ordgam.object: Object resulting from the fit of an additive proportional...
In ordgam: Additive Model for Ordinal Data using Laplace P-Splines
ordgam.object R Documentation
Object resulting from the fit of an additive proportional odds model using 'ordgam'
Description
An object returned by the ordgam function: this is a list
with various components related to the fit of such a model.
Value
An ordgam object is a list with following elements:
val : Value of the log-posterior at convergence.
val.start : Value of the log-posterior at the start of the Newton-Raphson (N-R) algorithm.
theta : (Penalized) MLE or MAP of the regression coefficients.
grad : Gradient of the log-posterior at theta.
Hessian : Hessian of the log-posterior at theta.
iter : Number of iterations of the N-R algorithm.
llik : Multinomial log likelihood.
Hessian0 : Hessian of the (non-penalized) log-likelihood at theta.
Sigma.theta : Variance-covariance of 'theta'.
ED.full : Effective degrees of freedom associated to each regression parameter, penalized parameters included.
se.theta : Standard errors of the regression coefficents.
theta.mat : Matrix containing the point estimate, standard error, credible interval, Z-score and P-value for theta.
nc : Number of categories for the ordinal response.
nalpha : Number of intercepts in the proportional odds model (=nc-1) .
nbeta : Number of regression parameters (intercepts excluded).
nfixed : Number of non-penalized regression parameters.
ci.level : Nominal coverage of the credible intervals (Default: .95).
n : Sample size.
call : Function call.
descending : Logical indicating if the odds of the response taking a value in the upper scale should be preferred over values in the lower scale.
use.prior : Logical indicating if a prior (such as a penalty) is assumed for the regression parameters.
lpost : Value of the log-posterior at convergence.
levidence : Log of the marginal likelihood (also named 'evidence').
AIC : Aikake information criterion: AIC = -2 logLik + 2 x edf where edf stands for the effective degrees of freedom.
BIC : Schwarz information criterion: BIC = -2 logLik + n x log(edf) where edf stands for the effective degrees of freedom.
y : Vector containing the values of the ordinal response.
regr : List created by the internal function DesignFormula and containing diverse objects associated to the model specification, including the part of the design matrix 'X' associated to regressors and its extended version 'Xcal' with B-spline bases for additive term.
ED.Chi2 : Matrix containing the Effective Degrees of Freedom associated to the additive terms with their respective significance Chi2 test and P-value.
ED.Tr : Matrix containing the Effective Degrees of Freedom associated to the additive terrms with their respective significance <Tr> test (described by S. Wood, Biometrika 2013) and P-value.
lpost.fun : Function with arguments (theta,lambda,gradient=TRUE,Hessian=TRUE) computing the log-posterior for given regression (and possibly spline) parameters theta and vector of penalty parameters lambda associated to the additive terms. Gradient and Hessian are also computed if requested.
lambda0 : Initial values for the vector of penalty parameters. Its length corresponds to the number of additive terms.
lambda : (Selected) vector of penalty parameters. Its length corresponds to the number of additive terms.
select.lambda : Logical indicating if lambda should be selected by maximizing the marginal likelihood or its marginal posterior.
lambda.family : Chosen prior for lambda: possible choices are "none", "dgamma" (i.e. dgamma(1,1e-4)), "BetaPrime" (BetaPrime(.5,.5)) or "myprior" (with log of the prior density function in myprior). When "none" is selected, the marginal likelihood is directly maximized.
lprior.lambda : Log of the prior density for the penalty parameters lambda when select.lambda is TRUE.
loglambda.loss : The function of log(lambda) that is minimized to select lambda. It is minus the log marginal likelihood (when lambda.family is "none") or minus the log of the marginal posterior for lambda otherwise.
nu.lpost : Function giving the log of the marginal posterior density of nu=log(lambda).
nu.hat : The mode of the marginal posterior density nu.lpost for nu=log(lambda).
V.nu : Variance of the marginal posterior for nu=log(lambda).
se.nu : Standard error of nu=log(lambda), i.e. the square-root of the diagonal elements of V.nu.
nu.dp : List containing the parameters of the skew-t approximation to the marginal posterior of nu[j]=loglambda[j] associated to each of the J additive terms.
formula : Formula used during the model specification.
elapsed.time : Elapsed time.
Author(s)
Philippe Lambert p.lambert@uliege.be
References
Lambert, P. and Gressani, 0. (2023) Penalty parameter selection and asymmetry corrections
to Laplace approximations in Bayesian P-splines models. Statistical Modelling. <doi:10.1177/1471082X231181173>. Preprint: <arXiv:2210.01668>.
