predict.BiProbitPartialb: predict method for class 'BiProbitPartialb'
In BiProbitPartial: Bivariate Probit with Partial Observability

Description Usage Arguments Value Examples

Note this produces a Bayesian posterior predictive distribution. This accounts for estimation uncertainty. If you desire a simple prediction that does not account for estimation uncertainty then the frequentist philosophy should be used. If nchains is greater than 1 then the chains are combined.

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## S3 method for class 'BiProbitPartialb'
predict(object, newdata, k1, k2,
  mRule = c(0.5, 0.5), jRule = NULL, ...)

`object`	a object of class `BiProbitPartialb`
`newdata`	a matrix of column dimension k1 + k2 where the first k1 columns correspond to the predictors of the first equations and the second k2 columns correspond to predictors of the second equation. If intercepts were used they need to be explicitly input.
`k1`	a numeric declaring the number of covariates (including intercept) in the first equation
`k2`	a numeric declaring the number of covariates (including intercept) in the second equation
`mRule`	a vector of length 1 or 2. This is the marginal decision rule for classifying the outcomes for stages 1 and 2. Stage 1 is classified as 1 if the probability of stage 1 being 1 is greater than or equal to `mRule[1]`. Likewise for stage 2. If length of `mRule` is 1 then that value is recycled. The values of `mRule` must be between 0 and 1. The default value is `mRule = c(0.5,0.5)`.
`jRule`	an optional numerical value between 0 and 1. If specified then the observable outcome (both stages being 1) is 1 if the joint probability of both stages being 1 is greater than jRule. If jRule is unspecified or set to `NULL` then the observable outcome is the product of the marginal outcomes. The default value is `jRule = NULL`. Note, if `jRule` is specified then the observable outcome might not equal the product of stages 1 and 2.
`...`	unused

method predict.bBiProbitPArtial returns a data.frame with columns

linPredict1: Predicted mean of the first stage latent outcome. This is tyically not interesting for a Bayesian analysis.
linPredict2: Predicted mean of the second stage latent outcome. This is tyically not interesting for a Bayesian analysis.
p1.: Probability the outcome of the first stage is 1
p.1: Probability the outcome of the second stage is 1
p00: Probability the outcome of both stages is 0
p01: Probability the outcome of the first stage is 0 and the second stage is 1
p10: Probability the outcome of stage 1 is 1 and stage 2 is 0
p11: Probability the outcome of both stages are 1
yHat1: Classification of the outcome for stage 1. This value is 1 if p1 >= mRule[1] and 0 else
yHat2: Classification of the outcome for stage 2. This value is 1 if p2 >= mRule[2] and 0 else
ZHat: Classification of the observable outcome. If jRule is specified then this value is 1 if p12 >= jRule and 0 else. If jRule is unspecified then this value is the element-wise product of yHat1 and yHat2.

##
# Perform a prediction with the same covariates the model is estimated with
##

data('Mroz87',package = 'sampleSelection')
Mroz87$Z = Mroz87$lfp*(Mroz87$wage >= 5)

# Run the frequentist version first to get starting values
f1 = BiProbitPartial(Z ~ educ + age + kids5 + kids618 + nwifeinc | educ + exper + city, 
    data = Mroz87, philosophy = "frequentist")

b1 = BiProbitPartial(Z ~ educ + age + kids5 + kids618 + nwifeinc | educ + exper + city, 
    data = Mroz87, philosophy = "bayesian", 
    control = list(beta = f1$par[1:(length(f1$par)-1)], rho = tail(f1$par,1)))

library(Formula)
eqn = Formula::Formula( ~ educ + age + kids5 + kids618 + nwifeinc | educ + exper + city)
matrix1 = model.matrix(eqn, lhs = 0, rhs=1, data= Mroz87)
matrix2 = model.matrix(eqn, lhs = 0, rhs=2, data= Mroz87)
newdat = cbind(matrix1,matrix2) 
preds1 = predict(b1,newdat,k1 = dim(matrix1)[2],k2 = dim(matrix2)[2])
head(preds1)
preds2 = predict(b1,newdat,k1 = dim(matrix1)[2],k2 = dim(matrix2)[2], jRule = .25)

# Compare predicted outcome with realized outcome
head(cbind(Mroz87$Z,preds1$ZHat,preds2$ZHat),20)