Interpret diagnostics¶

longmi refuses to impute from a demonstrably failed fit (optimizer failure, materially indefinite curvature). Everything softer is reported for you to judge. This page says what each diagnostic measures and what to do when it is concerning.

Negative-binomial backend (fit.diagnostics)¶

Diagnostic	Measures	Reassuring	Concerning	Action
optimizer_success, gradient_norm	Whether the marginal-likelihood fit reached an acceptable optimum	Success, small gradient	(You will not see this: a failed fit raises)	Rescale predictors; simplify the design; more quadrature nodes
hessian_eigenvalues (min)	Local identifiability / numerical stability	All clearly positive	Near zero: weakly identified parameter (often τ with few repeat observations)	Reconsider the random-effect structure; more data per participant
covariance_repaired, covariance_min_eigenvalue	Whether roundoff-level negative eigenvalues were clipped	False, or True with a tiny magnitude	(Materially indefinite raises instead)	—
n_quad + refit sensitivity	Quadrature adequacy	Estimates stable across e.g. n_quad=25/40/60	Material parameter movement	Increase nodes; suspect a very wide random-effect distribution
grid_max_boundary_mass (run metadata)	Containment of the random-intercept posterior grid	≤ 1e-8 (enforced)	(Exceeding tolerance after expansion raises)	Inspect the fit; τ draws may be extreme
kappa_draw_range, tau_draw_range (run metadata)	Stability of the parameter draws	Narrow, plausible ranges	Orders-of-magnitude spread → the normal approximation is strained	More data; fewer parameters; treat results cautiously

Joint Gaussian backend (metadata["diagnostics"])¶

Diagnostic	Measures	Reassuring	Concerning	Action
trace_lag1_autocorrelation	Per-sweep mixing of the data-augmentation chain (log det Σ trace)	Low/moderate	Near 1: sticky chain	Increase thin and burn_in
trace_ess	Crude single-chain effective sample size	Large relative to sweeps	Small	Same
kept_lag1_autocorrelation	Dependence between kept imputations	Near zero — imputations effectively independent	Clearly positive	Increase thin; this is the one that directly affects pooling

These are single-chain heuristics; multi-chain R-hat/ESS arrive with the simulation suite. Judge the defaults from the run's numbers, not from the defaults themselves.

Pooled result (summary())¶

Diagnostic	Measures	Concerning	Action
fmi	Fraction of missing information per parameter	> ~0.5: the conclusion leans heavily on the imputation model	Increase M (more imputations); add auxiliaries to the imputation model; widen the delta-sensitivity range and report it prominently
df	Barnard–Rubin degrees of freedom	Very small: unstable variance estimates	Increase M
MI SE vs single-fit SE	Honesty of the extra width	MI SE smaller than a complete-data fit's would indicate a bug — report it	—