---
title: "Implementation map"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Implementation map}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
```

<style>
@media (max-width: 575.98px) {
  main h1 {
    hyphens: none;
    overflow-wrap: normal;
    word-break: normal;
  }

  main table {
    display: block;
    min-width: 720px;
    max-width: 100%;
    overflow-x: auto;
  }
}
</style>

This map answers one practical question: what model surface can an applied user
fit today, and which neighbouring syntax is still planned? It is a status
ledger rather than a tutorial. Start here when a model combines random effects,
structured dependence, response-specific scale, zero inflation, hurdle
probability, or `corpairs()`.

The words below are used literally. "Fitted" means likelihood code, parser
support, extractors or diagnostics, tests, and user-facing documentation are in
place. "Planned" means the package may reserve syntax or describe the design,
but an analysis should not interpret that surface yet.

| Status word | Meaning |
| --- | --- |
| Stable | Routine fitted path with tests, diagnostics or interval status, and a reader-facing example or guide. |
| First slice | Fitted and tested inside a deliberately narrow boundary. Stay inside the named family, formula, q, and data-shape limits. |
| Fixed-effect only | Formula coefficients are fitted for this distributional parameter, but random effects or structured dependence for that parameter are not fitted. |
| Planned or reserved | Syntax, design notes, or a parser guard may exist, but `drmTMB()` should reject it or treat it as design-only until likelihood, tests, docs, and after-task evidence land. |
| Unsupported or blocked | Do not use as analysis syntax; choose the nearest fitted route or follow the named fallback in [Can I fit and report this model?](capability-and-limits.html). |

Location means the expected response (`mu`, `mu1`, `mu2`). Scale means residual
standard deviation, dispersion, or an equivalent response-family scale
(`sigma`, `sigma1`, `sigma2`). Shape means a family-specific tail, cutpoint, or
overdispersion control such as Student-t `nu`. Coscale means the residual
correlation layer, currently `rho12` in bivariate Gaussian models.

## How to read the project maps

The public site has three maps with different jobs. Use `model-map` when the
question is "what should I fit?". Use this implementation map when the question
is "is this surface fitted or planned?". Use the
[source map](source-map.html) when the question is "where are the code, tests,
and docs?". The validation-debt register is the evidence ledger behind these
pages. Contributor design ledgers record sequence and future work; they are not
the current-status authority.

When you are closing out a slice from this ledger and need to plot its
recovery evidence, see [Simulation plot grammar](https://itchyshin.github.io/drmTMB/articles/simulation-plot-grammar.html)
for the shared bias/RMSE/coverage display contract.

Every status row should be read across the same dimensions:

| Dimension | What it records |
| --- | --- |
| Family or component | Gaussian, Poisson, NB2, ordinal, `zi`, `hu`, shape, known `V`, or another fitted component. |
| Dependence layer | ordinary group, phylogenetic, coordinate spatial, animal, `relmat()`, known sampling covariance, or residual `rho12`. |
| Formula route | The public syntax that fits the row, such as `(1 + x | id)`, `spatial(1 | p | site, coords = coords)`, or `rho12 ~ x`. |
| q or endpoint class | q=1 intercept, independent slope, q=2, q>2, q=4, or future p8/q8 endpoint work. |
| Random-effect scope | Whether random intercepts, random slopes, and cross-parameter or bivariate combinations are fitted, first-slice, planned, or blocked. |
| Extractor route | Which of `summary()$parameters`, `summary()$covariance`, `ranef()$terms`, `corpairs()`, `profile_targets()`, and `check_drm()` exposes the result. |
| Evidence tier | Whether the surface has smoke evidence, artifact writers, small-grid admission, formal operating-characteristic evidence, or only diagnostic/failure-ledger evidence. |
| Interval tier | Whether intervals are fast Wald, direct profile-ready, profile-proven, direct bootstrap, derived-unavailable, private bootstrap smoke, not requested, or unavailable. |
| User route | What to fit now, and what smaller fitted route to use when the requested model is planned. |

Simulation and interval evidence are deliberately separate from fitted support.
A model can be fitted and still have only smoke or diagnostic evidence.

