SemiParBIVProbitObject: Fitted SemiParBIVProbit object
Description
A fitted semiparametric bivariate probit object returned by function SemiParBIVProbit and of class "SemiParBIVProbit".Value
- fitList of values and diagnostics extracted from the output of the algorithm. For instance,
fit$gradient, fit$Fisher and fit$S.h return
the gradient vector, Fisher information (when used) and overall penalty matrix scaled
by its smoothing parameters, for the fitted 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
Method = "BSS". - gam3Univariate fit for equation 3. This is available when the association parameter is modelled as functions of covariates.
- coefficientsThe coefficients of the fitted 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.
- 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 within the 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.
- nSample size.
- n.selNumber of selected observations in the sample selection model case.
- X1, X2Design matrices associated with the first and second linear predictors.
- X1.d2, X2.d2Number of columns of
X1 and X2. - l.sp1, l.sp2Number of smooth components in equations 1 and 2.
- HePenalized -hessian/Fisher. This is the same as
HeSh for unpenalized models. - HeShUnpenalized -hessian/Fisher.
- VbInverse of
He. This corresponds to the Bayesian variance-covariance matrix
used for confidence/credible interval calculations. - FThis is given by
Vb*HeSh. - t.edfTotal degrees of freedom of the estimated bivariate model. It is calculated as
sum(diag(F)). - edf1, edf2, edf3Degrees of freedom for the two equations of the fitted bivariate model (and for the third
equation as well if the dependence parameter is modelled as function of covariates). They
are calculated when splines are used.
- bs.mgfitList of values and diagnostics extracted from
magic in mgcv. - conv.spIf
TRUE then the smoothing parameter selection algorithm stopped before reaching the maximum number of iterations allowed. - wor.cWorking model quantities.
- p11, p10, p01, p00Model probabilities evaluated at (y_1 = 1, y_2 = 1), (y_1 = 1, y_2 = 0), (y_1 = 0, y_2 = 1) and (y_1 = 0, y_2 = 0).
- p0Distribution function of a standardised univariate normal evaluated at y_1 = 0. This is only provided when
Method = "BSS". - eta1, eta2, eta3Estimated linear predictors for the two equations (as well as the third equation if present).
- y1, y2Responses of the two equations.
- xi1, xi2Estimated shape 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.
- goodIndicator variable indicating the observations actually used in model fitting.
- respvecList containing response vectors.
- X2sFull design matrix of outcome equation in sample selection case.
- OR, GMOdds ratio and Gamma measure. See
summary.SemiParBIVProbit for details.