SemiParBIVProbitObject: Fitted SemiParBIVProbit object
Description
A fitted semiparametric bivariate probit object returned by function SemiParBIVProbit and of class.Value
- fitList of values and diagnostics extracted from the output of the algorithm. For instance,
fit$gradient and fit$S.h return
the gradient vector and overall penalty matrix scaled by its smoothing parameters, for the bivariate probit model. See the
documentation of trust for details on the diagnostics provided. - gam1Univariate fit for equation 1. See the documentation of
mgcv for full details. - gam2Univariate fit for equation 2.
- gam2.1Univariate fit for equation 2, estimated using an adaptation of the Heckman sample selection correction procedure when
selection = TRUE. - coefficientsThe coefficients of the fitted semiparametric sample selection model. They are given in the following
order: parametric and regression spline (if present)
coefficients for the first equation, parametric and regression spline
coefficients for the second equation, and association coefficient.
- weightsPrior weights used during model fitting.
- spEstimated smoothing parameters of the smooth components for the fitted bivariate probit model.
- iter.spNumber of iterations performed for the smoothing parameter estimation step.
- iter.ifNumber of iterations performed in the initial step of the algorithm.
- iter.innerNumber of iterations performed inside smoothing parameter estimation step.
- rhoEstimated correlation coefficient between the two equations, when a bivariate normal model is employed.
- thetaEstimated copula parameter linking the two equations.
- deltaThis is an additional estimated copula parameter linking the two equations and is provided when an archimedean copula with two parameters
is employed.
- KeTEstimated Kendall's tau coefficient between the two equations.
- nSample size.
- n.selNumber of selected observations in the sample selection case.
- X1, X2Design matrices associated with the first and second linear predictors.
- X1.d2, X2.d2Number of columns of the design matrices for equations 1 and 2.
- l.sp1, l.sp2Number of smooth components in equations 1 and 2.
- HePenalized hessian. This is the same as
HeSh for unpenalized models. - HeShUnpenalized hessian.
- VbInverse of
He. This corresponds to the Bayesian variance-covariance matrix
used for `confidence' interval calculations. - FThis is given by
Vb*HeSh. - fpIf
TRUE, then a fully parametric model was fitted. - aut.spIf
FALSE, then a fully parametric model with regression splines was fitted. - t.edfTotal degrees of freedom of the estimated bivariate model. It is calculated as
sum(diag(F)). - edf1, edf2Degrees of freedom for the two equations of the estimated bivariate model. It is calculated when splines are used.
- bs.mgfitList of values and diagnostics extracted from
magic. - conv.spIf
TRUE then the smoothing parameter selection algorithm stopped before reaching the maximum number of iterations allowed. - wor.cWorking model quantities given by the square root of
the weight matrix times the pseudo-data vector and design matrix,
rW.Z and rW.X. - p11, p10, p01, p00Distribution function of a bivariate normal with zero means, unit variances and correlation
rho evaluated at (y1 = 1, y2 = 1), (y1 = 1, y2 = 0), (y1 = 0, y2 = 1) and (y1 = 0, y2 = 0). - p0Distribution function of a standardised univariate normal evaluated at y1 = 0. This is only provided when
selection = TRUE. - eta1, eta2Estimated linear predictors for the two equations.
- y1, y2Responses of the two equations.
- selThis is used for internal calculations.
- BivD, nuThese are used for internal calculations.
- PL, eqPL, valPL, fitPL, spPLThese are used for internal calculations.
- xi1, xi2Shape parameters of the link functions of the two equations if an asymmetric link approach is used.
- logLikValue of the (unpenalized) log-likelihood evaluated at the (penalized or unpenalized) parameter
estimates.
- nCCopula identifier. This is used for internal calculations.
- H.nThis is used for internal calculations.
- pPen1, pPen2This is used for internal calculations. List specifying any penalties to be applied to the parametric model terms of the model equations.
- goodIndicator variable indicating the observations actually used in model fitting.
- y1.y2, y1.cy2, cy1.y2, cy1.cy2, cy1These are used for internal calculations.
- qu.mag, gp1, gp2These are used for internal calculations.
- X2sFull design matrix of second equation in sample selection case.