| Evidence tier | Meaning |
| --- | --- |
| Formal small grid | Likelihood, parser, extractors, diagnostics, interval status, focused recovery tests, and an ADEMP sheet exist. |
| Smoke/artifact only | The route is fitted and inspectable, but it does not yet have enough recovery or coverage evidence for broad claims. |
| Interval-heavy opt-in | Profiles or bootstrap checks are expensive or partial; status tables must show success, failure, or not-requested rows. |
| Diagnostic/failure ledger | The fit teaches us about boundaries or hard cases, but it is not a user-facing operating-characteristic claim. |
| Planned/blocked | Syntax or design may exist, but the fitter should reject the route or route users to a supported alternative. |

Use fast Wald intervals for routine fixed-effect coefficients and selected
direct fitted targets when `TMB::sdreport()` supplies the optimized-parameter
covariance. Direct SD intervals use the fitted log-SD scale before
exponentiating, and direct correlation intervals use the guarded atanh
correlation-link scale before returning to the correlation scale. Do not use
Wald intervals as a shortcut for derived q=4 correlations, repeatability,
phylogenetic signal, unavailable rows, or weak-Hessian fits that need
fit-specific diagnostics. Direct profile targets can be mechanically available
but still fail in a given fit. `confint(method = "bootstrap")` now provides a
narrow public simulate/refit route for selected direct targets, while Phase 18
bootstrap artifacts remain private simulation infrastructure and do not imply
bootstrap support in `summary()`, `corpairs()`, prediction tables, or derived
summaries.

## Family and component map

Use this table before combining a family with a random-effect or dependence
surface.

| Model family or component | Fitted formulas today | Random effects today | Dependence or correlation today | Main planned boundary |
| --- | --- | --- | --- | --- |
| Gaussian, one response | `mu` and `sigma` | ordinary `mu` intercepts, independent slopes, one-slope correlated blocks, q > 2 numeric `mu` blocks, `sigma` intercepts, independent `sigma` slopes, unlabelled correlated `sigma` intercept-slope and multi-slope blocks, and `sd(group) ~ x` for unlabelled `mu` intercept SDs | ordinary group-level `corpairs()` rows for fitted covariance blocks | labelled or cross-formula `sigma` slope covariance, coefficient-specific `sd(group, coef = "x")`, and broad p8 location-scale slope endpoints |
| Student-t | fixed-effect `mu`, `sigma`, and `nu` | ordinary unlabelled `mu` random intercepts and independent numeric slopes | the `spatial()` q1 `mu` intercept and `phylo()` `nu` intercept are diagnostic-only; the spatial intercept-plus-one-slope route is recovery-grade; no labelled covariance | `sigma` or other `nu` random effects, correlated slopes, skewness, and structured Student-t effects beyond those exact gates |
| Lognormal and Gamma | fixed-effect `mu` and family-specific `sigma` scale | separate gates for ordinary unlabelled `mu` random intercepts/independent numeric slopes or one ordinary `sigma` random intercept; the two sides cannot be combined | lognormal `sigma` intercept is inference-ready with caveats only in its exact ledger domain; Gamma `sigma` intercept is inference-ready with caveats only at true SD 0.40, `n_each=12`, and `M >= 32` (`M=16` borderline); Gamma also has a recovery-grade `relmat()` q=1 `mu` intercept/one-slope | `sigma` slopes, combined `mu`+`sigma` random effects, correlated or labelled slopes, known covariance, and further structured dependence |
| Beta | fixed-effect `mu` and `sigma` | ordinary unlabelled `mu` random intercepts and independent numeric slopes | recovery grade: `animal()` q=1 `mu` intercept/one-slope and `sigma` intercept | ordinary `sigma` random effects, correlated slopes, bounded-response known covariance, and further structured dependence |
| Tweedie | fixed-effect `mu`, `sigma`, and intercept-only `nu ~ 1` | ordinary unlabelled `mu` random intercepts and independent numeric slopes; exact `mc-0539` is inference-ready with caveats for true SD 0.50 and M>=16 | none | predictor-dependent power, `sigma` random effects, correlated/labelled `mu` slopes, structured dependence, and bivariate or mixed-response Tweedie |
