DALSM.object: Object resulting from the fit of a double additive...
In DALSM: Nonparametric Double Additive Location-Scale Model (DALSM)
DALSM.object R Documentation
Object resulting from the fit of a double additive location-scale model (DALSM).
Description
An object returned by the DALSM function: this is a list
with various components related to the fit of a double additive location-scale model using Laplace P-splines.
Value
A DALSM object has the following elements:
Essential part:
converged : logical convergence indicator.
derr : estimated standardized error distribution returned as a densLPS.object.
psi1 : estimated regression parameters for location (fixed effects, B-spline coefs for the J1 additive terms).
psi2 : estimated regression parameters for dispersion (fixed effects, B-spline coefs for the J2 additive terms).
fixed.loc : matrix with the estimated fixed effects (est,se,ci.low,ci.up) in the location sub-model.
fixed.disp : matrix with the estimated fixed effects (est,se,ci.low,ci.up) in the dispersion sub-model.
mu : n-vector with the fitted conditional mean.
sd : n-vector with the fitted conditional standard deviation.
Additional elements:
data : the original data frame used when calling the DALSM function.
phi : estimated B-spline coefs for the log-hazard of the error distribution.
K.error : number of B-splines used to approximate the log of the error hazard.
rmin, rmax : minimum and maximum values for the support of the standardized error distribution.
knots.error : equidistant knots on (rmin,rmax) used to specify the B-spline basis for the log of the error hazard.
bread.psi1, Sand.psi1, Cov.psi1: estimated Variance-Covariance matrix for \psi_1.
U.psi1 : gradient for \psi_1.
bread.psi2, Sand.psi2, Cov.psi2: estimated Variance-Covariance matrix for \psi_2.
U.psi2 : gradient for \psi_2.
U.psi : gradient for \psi=(\psi_1,\psi_2).
Cov.psi : variance-covariance for \psi=(\psi_1,\psi_2).
regr1 : object generated by DesignFormula for the specified submodel for location.
regr2 : object generated by DesignFormula for the specified submodel for dispersion.
res : n-vector or nx2 matrix (if IC data) with the standardized residuals for the fitted model.
expctd.res : n-vector with observed standardized residual for a non RC unit, or their expected value if right-censored.
REML : logical indicating whether REML estimation was performed.
n : the sample size.
n.uncensored : number of non-censored response data.
event : n-vector of event indicators (1: non right-censored ; 0: right censoring).
is.IC : n-vector with interval censoring indicators.
n.IC : number of interval-censored response data.
n.RC : number of right-censored response data.
perc.obs : percentage of exactly observed response data.
perc.IC : percentage of interval-censored response data.
perc.RC : percentage of right-censored response data.
cred.int : nominal level for the reported credible intervals.
alpha : user-specified \alpha with Bayesian (1-\alpha) credible intervals reported.
sandwich : logical indicating if variance-covariance and standard errors computed using sandwich estimator in the NP case.
diag.only : logical indicating if the correction to the Hessian under REML only concerns diagonal elements.
iter : number of iterations.
elapsed.time : time required by the model fitting procedure.
If there are additive terms in the location submodel:
K1 : number of B-splines used to describe an additive term in the location submodel.
xi1 : matrix with the selected log penalty parameters for the J1 additive terms in the location submodel (point estimate, se, ci.low, ci.up.
U.xi1 : gradient for the log of the penalty parameters for the J1 additive terms in the location submodel.
U.lambda1 : gradient for the penalty parameters for the J1 additive terms in the location submodel.
Cov.xi1 : estimated Variance-Covariance matrix for the parameters involved in the J1 additive terms in the location submodel.
lambda1.min : minimal value for the penalty parameters in the additive submodel for location.
lambda1 : matrix with the selected penalty parameters for the J1 additive terms in the location submodel (point estimate, se, ci.low, ci.up).
ED1 : matrix with the effective dimensions for each of the J1 additive terms in the location submodel (point estimate,ci.low,ci.up).
If there are additive terms in the dispersion submodel:
K2 : number of B-splines used to describe an additive term in the dispersion submodel.
xi2 : matrix with the selected log penalty parameters for the J2 additive terms in the dispersion submodel (point estimate, se, ci.low, ci.up).
U.xi2 : gradient for the log of the penalty parameters for the J2 additive terms in the dispersion submodel.
U.lambda2 : gradient for the penalty parameters for the J2 additive terms in the dispersion submodel.
Cov.xi2 : estimated Variance-Covariance matrix for the parameters involved in the J2 additive terms in the dispersion submodel.
lambda2.min : minimal value for the penalty parameters in the additive submodel for dispersion.
lambda2 : matrix with the selected penalty parameters for the J2 additive terms in the dispersion submodel (point estimate, se, ci.low, ci.up).
ED2 : matrix with the effective dimensions for each of the J2 additive terms in the dispersion submodel (point estimate,ci.low,ci.up).
Author(s)
Philippe Lambert p.lambert@uliege.be
References
Lambert, P. (2021). Fast Bayesian inference using Laplace approximations
in nonparametric double additive location-scale models with right- and
interval-censored data.
Computational Statistics and Data Analysis, 161: 107250.