See Also
ordgam, print.ordregr, plot.ordgam
ordgam documentation built on Sept. 14, 2023, 5:07 p.m.
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| ordgam.object | R Documentation |
Object resulting from the fit of an additive proportional odds model using 'ordgam'
Description
An object returned by the ordgam function: this is a list
with various components related to the fit of such a model.
Value
An ordgam object is a list with following elements:
val: Value of the log-posterior at convergence.val.start: Value of the log-posterior at the start of the Newton-Raphson (N-R) algorithm.theta: (Penalized) MLE or MAP of the regression coefficients.grad: Gradient of the log-posterior attheta.Hessian: Hessian of the log-posterior attheta.iter: Number of iterations of the N-R algorithm.llik: Multinomial log likelihood.Hessian0: Hessian of the (non-penalized) log-likelihood attheta.Sigma.theta: Variance-covariance of 'theta'.ED.full: Effective degrees of freedom associated to each regression parameter, penalized parameters included.se.theta: Standard errors of the regression coefficents.theta.mat: Matrix containing the point estimate, standard error, credible interval, Z-score and P-value fortheta.nc: Number of categories for the ordinal response.nalpha: Number of intercepts in the proportional odds model (=nc-1) .nbeta: Number of regression parameters (intercepts excluded).nfixed: Number of non-penalized regression parameters.ci.level: Nominal coverage of the credible intervals (Default: .95).n: Sample size.call: Function call.descending: Logical indicating if the odds of the response taking a value in the upper scale should be preferred over values in the lower scale.use.prior: Logical indicating if a prior (such as a penalty) is assumed for the regression parameters.lpost: Value of the log-posterior at convergence.levidence: Log of the marginal likelihood (also named 'evidence').AIC: Aikake information criterion: AIC = -2 logLik + 2 x edf where edf stands for the effective degrees of freedom.BIC: Schwarz information criterion: BIC = -2 logLik + n x log(edf) where edf stands for the effective degrees of freedom.y: Vector containing the values of the ordinal response.regr: List created by the internal functionDesignFormulaand containing diverse objects associated to the model specification, including the part of the design matrix 'X' associated to regressors and its extended version 'Xcal' with B-spline bases for additive term.ED.Chi2: Matrix containing the Effective Degrees of Freedom associated to the additive terms with their respective significance Chi2 test and P-value.ED.Tr: Matrix containing the Effective Degrees of Freedom associated to the additive terrms with their respective significance <Tr> test (described by S. Wood, Biometrika 2013) and P-value.lpost.fun: Function with arguments (theta,lambda,gradient=TRUE,Hessian=TRUE) computing the log-posterior for given regression (and possibly spline) parametersthetaand vector of penalty parameterslambdaassociated to the additive terms. Gradient and Hessian are also computed if requested.lambda0: Initial values for the vector of penalty parameters. Its length corresponds to the number of additive terms.lambda: (Selected) vector of penalty parameters. Its length corresponds to the number of additive terms.select.lambda: Logical indicating iflambdashould be selected by maximizing the marginal likelihood or its marginal posterior.lambda.family: Chosen prior forlambda: possible choices are "none", "dgamma" (i.e. dgamma(1,1e-4)), "BetaPrime" (BetaPrime(.5,.5)) or "myprior" (with log of the prior density function inmyprior). When "none" is selected, the marginal likelihood is directly maximized.lprior.lambda: Log of the prior density for the penalty parameterslambdawhenselect.lambdais TRUE.loglambda.loss: The function oflog(lambda)that is minimized to selectlambda. It is minus the log marginal likelihood (whenlambda.familyis "none") or minus the log of the marginal posterior forlambdaotherwise.nu.lpost: Function giving the log of the marginal posterior density ofnu=log(lambda).nu.hat: The mode of the marginal posterior densitynu.lpostfornu=log(lambda).V.nu: Variance of the marginal posterior fornu=log(lambda).se.nu: Standard error ofnu=log(lambda), i.e. the square-root of the diagonal elements ofV.nu.nu.dp: List containing the parameters of the skew-t approximation to the marginal posterior ofnu[j]=loglambda[j]associated to each of theJadditive terms.formula: Formula used during the model specification.elapsed.time: Elapsed time.
Author(s)
Philippe Lambert p.lambert@uliege.be
References
Lambert, P. and Gressani, 0. (2023) Penalty parameter selection and asymmetry corrections to Laplace approximations in Bayesian P-splines models. Statistical Modelling. <doi:10.1177/1471082X231181173>. Preprint: <arXiv:2210.01668>.
See Also
ordgam, print.ordregr, plot.ordgam
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