DoubleGam: Double Generalized Additive Models
In ilapros/DoubleRobGam: Double Robust Generalised Additive Models

Description Usage Arguments Value Author(s) References See Also

A function to estimate both the mean and the dispersion function using B-splines bases.

DoubleGam(formulaM, formulaG = NULL, family = "gaussian", data,
  startM = NULL, startG = NULL, method = "quasi", selection = "GCV",
  weights = NULL, control = DoubleGamControl(), trace = FALSE,
  scale = 1, conf.type = "bayesian", ...)

`formulaM`	the mean formula - typically of the type y ~ bsp(x1) + bsp(x2). Parametric models or mixtures of parametric and non parametric bases can be specified
`formulaG`	the dispersion formula - as for formulaM, but no response variable to be specified. `formulaG = ~ 1` corresponds to the estimation of the dispersion as a constant (i.e. standard GAM)
`family`	as in glm, can be "gaussian", "poisson" or "Binomial"
`data`	dataset where variables are stored (optional)
`startM`	starting value for the coefficients needed to estimate the mean function
`startG`	starting value for the coefficients needed to estimate the dispersion function
`method`	can be "quasi" (the default) or "pseudo", according to whether deviance or pearson's residuals should be used as response variables when fitting the dispersion function
`selection`	the method used to select the smoothing parameter. can be "GCV" (the default), "AIC" or "none", in which case no selection is done and a smoothing parameter value should be provided in the `bsp()` call.
`weights`	as in glm - to be used with care, since the data get always weigthed by the estimated variance function
`control`	a list to control some behaviours of the estimation procedure, see DoubleGamControl
`trace`	should a trace to follow the convergence be printed? Default is FALSE
`scale`	similar to weigth, to be used if the dispersion function should be kept fixed
`conf.type`	character describing how to compute confidence intervals for the smooth components; can "bayesian" (default) or "naive" as per Wood (2006)

An object of the gamMD class. If both the mean and the dispersion function are estimated the object will contain the following elements: converged, convVec, data, fitG, fitM, iter, relE. fitM contains information on the mean estimation procedure; fitG contains information on the dispersion estimation procedure and has the same elements as fitM.

If only the mean function is estimated all the values of the fitM object are given in gamMD object.

The elements of fitM and fitG are:

`coefficients`	the estimated regression coefficients
`fitted.values`	the fitted values of the model
`desMat`	the full design matrix of the model
`dims`	the dimension of the design matrix associated to each component
`family`	family used for fitting the model - set to `Gamma` for `fitG`
`linear.predictors`	estimated linear predictors for the model
`deviance`	deviance residuals - in `fitM` these are be scaled by the estimated dispersion function, if present
`residuals`	Pearson residuals
`s.resid`	standardised Pearson residuals
`y, yd`	response variable used in, respectively, the mean and diseprsion estimation procedure
`converged`	logic indicator on whether the last inner iteration has converged
`sm.p`	smoothing parameters used in the estimation procedure - either fixed or chosen
`GCV`	Generalised Cross Validation value
`AIC`	Akaike Information criterion value
`yt`	the variable response variable transformed according to the link function and then centered
`df`	overall equivalent sdegrees of freedom for the fit
`vecdf`	a vector given the giving of freedom used by each covariate in the model
`cov.coef`	covariance matrix of the coefficients
`formula`	formula used
`dimsP`	size of the parametric part of the model

Ilaria Prosdocimi (ilapro@ceh.ac.uk)

Gijbels, Prosdocimi and Claeskens (2010), Nonparametric estimation of mean and dispersion functions in extended generalized linear models, Test, 19(3), 560-608, doi:10.1007/s11749-010-0187-1,

Gijbels and Prosdocimi (2011), Smooth estimation of mean and dispersion function in extended generalized additive models with application to Italian induced abortion data, Journal of Applied Statistics, 38(11), 2391-2411, doi:10.1080/02664763.2010.550039

DoubleGamControl, DoubleRobGam, gamMD

ilapros/DoubleRobGam documentation built on Aug. 29, 2021, 12:19 a.m.