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Fitted-model wrappers for the iterative bootstrap (ib)

Description

S4 classes that wrap fitted model objects and attach extra metadata from theiterative bootstrap procedure.

Members:IbBetareg,IbGlm,IbLm,IbLmer,IbGlmer,IbNegbin,IbNls,IbVglm.

Details

Members include wrappers around models frombetareg,stats,lme4,MASS, andVGAM.

These classes are light wrappers: they store the corrected fitted object in@object (seegetObject) and additional information in@ib_extra (seegetExtra).

Value

Objects of the respective S4 classes.

Slots

object

The original fitted model object, corrected byib.

ib_extra

Alist of extra metadata fromib.

See Also

getObject,getExtra,Ib,SummaryIb

Summaries forib wrappers

Description

S4 classes that wrap summary objects corresponding to theIb* classes.

Members:SummaryIbBetareg,SummaryIbGlm,SummaryIbLm,SummaryIbLmer,SummaryIbGlmer,SummaryIbNegbin,SummaryIbNls,SummaryIbVglm.

Slots

summ

Thesummary.* object.

ib_extra

Alist of extra metadata fromib.

See Also

SummaryIb,Ib

Parametric bootstrap

Description

Method for generating parametric bootstrap estimates froma fitted model.

Usage

bootstrap(object, B = 1000, extra_param = FALSE, ...)

Arguments

Details

This method is a simple wrapper around theib methodwhere number of iterations is set to 1.

Value

Amatrix p (size of parameter) times B of bootstrapped estimates.

Author(s)

Samuel Orso

See Also

ib,ibControl

Method for extracting coefficients from an object in class union "Ib"

Description

Method for extracting coefficients from an object in class union "Ib"

Usage

## S4 method for signature 'Ib'coef(object, ...)

Arguments

See Also

Ib,coef

Method for extracting effects from an object in class union "Ib"

Description

Method for extracting effects from an object in class union "Ib"

Usage

## S4 method for signature 'Ib'effects(object, ...)

Arguments

See Also

Ib,effects

Method for extracting fitted values from an object in class union "Ib"

Description

Method for extracting fitted values from an object in class union "Ib"

Usage

## S4 method for signature 'Ib'fitted(object, ...)

Arguments

See Also

Ib,fitted.values

Accessor to the object in class union "Ib"

Description

Method for obtaining estimates from fitted model withinany object of class unionIb.

Usage

getEst(x)## S4 method for signature 'Ib'getEst(x)

Arguments

Details

This methods allow to access extra parameterestimates. Ifextra_param=TRUE, it becomes equivalenttocoef.

Value

an estimate (as ingetExtra).

See Also

Ib

Accessor to an extra part in class union "Ib"

Description

Method for obtaining a extra values generated bythe iterative bootstrap procedure withinany object of class unionIb.

Usage

getExtra(x)## S4 method for signature 'Ib'getExtra(x)

Arguments

Value

alist with the following components:

See Also

Ib

Accessor to the object in class union "Ib"

Description

Method for obtaining the number of iteration from fitted model withinany object of class unionIb.

Usage

getIteration(x)## S4 method for signature 'Ib'getIteration(x)

Arguments

Details

This methods allow to access extra information aboutthe number of iterations.

Value

a number of iterations (as ingetExtra).

See Also

Ib

Accessor to the object in class union "Ib"

Description

Method for obtaining a fitted model withinany object of class unionIb.

Usage

getObject(x)## S4 method for signature 'Ib'getObject(x)

Arguments

See Also

Ib

Bias correction via iterative bootstrap

Description

ib is used to correct the bias of a fitted modelobjectwith the iterative bootstrap procedure.

Usage

ib(object, thetastart = NULL, control = list(...), extra_param = FALSE, ...)## S4 method for signature 'betareg'ib(object, thetastart = NULL, control = list(...), extra_param = FALSE, ...)## S4 method for signature 'glm'ib(object, thetastart = NULL, control = list(...), extra_param = FALSE, ...)## S4 method for signature 'glmerMod'ib(object, thetastart = NULL, control = list(...), extra_param = FALSE, ...)## S4 method for signature 'lm'ib(object, thetastart = NULL, control = list(...), extra_param = FALSE, ...)## S4 method for signature 'lmerMod'ib(object, thetastart = NULL, control = list(...), extra_param = FALSE, ...)## S4 method for signature 'nls'ib(object, thetastart = NULL, control = list(...), extra_param = FALSE, ...)## S4 method for signature 'vglm'ib(object, thetastart = NULL, control = list(...), extra_param = FALSE, ...)

