Fast (MCMC-free) AME estimation for a longitudinal network

Fits an additive and multiplicative effects (AME) model to a longitudinal (replicated) network by iterative block coordinate descent, producing a fast point estimate with no MCMC and no credible intervals. This is the longitudinal counterpart of ame_als; the estimated effects (mu, beta, a, b, U, V) are static (pooled across time), as in a non-dynamic lame fit.

The estimation algorithm adapts the iterative block coordinate descent estimator of the Social Influence Regression model of Hoff & Minhas (sir::sir_alsfit()) to the AME model; it is a port and adaptation, not original lame methodology. See ame_als for the algorithm details.

Usage

lame_als(
  Y,
  Xdyad = NULL,
  Xrow = NULL,
  Xcol = NULL,
  R = 0,
  family = "normal",
  mode = c("unipartite", "bipartite"),
  symmetric = FALSE,
  max_iter = 200,
  tol = 1e-06,
  lowrank_method = c("mm", "als", "hybrid"),
  non_normal_method = c("irls", "transform"),
  link = c("probit", "logit"),
  linear_solver = c("eigen", "qr", "auto"),
  multistart = c("none", "cheap", "full"),
  bootstrap = 0L,
  bootstrap_type = c("parametric", "block"),
  bootstrap_block_length = 1L,
  bootstrap_seed = NULL,
  verbose = TRUE,
  seed = 6886
)

Arguments

Y: a list of t relational matrices, or a 3d array [n_row, n_col, t]. A named list may have changing actor composition; every slice must carry row and column names so actors can be aligned to the union panel. Unnamed lists and arrays are treated positionally and must have one fixed layout. A longitudinal netify object is also accepted and converted with netify::to_lame(lame = TRUE).
Xdyad: a list of T dyadic covariate matrices/arrays, or NULL.
Xrow: a list of T row/sender covariate matrices, or NULL.
Xcol: a list of T column/receiver covariate matrices, or NULL.
R: integer dimension of the multiplicative effects (default 0). The covariate coefficients are conditional on this choice. The multiplicative term $u_i'v_j$ is a flexible high-variance regressor that can correlate with the dyadic covariates, so the estimated beta can shift – and occasionally change sign – as R increases. Comparing against an R = 0 fit is a useful check on whether the covariate story is being driven by the latent rank.
family: one of "normal", "binary", or "poisson". The rank and censoring families are MCMC-only.
mode: "unipartite" (square) or "bipartite" (rectangular).
symmetric: logical; fit a symmetric (undirected) model. Unipartite only.
max_iter: maximum number of block coordinate descent iterations (default 200).
tol: convergence tolerance on the relative change in residual sum of squares (default 1e-6).
lowrank_method: inner solver for the multiplicative (low-rank) block: "mm" (default) weighted majorise-minimise; "als" alternating least squares; "hybrid" runs both and keeps the lower-objective result. "als"/"hybrid" converge faster than "mm" on strongly unbalanced longitudinal panels and are available for directed and bipartite models (symmetric fits always use "mm"). All three minimise the same objective, so the point estimate is unchanged for balanced data.
non_normal_method: for the non-normal ALS families, "irls" (default for binary/poisson) runs iteratively reweighted least squares, giving a fast approximate GLM AME fit with coefficients on the requested link scale (Poisson log, binary logit/probit). "transform" fits one fixed Gaussian working response (log(y+1) for Poisson, rank-normal scores for binary); its coefficients are on an uncalibrated working scale and are mainly useful for direction/ranking checks. A directed R > 0 IRLS fit uses the hybrid low-rank solver internally because the IRLS weights are unbalanced. Uncertainty for either path comes from the bootstrap or sandwich covariance.
link: link for non_normal_method = "irls" with a binary family: "probit" (default; matches ame/lame) or "logit". poisson always uses the log link; ignored otherwise.
linear_solver: solver for the regression block: "eigen" (default) eigendecomposes the normal equations; "qr" uses a QR factorisation of the observed design, which is more stable for ill-conditioned covariates; "auto" picks "qr" when the design is ill-conditioned but full rank. All give the same answer for well-conditioned designs.
multistart: for R > 0 (a non-convex objective), "none" (default) fits from a single deterministic start; "cheap" (4 starts) and "full" (8 starts) also try random low-rank starts and keep the lowest-SSE fit, warning when the starts reach materially different optima. Reproducible given seed; the global RNG stream is left unchanged.
bootstrap: integer: if > 0, additionally run bootstrap replicates of the parametric or block bootstrap (via ame_als_bootstrap) after the point fit and attach the result as fit$bootstrap. The downstream accessors (confint.ame_als, summary, print) then surface bootstrap intervals instead of the anti-conservative sandwich Wald intervals. Default 0 (no bootstrap) – bootstrap is expensive, so it is not imposed on a user who just wants a quick fit.
bootstrap_type: character: "parametric" (default) or "block" – the bootstrap scheme to use when bootstrap > 0.
bootstrap_block_length: integer: block length for the block bootstrap; only used when bootstrap_type = "block".
bootstrap_seed: optional integer seed for the bootstrap (the point fit uses seed).
verbose: logical; print progress (default TRUE).
seed: random seed (default 6886). The block coordinate descent is deterministic, so the point estimate is reproducible regardless; the argument is retained for API consistency with ame.

Value

An object of class "ame_als"; see ame_als.

References

Minhas, S. and Hoff, P. D. (2025). Decomposing Network Dynamics: Social Influence Regression. Political Analysis. The iterative block coordinate descent estimator adapted here originates with that work (implemented in sir::sir_alsfit()).

Author

Cassy Dorff, Shahryar Minhas, Tosin Salau

Examples

Y <- replicate(4, { m <- matrix(rnorm(400), 20, 20); diag(m) <- NA; m },
               simplify = FALSE)
fit <- lame_als(Y, R = 1, family = "normal", verbose = FALSE)
coef(fit)
#>   intercept 
#> -0.03679402