| Zero-one beta | fixed-effect `mu`, `sigma`, `zoi`, and `coi` | ordinary unlabelled `mu` random intercepts and independent numeric slopes; exact `mc-0575` is inference-ready with caveats for true SD 0.50 and M>=16, under its generator-qualified evidence; exact ordinary `zoi ~ 1 + (1 | id)`, same-raw-symbol `zoi ~ x + (0 + x | id)`, `coi ~ 1 + (1 | id)`, and same-raw-symbol `coi ~ x + (0 + x | id)` are point-fit-only | no direct profile, interval, or coverage claim for the atom-side q1 gates; the `coi` routes have population-level recovery at `M = 64`, 50 observations/group, with sparse-atom and boundary-predictor-spread conditional-mode warnings | transformed or mismatched atom slopes, other `zoi` random effects, covariance blocks, known covariance, denominator syntax, bivariate bounded responses, and structured dependence |
| Beta-binomial | fixed-effect `mu` and `sigma` with row trials | ordinary unlabelled `mu` random intercepts and independent numeric slopes | none | correlated slopes, `sigma` random effects, zero-one inflation, and structured dependence |
| Binomial | fixed-effect `mu` for 0/1 or `cbind(successes, failures)` responses | ordinary unlabelled `mu` random intercepts and independent numeric slopes | the exact independent-slope ledger domain is inference-ready with caveats | correlated or labelled slopes, structured effects, non-logit links, and bivariate or mixed responses |
| Poisson and NB2 | fixed-effect `mu`; NB2 also has fixed-effect `sigma` and the first ordinary log-`sigma` random-intercept gate | ordinary non-zero-inflated `mu` random intercepts/slopes; Poisson/NB2 single-provider q1 structured `mu`; NB2 q1 structured `sigma`; one exact crossed NB2 spatial-plus-relatedness `mu` route | single-provider routes have row-specific source/smoke/recovery evidence; the exact crossed NB2 route is recovery-only with no intervals or coverage | correlated ordinary count slopes, unsupported inflation/hurdle count-`mu` effects, plain NB2 `sigma` slopes, richer/labelled structured routes, simultaneous structured types beyond the exact crossed NB2 gate, and broader count covariance |
| Zero-inflated Poisson and zero-inflated NB2 | fixed-effect `mu`; `zi ~ ...`; NB2 also has fixed-effect `sigma` | exact diagnostic-only q=1 Poisson `zi ~ spatial(1 | id, coords = coords)` intercept only | same exact structured intercept only (no NB2 `zi` structure) | random effects in `zi` beyond the exact Poisson spatial intercept, structured zero inflation beyond the Poisson `zi ~ spatial()` intercept, NB2 `zi` structure, and `corpairs()` for count latent effects |
| Truncated NB2 and hurdle NB2 | fixed-effect `mu`; fixed-effect `sigma`; hurdle NB2 also has `hu ~ ...` | ordinary unlabelled zero-truncated NB2 `mu` random intercepts and independent numeric slopes for non-hurdle models | diagnostic-only: one `relmat()` q=1 `hu` intercept with `K` or `Q` (hurdle NB2, inherited by the alias) | random effects in `hu` beyond the exact `relmat()` q=1 intercept, random effects in hurdle count `mu`, correlated zero-truncated slopes, and other structured hurdle effects |
| Cumulative-logit ordinal | fixed-effect ordinal location with estimated cutpoints | ordinary unlabelled `mu` random intercepts and independent numeric slopes, plus one exact q1 `mu ~ phylo(1 | id, tree = tree)` intercept | exact phylogenetic intercept is diagnostic-only | other structured ordinal effects, scale or discrimination formulas, intervals/coverage for the phylogenetic gate, and bivariate ordinal models |
| Gaussian meta-analysis | `meta_V(V = V)` or deprecated compatibility alias `meta_known_V(V = V)` | ordinary Gaussian random effects may be combined with estimated residual terms where supported | known sampling covariance is observation-level input, not a weight or latent relatedness effect; vector and dense `V` routes are implemented and tested, but their capability tier is unregistered | non-Gaussian known covariance, proportional-variance `meta_V(w = w)`, sparse/block-sparse known covariance, and dense known `V` with non-unit weights |
| Bivariate Gaussian | `mu1`, `mu2`, `sigma1`, `sigma2`, and fixed-effect `rho12` | ordinary bivariate random-intercept slices, same-response `mu`/`sigma` intercept and slope-only covariance, all-four q=4 intercept blocks, matching slope-only `mu1`/`mu2` and `sigma1`/`sigma2` blocks, matching q4/q6 `mu1`/`mu2` location blocks with smoke artifact routing, and the first ordinary q8 all-endpoint block with smoke/recovery artifact routing | residual `rho12()` and group-level `corpairs()` stay separate | random effects in `rho12`, mixed-response bivariate families, broader p8/q8 endpoint variants, and broad q > 2 recovery |

`zi` is currently a fixed-effect probability component except for the exact
diagnostic-only Poisson spatial q=1 intercept. `hu` is fixed-effect by default,
with one diagnostic-only truncated-NB2 q=1 `hu ~ relmat(1 | id, K/Q = ...)`
intercept route. Do not infer other random-effect or structured-dependence
support from either narrow gate.