Arguments

Details

The iterative bootstrap procedure is described inKuk (1995) and furtherstudied by Guerrier et al. (2019) andGuerrier et al. (2020). Thekth iteration of thisalgorithm is

\hat{\theta}^{k} = \hat{\theta}^{k-1} + \hat{\pi} -\frac{1}{H}\sum_{h=1}^H\hat{\pi}_h(\hat{\theta}^{k-1})

fork=1,2,\ldots and where the sum is overh=1,\ldots,H.The estimate\hat{\pi} is provided by theobject.The value\hat{\pi}_h(\hat{\theta}) is a parametric bootstrapestimate where the bootstrap sample is generated from\hat{\theta}and a fixedseed (seeibControl).The greater the parameter valueH generally the better bias correctionbut the more computation it requires (seeibControl).Ifthetastart=NULL, the initial value of the procedure is\hat{\theta}^{0}=\hat{\pi}.The number of iterations are controlled bymaxit parameter ofibControl.

By default, the method correctcoefficients only. Forextra parameters, it depends on the model. These extra parameters may havesome constraints (e.g. positivity). Ifconstraint=TRUE (seeibControl), then a transformation from the constraint space to thereal is used for the update.

Forbetareg,extra_param is not availableas by default mean and precision parameters are corrected.Currently the 'identity' link function is not supported for precisionparameters.

Forglm, ifextra_param=TRUE: the shape parameter for theGamma, the variance of the residuals inlm orthe overdispersion parameter of the negative binomial regression inglm.nb,are also corrected. Note that thequasi familiesare not supported for the moment as they have no simulation method(seesimulate). Bias correction for extra parametersof theinverse.gaussian is not yet implemented.

Forglmer, by default, only the fixed effects are corrected.Ifextra_param=TRUE: all the random effects(variances and correlations) are also corrected.

Forlm, ifextra_param=TRUE: the variance of the residuals isalso corrected. Note that using theib is not useful as coefficientsare already unbiased, unless one considers differentdata generating mechanism such as censoring, missing valuesand outliers (seeibControl).

Forlmer, by default, only the fixed effects are corrected.Ifextra_param=TRUE: all the random effects(variances and correlations) and the varianceof the residuals are also corrected.Note that using theib iscertainly not useful with the argumentREML=TRUE inlmer as the bias of variance components isalready addressed, unless one considers differentdata generating mechanism such as censoring, missing valuesand outliers (seeibControl).

Fornls, ifextra_param=TRUE: the variance of the residuals isalso corrected.

Forvglm,extra_param is currently not used.Indeed, the philosophy of a vector generalized linear model is topotentially model all parameters of a distribution with a linear predictor.Hence, what would be considered as an extra parameter inglmfor instance, may already be captured by the defaultcoefficients.However, correcting the bias of acoefficients does not implythat the bias of the parameter of the distribution is corrected(byJensen's inequality),so we may use this feature in a future version of the package.Note that we currently only support distributionswith asimslot (seesimulate.vlm).

Value

A fitted modelobject of classIb.

Author(s)

Samuel Orso

References

Guerrier S, Dupuis-Lozeron E, Ma Y, Victoria-Feser M (2019).“Simulation-Based Bias Correction Methods for Complex Models.”Journal of the American Statistical Association,114(525), 146-157.doi:10.1080/01621459.2017.1380031, https://doi.org/10.1080/01621459.2017.1380031.

Guerrier S, Karemera M, Orso S, Victoria-Feser M, Zhang Y (2020).“A General Approach for Simulation-based Bias Correction in High Dimensional Settings.”https://arxiv.org/pdf/2010.13687.pdf.Version 2: 13 Nov 2020, 2010.13687,https://arxiv.org/pdf/2010.13687.pdf.

Kuk AYC (1995).“Asymptotically Unbiased Estimation in Generalized Linear Models with Random Effects.”Journal of the Royal Statistical Society: Series B (Methodological),57(2), 395-407.doi:10.1111/j.2517-6161.1995.tb02035.x, https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1995.tb02035.x,https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.2517-6161.1995.tb02035.x.

