Compute the bread matrix

Computes the bread matrix for the empirical sandwich variance estimator. The bread is the negative Jacobian of the summed estimating equations. It is returned unscaled: the callers that assemble a sandwich divide it by the number of observations, and the meat with it.

Usage

compute_bread(
  stacked_equations,
  theta,
  deriv_method = "capprox",
  dx = 1e-09,
  summed_equations = NULL
)

Arguments

stacked_equations

A function that takes a numeric vector theta and returns a p-by-n matrix of estimating equation contributions.

theta

Numeric vector of parameter estimates.

deriv_method

Character string for the derivative method. One of "capprox" (central), "fapprox" (forward), or "bapprox" (backward).

dx

Numeric step size (default 1e-9). The step is absolute, floored at the floating-point resolution of each estimate; see approx_differentiation().

summed_equations

A function of theta returning the length-p vector of row sums of stacked_equations at theta, or NULL (default) to derive that reduction from the full p-by-n return. See compute_sandwich() for what a supplied reduction saves and what it must satisfy.

Anything that is neither NULL nor a function, and any return at theta that is not numeric or holds fewer values than there are parameters, raises an error carrying the class deli_summed_equations_error. The values themselves are taken on trust: this function evaluates the estimating equations nowhere, so it has nothing to compare them against, and a reduction that sums some other system returns the Jacobian of that other system with nothing to say so.

Value

The negated Jacobian of the summed estimating equations, with one row per estimating equation and one column per parameter. That is p-by-p for an M-estimation system, which has one equation per parameter, and n_eqs-by-p for an over-identified GMM system, whose rectangular bread build_sandwich() pseudo-inverts. No scaling is applied here; the division by n that puts the bread on the mean scale belongs to the callers that assemble a sandwich, compute_sandwich() and estimate().

A bread holding NA is returned as it stands, alongside a warning carrying the class deli_bread_na. What to do about it is the caller's, and the two callers differ: a fit records no variance and says so, while compute_sandwich() has nothing but the matrix to return and fails.