## Current capability and evidence map

This table connects fitted status to inference status. A first-slice fitted row
is useful, but it is not the same as a formal coverage claim.

| Surface | Intercepts | Slopes | Combinations | Simulation or evidence tier | Interval tier |
| --- | --- | --- | --- | --- | --- |
| Ordinary Gaussian `mu` | fitted | independent, one correlated slope, q>2 advanced | ordinary group covariance | formal small grids for named subsets; q>2 remains advanced | direct SD/profile targets; q>2 correlations derived-unavailable |
| Ordinary Gaussian `sigma` | fitted | independent plus unlabelled correlated `log(sigma)` intercept-slope and multi-slope blocks | labelled blocks and cross-formula `mu`-`sigma` slope covariance remain planned | smoke and small-grid evidence for named independent routes; correlated blocks have fit/extractor contracts but no blanket interval claim | direct SD targets and Wald fixed effects where row-specific evidence allows |
| `sd(group)` | fitted for unlabelled Gaussian `mu` intercept SD | no coefficient-specific slope SD yet | direct SD surface | focused recovery | coefficient intervals only where direct; row-specific SDs are derived |
| Bivariate ordinary Gaussian | q=2 intercepts fitted | matching slope-only `mu1`/`mu2`, same-response q2 `mu`/`sigma`, q2 `sigma1`/`sigma2`, q4/q6 location `mu1`/`mu2`, and the first ordinary q8 all-endpoint block fitted | selected q=2, same-response `mu`/`sigma`, all-four q=4 intercept blocks, q > 2 location blocks, and the first q8 endpoint block | q=2 admitted; same-response q2 and q2 scale-slope artifact-backed; q4/q6 location smoke only; q8 diagnostic artifacts only, with no coverage or power claim | q=2 direct profile; q > 2 location SDs and q8 endpoint SDs direct; q > 2 and q8 correlations derived-unavailable |
| Residual `rho12` | not a random effect | predictor-dependent fixed effects | residual coscale only | admitted and interval-heavy | default direct Wald for constant rows; direct profile for constant or supplied `newdata` rows; direct bootstrap only through selected `confint()` targets |
| Phylogenetic Gaussian | `mu` intercept fitted | one `mu` slope fitted | q=2 `mu1`/`mu2` and q=4 location-scale fitted, with Ayumi hard cases diagnostic | small controlled grids; full-species hard cases stay diagnostic | direct targets for q=2; q=4 derived-unavailable |
| Coordinate spatial Gaussian | `mu` intercept fitted | one `mu` slope fitted | q=2 `mu1`/`mu2` fitted; constant all-four q=4 fitted | q=2 admitted; q=4 extractor/diagnostic smoke only | fixed-effect Wald and opt-in profiles for q=2 artifacts; q=4 derived-unavailable |
| Animal Gaussian | `mu` intercept fitted | one `mu` slope fitted | q=2 and q=4 fitted for small dense or known-matrix routes | q=2/q=4 smoke artifacts, not broad coverage | q=2 fixed-effect Wald plus opt-in profile status; q=4 derived-unavailable |
| `relmat()` Gaussian | `mu` intercept fitted | one `mu` slope fitted | q=2 and q=4 fitted for known matrices | q=2/q=4 smoke artifacts, not broad coverage | same as animal |
| Poisson/NB2 ordinary `mu` | fitted | independent numeric slopes fitted | no labelled or correlated count blocks | first small count grids | Wald fixed effects; direct SD profile artifacts |
