Attach a corrected covariance to a component model of an IPW fit

new_ipw_model() wraps one of the models an ipw() method was given so that the model reports the covariance the two-step estimation implies rather than the one it computed for itself. It is intended for package developers writing an ipw() method, not for end users, and beyond the shape of vcov it assumes its arguments are already validated.

Usage

new_ipw_model(model, vcov)

# S3 method for class 'ipw_model'
vcov(object, ...)

Arguments

model: The fitted component model to wrap, such as the outcome model or the weighting model of an ipw() result.
vcov: The corrected covariance of that model's parameters: a square numeric matrix with dimnames on both margins.
object: An ipw_model object.
...: Further arguments. vcov() ignores them.

Value

new_ipw_model() returns model with "ipw_model" prepended to its class vector and vcov attached as the ipw_vcov attribute. Everything else about the model is untouched. vcov() returns that matrix, and raises an error of class causalgenerics_no_vcov_ipw_model, and of the general class causalgenerics_no_vcov, when the attribute is absent. The constructor puts the class and the attribute on together, so a model carrying the class with nothing behind it passed through code that dropped its attributes and kept its class, and the covariance the model computed for itself is not a substitute for the one it lost.

Details

A weighted outcome model fitted as though its weights were fixed understates its own uncertainty, because the weights were estimated from the same data. A method that solves the estimating equations of both steps as one stacked system has the corrected block on hand, and wrapping the model is how that block reaches a caller who writes vcov(result$outcome_mod).

The wrapper is two changes and no more: "ipw_model" is prepended to the model's class vector, and the matrix is attached as the ipw_vcov attribute. Nothing is registered for the class beyond vcov(), so predict(), coef(), model.frame(), and every other generic walk past it to the model's own methods. That is what lets the corrected covariance travel with the model rather than beside it.

The dimnames of vcov are the fitting package's to choose. They are ordinarily names(coef(model)), but a method whose stacked system is parameterized some other way labels the block with its own parameter names. The constructor checks that both margins are labeled rather than what the labels say, since only the fitting package knows which block of the sandwich belongs to which model.

Examples

dat <- data.frame(
  x = rep(c(-1.5, -0.5, 0.5, 1.5), each = 5),
  z = rep(c(0, 1), 10),
  y = rep(c(0, 1, 1, 0, 1), 4)
)

ps <- fitted(glm(z ~ x, family = binomial(), data = dat))
wts <- ifelse(dat$z == 1, 1 / ps, 1 / (1 - ps))
outcome_mod <- glm(y ~ z, family = quasibinomial(), data = dat, weights = wts)

# Standing in for the outcome block of a stacked sandwich. A real method
# computes this from the estimating equations of both steps; treating the
# weights as estimated rather than fixed ordinarily widens it.
corrected <- vcov(outcome_mod) * 1.4

wrapped <- new_ipw_model(outcome_mod, corrected)

class(wrapped)
#> [1] "ipw_model" "glm"       "lm"       

# The corrected covariance rather than the model's own.
vcov(wrapped)
#>             (Intercept)         z
#> (Intercept)    0.646421 -0.646421
#> z             -0.646421  1.292842

# Everything else about the model reaches its own methods.
coef(wrapped)
#>  (Intercept)            z 
#> 3.919028e-01 1.012353e-15