Predictions from a panel sample-selection fit

Predictions from a panselect() fit on newdata, a long data frame with the panel index columns and the variables of both equations (the outcome and the selection indicator themselves are not needed).

Usage

# S3 method for class 'panselect'
predict(
  object,
  newdata,
  type = c("unconditional", "conditional", "selection"),
  ...
)

Arguments

object: a "panselect" fit
newdata: a data frame in long format (see Details); the fit does not store its data, so newdata is required (pass the fitting data for in-sample predictions)
type: "unconditional", "conditional" or "selection"
...: unused

Value

a numeric vector with one prediction per row of newdata

Details

type = "unconditional": the linear index of the outcome equation, x'b, the mean of the outcome in the whole population (selected or not) given the regressors. With model = "pooling" it includes the intercept and, with mundlak = TRUE, the Mundlak means; with model = "within" it excludes the individual effect (and the intercept, which the within transformation removes).
type = "conditional": the mean in the selected population, x'b + sum_t g_t lambda_it, adding the inverse Mills ratio terms with their estimated coefficients (one per period with lambda = "period", a single one with lambda = "common").
type = "selection": the selection probability pnorm(z'd_t) of the first-step probit of each row's period.

The inverse Mills ratios and probabilities use the first-step probit of the row's period; the Mundlak means are the means of the time-varying selection regressors over the rows of each individual in newdata, so newdata should hold every period of an individual (as in the fit). A period without a probit in the fit (every observation selected) has an inverse Mills ratio of zero and a missing selection probability; a period that is not in the fit gives a missing prediction for the conditional and selection types.

Validation

Numerical accuracy is checked in the package tests and in the validation suite; see the validation article on the package website.

Examples

set.seed(1)
d <- data.frame(id = rep(1:150, each = 3), t = rep(1:3, 150))
d$x <- rnorm(450); d$z <- rnorm(450); v <- rnorm(450)
d$s <- as.numeric(0.5 + d$x + d$z + v > 0)
d$y <- ifelse(d$s == 1, 1 + d$x + 0.5 * v + rnorm(450), NA)
fit <- panselect(s ~ x + z, y ~ x, data = d, index = c("id", "t"),
                 model = "pooling", boot = 0)
head(predict(fit, newdata = d, type = "conditional"))
#> [1] 0.4389674 1.5181401 2.2310140 3.0856300 1.7378664 0.7881404
head(predict(fit, newdata = d, type = "selection"))
#> [1] 0.78550320 0.48020531 0.02973796 0.33258371 0.32511926 0.39075972