| NB2 ordinary `sigma` | fitted for independent log-`sigma` random intercepts | no plain `sigma` slopes yet | recovery-grade q=1 structured `sigma` one-slope slices (`phylo()`/`spatial()`/`animal()`/`relmat()`); no labelled, joint `mu`/`sigma`, zero-inflated, truncated, or hurdle scale blocks | separate overdispersion-random-intercept smoke lane | Direct `log_sd_sigma` profile target |
| Non-Gaussian structured dependence | Poisson/NB2 q1 single-provider `mu` routes, NB2 q1 structured `sigma`, and one exact crossed NB2 spatial-plus-relatedness `mu` route | unlabelled single-provider intercept-plus-one-slope blocks are fitted; the crossed two-provider route is intercept-only on each field | pure, labelled, or multiple slopes, richer covariance, and simultaneous providers beyond the exact crossed gate remain planned | focused tests cover extraction/diagnostics; the crossed design has recovery-only evidence | Direct `log_sd_phylo` targets where exposed; no crossed-route interval/coverage promotion |
| `zi`, `hu`, `zoi`, and `coi` | fixed effects where supported | diagnostic-only q=1 intercept gates for Poisson `zi ~ spatial()` and truncated-NB2 `hu ~ relmat(K/Q)`; point-fit-recovery zero-one-beta `zoi` and `coi` q1 intercept/same-raw-symbol slope gates | no labelled or correlated covariance layer | fixed-effect tests plus focused route tests; the exact zero-one-beta atom gates have independent likelihood and retained recovery evidence | Wald fixed effects where implemented; zero-one-beta atom q1 remains point-fit-only, with profiles, intervals, and coverage unavailable |
| Ordinal, shape, bounded scale | fixed effects where supported; eligible cumulative-logit, Student-t, beta, Tweedie, skew-normal, and zero-one-beta routes also fit ordinary `mu` intercepts/slopes | diagnostic-only cumulative-logit q1 `mu ~ phylo()`; recovery-grade Student-t `mu ~ spatial(1 + x | ...)` and beta `mu`/`sigma ~ animal()` gates; Student-t intercept-only `mu ~ spatial(1 | ...)` and `nu ~ phylo()` are diagnostic-only | other distributional-parameter random effects, correlated/labelled slopes, and structured neighbours beyond the exact gates remain planned | family recovery tests plus route-specific source/local-fit tests | retain each live-ledger tier; no blanket recovery, interval, or coverage promotion |
| `meta_V(V = V)` | estimated effects plus known sampling covariance | ordinary Gaussian random effects only where otherwise supported | `V` is input data, not a weight or latent dependence; vector and dense forms are implemented and tested, but their capability tier is unregistered | no interval or coverage claim for this route; predictor-dependent `sigma` needs fit-specific Hessian checks | never interval-target `V`; Wald SEs and intervals for `sigma ~ moderator` are unreliable when `pdHess = FALSE` |

## Random-effect and dependence map

Here q is the number of latent endpoints in one covariance block. A q=2 block
has two endpoints, such as `mu1` and `mu2` random intercepts. A q=4 block has
four endpoints, such as `mu1`, `mu2`, `sigma1`, and `sigma2` random intercepts.
The q8 language now includes one fitted ordinary all-endpoint diagnostic lane
with smoke/recovery artifacts. The broader p8/q8 future-work design still refers to
future all-endpoint location-scale slope variants, not routine tutorial or
coverage-supported routes.

