gam: Fitting Generalized Additive Models in gam: Generalized Additive Models (2024)

a formula expression as for other regression models, of theform response ~ predictors. See the documentation of lm andformula for details. Built-in nonparametric smoothing terms areindicated by s for smoothing splines or lo for loesssmooth terms. See the documentation for s and lo for theirarguments. Additional smoothers can be added by creating the appropriateinterface functions. Interactions with nonparametric smooth terms are notfully supported, but will not produce errors; they will simply produce theusual parametric interaction.

a description of the error distribution and link function tobe used in the model. This can be a character string naming a familyfunction, a family function or the result of a call to a family function.(See family for details of family functions.)

an optional data frame containing the variables in the model.If not found in data, the variables are taken fromenvironment(formula), typically the environment from which gamis called.

an optional vector of weights to be used in the fittingprocess.

an optional vector specifying a subset of observations to beused in the fitting process.

a function which indicates what should happen when the datacontain NAs. The default is set by the na.action setting ofoptions, and is na.fail if that is unset. The“factory-fresh” default is na.omit. A special methodna.gam.replace allows for mean-imputation of missing values(assumes missing at random), and works gracefully with gam

starting values for the parameters in the additive predictor.

starting values for the additive predictor.

starting values for the vector of means.

a list of parameters for controlling the fitting process.See the documentation for gam.control for details. These canalso be set as arguments to gam() itself.

a logical value indicating whether model frame should beincluded as a component of the returned value. Needed if gam iscalled and predicted from inside a user function. Default is TRUE.

the method to be used in fitting the parametric part of themodel. The default method "glm.fit" uses iteratively reweightedleast squares (IWLS). The only current alternative is "model.frame"which returns the model frame and does no fitting.

For gam: logical values indicating whether the responsevector and model matrix used in the fitting process should be returned ascomponents of the returned value.

For gam.fit: x is a model matrix of dimension n * p,and y is a vector of observations of length n.

further arguments passed to or from other methods.

for gam.fit only. This is essentially a subset ofthe model frame corresponding to the smooth terms, and has the ingredientsneeded for smoothing each variable in the backfitting algorithm. Theelements of this frame are produced by the formula functions lo ands.

this can be used to specify an a priori known componentto be included in the additive predictor during fitting.

the coefficients of the parametric part of theadditive.predictors, which multiply the columns of the model matrix.The names of the coefficients are the names of the single-degree-of-freedomeffects (the columns of the model matrix). If the model is overdeterminedthere will be missing values in the coefficients corresponding toinestimable coefficients.

the additive fit,given by the product of the model matrix and the coefficients, plus thecolumns of the $smooth component.

the fittedmean values, obtained by transforming the componentadditive.predictors using the inverse link function.

these four characterize the nonparametric aspect ofthe fit. smooth is a matrix of smooth terms, with a columncorresponding to each smooth term in the model; if no smooth terms are inthe Gam model, all these components will be missing. Each columncorresponds to the strictly nonparametric part of the term, while theparametric part is obtained from the model matrix. nl.df is a vectorgiving the approximate degrees of freedom for each column of smooth.For smoothing splines specified by s(x), the approximate dfwill be the trace of the implicit smoother matrix minus 2. nl.chisqis a vector containing a type of score test for the removal of each of thecolumns of smooth. var is a matrix like smooth,containing the approximate pointwise variances for the columns ofsmooth.

This is essentially a subset of themodel frame corresponding to the smooth terms, and has the ingredientsneeded for making predictions from a Gam object

the residuals from the final weighted additive fit; also known as residuals,these are typically not interpretable without rescaling by the weights.

up to a constant, minus twice the maximized log-likelihood.Similar to the residual sum of squares. Where sensible, the constant ischosen so that a saturated model has deviance zero.

The deviance for the null model, comparable withdeviance. The null model will include the offset, and an intercept ifthere is one in the model

the number of local scoringiterations used to compute the estimates.

a vector oflength iter giving number of backfitting iterations used at eachinner loop.

a three-element character vector giving the nameof the family, the link, and the variance function; mainly for printingpurposes.

the working weights, that is the weightsin the final iteration of the local scoring fit.

thecase weights initially supplied.

the residual degrees offreedom.

the residual degrees of freedom for the nullmodel.