See Also

betareg

glm,glm.nb

glmer

lm

lmer

nls

vglm

Examples

## beta regressionlibrary(betareg)data("GasolineYield", package = "betareg")## currently link.phi = "identity" is not supported## fit_beta <- betareg(yield ~ batch + temp, data = GasolineYield)fit_beta <- betareg(yield ~ batch + temp, link.phi = "log", data = GasolineYield)fit_ib <- ib(fit_beta)# precision parameter can also depend on covariatesfit_beta <- betareg(yield ~ batch + temp | temp, data = GasolineYield)fit_ib <- ib(fit_beta)## poisson regressioncounts <- c(18,17,15,20,10,20,25,13,12)outcome <- gl(3,1,9)treatment <- gl(3,3)pois_fit <- glm(counts ~ outcome + treatment, family = poisson())fit_ib <- ib(pois_fit)summary(fit_ib)## Set H = 1000## Not run: fit_ib <- ib(pois_fit, control=list(H=1000))summary(fit_ib)## End(Not run)## gamma regressionclotting <- data.frame(  u = c(5,10,15,20,30,40,60,80,100),  lot1 = c(118,58,42,35,27,25,21,19,18),  lot2 = c(69,35,26,21,18,16,13,12,12))fit_gamma <- glm(lot2 ~ log(u), data = clotting, family = Gamma(link = "inverse"))fit_ib <- ib(fit_gamma)## summary(fit_ib)## correct for shape parameter and show iterations## Not run: fit_ib <- ib(fit_gamma, control=list(verbose=TRUE), extra_param = TRUE)summary(fit_ib)## End(Not run)## negative binomial regressionlibrary(MASS)fit_nb <- glm.nb(Days ~ Sex/(Age + Eth*Lrn), data = quine)fit_ib <- ib(fit_nb)## summary(fit_ib)## correct for overdispersion with H=100## Not run: fit_ib <- ib(fit_nb, control=list(H=100), extra_param = TRUE)summary(fit_ib)## End(Not run)## generalized linear mixed-effects regression## Not run:   library(lme4)  fit_glmm <- glmer(incidence / size ~ period + (1 | herd), weights = size,                    family = binomial, data = cbpp)  fit_ib <- ib(fit_glmm)  summary(fit_ib)  ## correct for variances and correlation  fit_ib <- ib(fit_glmm, extra_param = TRUE)  summary(fit_ib)## End(Not run)## linear regressionfit_lm <- lm(disp ~ cyl + hp + wt, data = mtcars)fit_ib <- ib(fit_lm)summary(fit_ib)## correct for variance of residualsfit_ib <- ib(fit_lm, extra_param = TRUE)summary(fit_ib)## linear mixed-effects regression## Not run: library(lme4)fit_lmm <- lmer(Reaction ~ Days + (Days | Subject), data = sleepstudy, REML = FALSE)fit_ib <- ib(fit_lmm)summary(fit_ib)## correct for variances and correlationfit_ib <- ib(fit_lmm, extra_param = TRUE)summary(fit_ib)## End(Not run)## nonlinear regressionDNase1 <- subset(DNase, Run == 1)fit_nls <- nls(density ~ SSlogis(log(conc), Asym, xmid, scal), data = DNase1)fit_ib <- ib(fit_nls)summary(fit_ib)## student regressionlibrary(VGAM)tdata <- data.frame(x = runif(nn <- 1000))tdata <- transform(tdata,                   y = rt(nn, df = exp(exp(0.5 - x))))fit_vglm <- vglm(y ~ x, studentt3, data = tdata)fit_ib <- ib(fit_vglm)summary(fit_ib)

ib method fornegbin objectfromglm.nb function ofMASSpackage.

Description

ib method fornegbin objectfromglm.nb function ofMASSpackage.

Usage

## S4 method for signature 'negbin'ib(object, thetastart = NULL, control = list(...), extra_param = FALSE, ...)

Arguments

Auxiliary for controlling IB

Description

Auxiliary function forib bias correction.

Usage

ibControl(  tol = 1e-05,  maxit = 25,  verbose = FALSE,  seed = 123L,  H = 1L,  constraint = TRUE,  early_stop = FALSE,  cens = FALSE,  right = NULL,  left = NULL,  mis = FALSE,  prop = NULL,  out = FALSE,  eps = NULL,  G = NULL,  func = function(x) rowMeans(x, na.rm = T),  sim = NULL)

Arguments

Details

sim allows the user to provide its own function for generatingresponses. Currently it is only supported for generalized linear models withthe prototype 'fun(object, control, extra_param, ...)' (seeib).

Value

a list with components named as the arguments.

See Also

ib, the iterative procedure for bias correction.

Method for plotting an object in class union "Ib"

Description

Method for plotting an object in class union "Ib"

Usage

## S4 method for signature 'Ib,ANY'plot(x, y = NULL, ...)

Arguments

See Also

Ib,plot.lm

Method for making predictions from an object in class union "Ib"

Description

Method for making predictions from an object in class union "Ib"

Usage

## S4 method for signature 'Ib'predict(object, ...)

Arguments

See Also

Ib,predict

Method for extracting residuals from an object in class union "Ib"

Description

Method for extracting residuals from an object in class union "Ib"

Usage

## S4 method for signature 'Ib'residuals(object, ...)

Arguments

See Also

Ib,residuals

Method for printing object in class union "Ib"

Description

Method for printing object in class union "Ib"

Usage

## S4 method for signature 'Ib'show(object)

Arguments

See Also

Ib

Summarizing a fitted model corrected by the ib procedure

Description

Method for printing asummary ofclass unionSummaryIb.

