Requested addition: to trust conclusions from the mixed-effects models,
need ICC and heterogeneity diagnostics alongside the fixed-effect
estimates, not just "did the model fit without erroring".

- model_diagnostics(): for lmer models, ICC (icc_adjusted/icc_conditional
  -- how much variance is between-animal, the entire justification for the
  random-effect structure), marginal/conditional R2, a likelihood-ratio
  test of whether the random intercept is statistically supported
  (lmerTest::ranova()), a singular-fit flag, and a heteroscedasticity
  check (Breusch-Pagan via performance::check_heteroscedasticity()). For
  the lm fallback case, only plain R2 and heteroscedasticity apply; the
  random-effect-specific columns are NA.
- Refactored stats_funs.R so each model is fit once and both the tidy
  fixed-effect table and the diagnostics table are derived from that same
  fit (fit_models_for_responses() + tidy_models()/diagnose_models()),
  rather than fitting twice.
- 04.Statistics.R now writes a diagnostics_*.csv alongside each stats_*.csv.

Caught two real bugs while validating against actual data (both fixed,
not routed around):

- fit_models_for_responses() used purrr's `~ fn(df, .x, ...)` tilde
  shorthand to forward extra args. With nothing to forward, that bare `...`
  turned out to leak the response's own value into the next positional
  argument (covariates) -- every model silently became `response ~
  response` instead of `response ~ <real covariates>`. No error, just an
  R2 of ~0 and a model.matrix warning easy to miss. Caught by cross-
  checking a diagnostic against an independently-verified value for the
  same model. Fixed by using an explicit closure instead of the tilde
  shorthand, which forwards ... correctly.
- performance::icc() returns a plain NA (not the documented list/data.frame)
  when a model has a singular fit -- observed for real with the 12-animal
  synthetic repeated-measures dataset. `$ICC_adjusted` on that NA is a hard
  error ("$ operator is invalid for atomic vectors"), not a graceful
  missing value. Added a safe_field() accessor used for every performance-
  package field extraction (icc, r2) so a singular fit degrades to NA
  diagnostics instead of crashing the whole batch.

Validated against both real data (9 animals, 1 session each -- lm fallback
path, diagnostics correctly NA for the random-effect-specific columns) and
the synthetic 12-animal repeated-measures dataset (lmer path: differentiated
real results per response, including one genuine singular fit handled
gracefully and two responses with significant heteroscedasticity flagged).

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>