Add coef() and vcov() S3 methods for MP and AGGTEobj

[pedrohcgs]

Overview

Building on the excellent proposal in #233, this issue tracks a correct and complete implementation of coef() and vcov() S3 methods for MP and AGGTEobj objects. Before implementing, several scaling and clustering questions need to be resolved.

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coef.MP

Straightforward — just names the ATT(g,t) vector:

coef.MP <- function(object, ...) {
  x <- object$att
  names(x) <- paste0("ATT(", object$group, ",", object$t, ")")
  x
}

---

vcov.MP

vcov() must return $\widehat{\text{Var}}(\hat\theta)$, the estimated variance matrix of the ATT(g,t) estimator itself.

Analytical case (bstrap = FALSE)

V_analytical stored on MP estimates $\hat\Sigma = \frac{1}{n}\sum_i \psi_i\psi_i'$ (the asymptotic variance of $\sqrt{n}\hat\theta$). The correct vcov is:

vcov.MP <- function(object, ...) as.matrix(object$V_analytical) / object$n

This is consistent with the existing Wald pre-test (W = n * t(att) %*% solve(V) %*% att).

Bootstrap case (bstrap = TRUE, no extra clustering)

mboot() scales bootstrap draws by sqrt(n), so cov(bres) also estimates $\hat\Sigma$. Same division by n applies.

Bootstrap case with clustervars

mboot() aggregates influence functions to cluster means and scales by sqrt(n_clusters), so cov(bres_cl) estimates $n_{cl} \cdot \text{Var}(\hat\theta)$. The correct vcov is cov(bres_cl) / n_clusters. This is consistent with how mboot already computes se = bSigma / sqrt(n_clusters).

Changes needed for bootstrap VCV

bout$V is already computed inside mboot() but currently discarded. n_clusters is also computed inside mboot() but not returned. Both need to be threaded through to the MP object. Memory cost is negligible — same size as V_analytical which is already stored.

Correctness guard under clustering

V_analytical ignores between-cluster correlation and is known to be anti-conservative when clustervars is set — the Wald pre-test already suppresses itself in this case. vcov.MP must apply the same guard: warn (or error) when clustervars is set and no bootstrap VCV is available.

Analytical cluster-robust VCV

Currently the package requires bstrap = TRUE whenever clustervars is specified. In principle, an analytical cluster-robust sandwich estimator is available:

$$\hat\Sigma_{cl} = \frac{1}{n_{cl}} \sum_c \bar\psi_c \bar\psi_c'$$

where $\bar\psi_c = \frac{1}{n_c}\sum_{i \in c} \psi_i$ is the cluster-mean influence function — already computed inside mboot() as cluster_mean_if. Exposing this analytically would allow vcov() to be correct under clustering without bootstrap, and would remove the forced-bootstrap requirement for clustered SEs.

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vcov.AGGTEobj

This is fully feasible — the influence functions are already stored on every AGGTEobj and the computation is identical in structure to V_analytical on MP.

What is stored

Type	Per-estimate IFs	Overall IF
"dynamic"	dynamic.inf.func.e (n × K, one col per event time)	dynamic.inf.func (n × 1)
"group"	selective.inf.func.g (n × G, one col per cohort)	selective.inf.func (n × 1)
"calendar"	calendar.inf.func.t (n × T, one col per calendar period)	calendar.inf.func (n × 1)
"simple"	single estimate only — VCV reduces to a 1×1 scalar	simple.att (n × 1)

Construction

# e.g. for dynamic type
IF <- object$inf.function$dynamic.inf.func.e   # n × K
n  <- nobs(object)
V  <- t(IF) %*% IF / n    # estimates Σ (asymptotic variance of sqrt(n)*θ̂)
vcov <- V / n              # estimates Var(θ̂)

Subtlety for "group" type

tidy.AGGTEobj for "group" includes an overall average row alongside the per-cohort rows. A complete (G+1)×(G+1) VCV requires stacking the overall IF with the per-cohort IFs: cbind(selective.inf.func, selective.inf.func.g).

Bootstrap and clustering

Same considerations as vcov.MP apply — bout$V and n_clusters need to be stored to support the clustered case correctly.

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coef.AGGTEobj

Returns the named vector of aggregated estimates (att.egt, plus overall.att for "group" type):

coef.AGGTEobj <- function(object, ...) {
  # example for dynamic type
  x <- object$att.egt
  names(x) <- paste0("ATT(", object$egt, ")")
  x
}

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Why this matters

Once coef() and vcov() are available, users can directly use standard R tools for linear hypothesis testing — for example car::linearHypothesis() — without having to reconstruct these objects manually. This would also allow replicating and extending the existing Wald pre-test (mp$W) to arbitrary linear combinations of ATT estimates.