Usage

## S4 method for signature 'SummaryIb'show(object)

Arguments

See Also

SummaryIb

Generic for simulating from the object

Description

Method for simulating responses from an object.

Usage

simulation(object, control = list(...), ...)## S4 method for signature 'Ib'simulation(object, control = list(...), ...)

Arguments

Value

simulated responses.

Examples

## bootstrap poisson regressioncounts <- c(18,17,15,20,10,20,25,13,12)outcome <- gl(3,1,9)treatment <- gl(3,3)pois_fit <- glm(counts ~ outcome + treatment, family = poisson())## make 100 paramtric bootstrap replicatesboot_dist <- simulate(pois_fit, nsim = 100)

Simulation for a beta regression

Description

simulation method for classIbBetareg, seeIb

Usage

## S4 method for signature 'betareg'simulation(object, control = list(...), extra = NULL, ...)

Arguments

Simulation for a Generalized Linear Model regression

Description

simulation method for classIbGlm, seeIb

Usage

## S4 method for signature 'glm'simulation(object, control = list(...), extra = NULL, ...)

Arguments

Simulation for linear mixed model regression

Description

simulation method for classIbGlmer, seeIb

Usage

## S4 method for signature 'glmerMod'simulation(object, control = list(...), ...)

Arguments

Simulation for linear regression

Description

simulation method for classIbLm, seeIb

Usage

## S4 method for signature 'lm'simulation(object, control = list(...), std = NULL, ...)

Arguments

Simulation for linear mixed model regression

Description

simulation method for classIb, seeIb

Usage

## S4 method for signature 'lmerMod'simulation(object, control = list(...), ...)

Arguments

Simulation for a negative binomial regression

Description

simulation method for classIbNegbin, seeIb

Usage

## S4 method for signature 'negbin'simulation(object, control = list(...), extra = NULL, ...)

Arguments

Simulation for nonlinear regression

Description

simulation method for classIbNls, seeIb

Usage

## S4 method for signature 'nls'simulation(object, control = list(...), std = NULL, ...)

Arguments

Simulation for vector generalized linear model regression

Description

simulation method for classIbVglm, seeIb

Usage

## S4 method for signature 'vglm'simulation(object, control = list(...), extra_param = NULL, ...)

Arguments

Summarizing a beta regression fit corrected bythe iterative bootstrap

Description

summary method for classIbBetareg

Usage

## S4 method for signature 'IbBetareg'summary(object, ...)

Arguments

See Also

summary.betareg

Summarizing a Generalized Linear Model regression fit corrected bythe iterative bootstrap

Description

summary method for classIbGlm

Usage

## S4 method for signature 'IbGlm'summary(object, ...)

Arguments

See Also

summary.glm

Summarizing a generalized linear mixed model regression fit corrected bythe iterative bootstrap

Description

summary method for classIbGlmer

Usage

## S4 method for signature 'IbGlmer'summary(object, ...)

Arguments

Summarizing a linear regression fit corrected bythe iterative bootstrap

Description

summary method for classIbLm

Usage

## S4 method for signature 'IbLm'summary(object, ...)

Arguments

See Also

summary.lm

Summarizing a linear mixed model regression fit corrected bythe iterative bootstrap

Description

summary method for classIbLmer

Usage

## S4 method for signature 'IbLmer'summary(object, ...)

Arguments

Summarizing a negative binomial regression fits corrected bythe iterative bootstrap

Description

summary method for classIbNegbin

Usage

## S4 method for signature 'IbNegbin'summary(object, ...)

Arguments

See Also

summary.negbin

Summarizing a nonlinear regression fit corrected bythe iterative bootstrap

Description

summary method for classIbNls

Usage

## S4 method for signature 'IbNls'summary(object, ...)

Arguments

Summarizing a vector generalized linear model regressionfit corrected by the iterative bootstrap

Description

summary method for classIbVglm

Usage

## S4 method for signature 'IbVglm'summary(object, ...)

Arguments

Method for calculating covariance matrix from an object in class union "Ib"

Description

Method for calculating covariance matrix from an object in class union "Ib"

Usage

## S4 method for signature 'Ib'vcov(object, ...)

Arguments

See Also

Ib,vcov