothness estimation. 
residuals 
the working residuals for the fitted model. 
rV 
If present, 
scale 
when present, the scale (as 
scale.estimated 

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 
sp 
estimated smoothing parameters for the model. These are the underlying smoothing
parameters, subject to optimization. For the full set of smoothing parameters multiplying the
penalties see 
terms 

var.summary 
A named list of summary information on the predictor variables. If
a parametric variable is a matrix, then the summary is a one row matrix, containing the
observed data value closest to the column median, for each matrix column. If the variable
is a factor the then summary is the modal factor level, returned as a factor, with levels
corresponding to those of the data. For numerics and matrix arguments of smooths, the summary
is the mean, nearest observed value to median and maximum, as a numeric vector. Used by

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. 
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. 
Vc 
Under ML or REML smoothing parameter estimation it is possible to correct the covariance
matrix 
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@rproject.org
References
A Key Reference on this implementation:
Wood, S.N. (2017) Generalized Additive Models: An Introduction with R (2nd edition). Chapman & Hall/ CRC, Boca Raton, Florida
Key Reference on GAMs generally:
Hastie (1993) in Chambers and Hastie (1993) Statistical Models in S. Chapman and Hall.
Hastie and Tibshirani (1990) Generalized Additive Models. Chapman and Hall.