<doi:10.1016/j.csda.2021.107250>
See Also
DALSM, print.DALSM, plot.DALSM, densityLPS, densLPS.object
DALSM documentation built on Oct. 2, 2023, 5:09 p.m.
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| DALSM.object | R Documentation |
Object resulting from the fit of a double additive location-scale model (DALSM).
Description
An object returned by the DALSM function: this is a list
with various components related to the fit of a double additive location-scale model using Laplace P-splines.
Value
A DALSM object has the following elements:
Essential part:
converged: logical convergence indicator.derr: estimated standardized error distribution returned as a densLPS.object.psi1: estimated regression parameters for location (fixed effects, B-spline coefs for the J1 additive terms).psi2: estimated regression parameters for dispersion (fixed effects, B-spline coefs for the J2 additive terms).fixed.loc: matrix with the estimated fixed effects (est,se,ci.low,ci.up) in the location sub-model.fixed.disp: matrix with the estimated fixed effects (est,se,ci.low,ci.up) in the dispersion sub-model.mu: n-vector with the fitted conditional mean.sd: n-vector with the fitted conditional standard deviation.
Additional elements:
data: the original data frame used when calling theDALSMfunction.phi: estimated B-spline coefs for the log-hazard of the error distribution.K.error: number of B-splines used to approximate the log of the error hazard.rmin, rmax: minimum and maximum values for the support of the standardized error distribution.knots.error: equidistant knots on (rmin,rmax) used to specify the B-spline basis for the log of the error hazard.bread.psi1, Sand.psi1, Cov.psi1: estimated Variance-Covariance matrix for\psi_1.U.psi1: gradient for\psi_1.bread.psi2, Sand.psi2, Cov.psi2: estimated Variance-Covariance matrix for\psi_2.U.psi2: gradient for\psi_2.U.psi: gradient for\psi=(\psi_1,\psi_2).Cov.psi: variance-covariance for\psi=(\psi_1,\psi_2).regr1: object generated byDesignFormulafor the specified submodel for location.regr2: object generated byDesignFormulafor the specified submodel for dispersion.res: n-vector or nx2 matrix (if IC data) with the standardized residuals for the fitted model.expctd.res: n-vector with observed standardized residual for a non RC unit, or their expected value if right-censored.REML: logical indicating whether REML estimation was performed.n: the sample size.n.uncensored: number of non-censored response data.event: n-vector of event indicators (1: non right-censored ; 0: right censoring).is.IC: n-vector with interval censoring indicators.n.IC: number of interval-censored response data.n.RC: number of right-censored response data.perc.obs: percentage of exactly observed response data.perc.IC: percentage of interval-censored response data.perc.RC: percentage of right-censored response data.cred.int: nominal level for the reported credible intervals.alpha: user-specified\alphawith Bayesian(1-\alpha)credible intervals reported.sandwich: logical indicating if variance-covariance and standard errors computed using sandwich estimator in the NP case.diag.only: logical indicating if the correction to the Hessian under REML only concerns diagonal elements.iter: number of iterations.elapsed.time: time required by the model fitting procedure.
If there are additive terms in the location submodel:
K1: number of B-splines used to describe an additive term in the location submodel.xi1: matrix with the selected log penalty parameters for the J1 additive terms in the location submodel (point estimate, se, ci.low, ci.up.U.xi1: gradient for the log of the penalty parameters for the J1 additive terms in the location submodel.U.lambda1: gradient for the penalty parameters for the J1 additive terms in the location submodel.Cov.xi1: estimated Variance-Covariance matrix for the parameters involved in the J1 additive terms in the location submodel.lambda1.min: minimal value for the penalty parameters in the additive submodel for location.lambda1: matrix with the selected penalty parameters for the J1 additive terms in the location submodel (point estimate, se, ci.low, ci.up).ED1: matrix with the effective dimensions for each of the J1 additive terms in the location submodel (point estimate,ci.low,ci.up).
If there are additive terms in the dispersion submodel:
K2: number of B-splines used to describe an additive term in the dispersion submodel.xi2: matrix with the selected log penalty parameters for the J2 additive terms in the dispersion submodel (point estimate, se, ci.low, ci.up).U.xi2: gradient for the log of the penalty parameters for the J2 additive terms in the dispersion submodel.U.lambda2: gradient for the penalty parameters for the J2 additive terms in the dispersion submodel.Cov.xi2: estimated Variance-Covariance matrix for the parameters involved in the J2 additive terms in the dispersion submodel.lambda2.min: minimal value for the penalty parameters in the additive submodel for dispersion.lambda2: matrix with the selected penalty parameters for the J2 additive terms in the dispersion submodel (point estimate, se, ci.low, ci.up).ED2: matrix with the effective dimensions for each of the J2 additive terms in the dispersion submodel (point estimate,ci.low,ci.up).
Author(s)
Philippe Lambert p.lambert@uliege.be
References
Lambert, P. (2021). Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data. Computational Statistics and Data Analysis, 161: 107250. <doi:10.1016/j.csda.2021.107250>
See Also
DALSM, print.DALSM, plot.DALSM, densityLPS, densLPS.object
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