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. If
RE=TRUE and RE.type="N", then
the paramaters of the bivariate normal random effect distribution are also given. - 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.
- sigma1,rho.u,sigma2If
RE=TRUE and RE.type="N" then these are the paramaters of the bivariate normal random effect distribution. - 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.
- KNumber of bivariate mass points.
- massesProbabilities associated with the
K biavariate mass points in a random effect model. - RE,RE.type,BivD,nu,PL,eqPLThese are used for internal calculations.
- xi1,xi2Power or shape parameters of the link functions of the two equations if a power link approach is used.
- logLikValue of the (unpenalized) log-likelihood evaluated at the (penalized or unpenalized) parameter
estimates.
- eb.u1,eb.u2Estimated random effects for each identifier.
- Eb.u1,Eb.u2Estimated random effects for each observation.
- idIndividual identifier.
- uidfNumber of observations within each group.
- T.svThis is used for internal calculations.
- eta1S,eta2S,ass.pSSimulated
eta1, eta2 and transformed rho or theta. These are useful for calculating standard errors of predictions in the sample selection case. - deltaSSimulated transformed
delta (for two-parameter copulas). This is useful for calculating standard errors of predictions in the sample selection case. - 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.