| Layer | Fitted q and slope support | Main extractors or diagnostics | Planned or blocked neighbours |
| --- | --- | --- | --- |
| Ordinary Gaussian `mu` | q=1 random intercepts and independent slopes; q=2 intercept-slope correlations; q > 2 numeric `mu` blocks | `summary()$parameters`, `summary()$covariance`, `ranef()$terms`, `corpairs()`, `profile_targets()`, `check_drm()` | q > 2 correlations are derived-unavailable for direct profile intervals and larger q blocks remain advanced |
| Ordinary Gaussian `sigma` | q=1 residual-scale intercepts, independent numeric slopes, and unlabelled correlated intercept-slope and multi-slope blocks on `log(sigma)` | `summary()$parameters`, `summary()$covariance`, `profile_targets()`, `check_drm()`, `sigma()` | labelled residual-scale blocks and cross-formula `mu`-`sigma` slope covariance |
| Random-effect SD surface | `sd(group) ~ x_group` for unlabelled Gaussian `mu` random intercepts | `predict_parameters(dpar = "sd(group)")`, `marginal_parameters()`, fixed-effect summaries | coefficient-specific `sd(group, coef = "x")`, spatial/animal/relmat direct-SD siblings, and generic `sd*()` unification |
| Ordinary bivariate `mu1`/`mu2` | q=2 matching labelled random intercepts, q=2 matching slope-only random-slope blocks, q4/q6 location blocks with smoke artifact routing, and the location endpoints of the first q8 diagnostic lane | `corpairs(class = "mean-mean")`, `summary()$covariance`, `profile_targets()`, `check_drm()` | broader p8/q8 endpoint variants and predictor-dependent slope `corpair()` regressions |
| Ordinary bivariate `sigma1`/`sigma2` | q=2 matching labelled random intercepts, slope-only scale-slope blocks, and the scale endpoints of the first q8 diagnostic lane | `corpairs(class = "scale-scale")`, `summary()$covariance`, `profile_targets()` | broader p8/q8 endpoint variants |
| Same-response `mu`/`sigma` | one or more q=2 matching random-intercept blocks, plus matching slope-only blocks within a response | `corpairs(class = "mean-scale")`, `corpairs(class = "mean-scale-slope")`, `summary()$covariance` | cross-response and mismatched-coefficient covariance |
| All-four ordinary location-scale | constant q=4 random-intercept block across `mu1`, `mu2`, `sigma1`, and `sigma2`, plus the first q8 all-endpoint diagnostic lane with matching `(1 + x | p | id)` terms | `corpairs()` and `summary()$covariance` report derived latent correlations; Phase 18 q8 recovery artifacts report bias, RMSE, MCSE, and interval unavailability | derived q=4/q8 correlation intervals and broader p8/q8 random-slope endpoint variants |
| Residual coscale | fixed-effect `rho12 ~ ...` | `rho12()`, `confint(..., parm = "rho12", newdata = ...)`, `summary()` | random effects or structured dependence in `rho12` |
| Ordinary `corpair()` regression | q=2 predictor-dependent group-level correlation for an already fitted block | `corpairs(newdata = ...)`, `plot_corpairs()` | q=4 correlation regressions and slope-level `corpair()` regressions |
| Phylogenetic structure | Gaussian q=1 univariate `mu` and `sigma` intercepts with optional matching `mu`/`sigma` correlation; one numeric `mu` slope; the exact q1 `sigma` one-slope route; Gaussian q=2 bivariate `mu1`/`mu2`; Gaussian constant q=4 location-scale intercept block; ordinary Poisson/NB2 q=1 `mu` intercept-plus-one-slope routes; separate recovery-grade NB2 q1 structured `sigma` intercept-plus-one-slope | `summary()$parameters`, marker-specific `ranef()$terms`, `corpairs(level = "phylogenetic")` for Gaussian q>=2, `profile_targets()`, `check_drm()`; the Gaussian sigma slope is inference-ready with caveats | pure, multiple, or labelled Poisson/NB2 phylogenetic slopes, zero-inflated phylogenetic effects, multiple or labelled Gaussian phylogenetic slopes, phylogenetic slope correlations, direct-SD formulas combined with structured `sigma`, and structured `rho12` |
| Phylogenetic direct SD | `sd_phylo()`, `sd_phylo1()`, and `sd_phylo2()` direct-SD surfaces where documented | fixed-effect summaries, prediction helpers, profile targets where direct | generic `sd*()` naming across phylo, spatial, animal, and `relmat()` remains a future unification lane |
| Coordinate spatial structure | q=1 univariate `mu` and `sigma` intercepts with optional matching `mu`/`sigma` correlation; one numeric `mu` slope; a q1 `sigma` one-slope point-fit/extractor route; q=2 bivariate `mu1`/`mu2` intercept covariance; constant q=4 location-scale intercept block; ordinary Poisson/NB2 q=1 `mu` intercept-plus-one-slope routes; separate recovery-grade NB2 q1 structured `sigma` intercept-plus-one-slope; the exact diagnostic-only Poisson `zi ~ spatial()` intercept; the exact diagnostic-only fixed-`zi` Poisson `mu ~ spatial()` intercept; and the exact diagnostic-only fixed-`zi` NB2 `mu ~ spatial()` intercept | `summary()$parameters`, marker-specific `ranef()$terms`, `corpairs(level = "spatial")`, `summary()$covariance`, `profile_targets()`, `check_drm()` | the Gaussian spatial sigma-slope interval gate, mesh/SPDE, multiple or labelled Gaussian slopes, slope correlations, direct-SD surfaces, spatial `corpair()` regression, pure, multiple, or labelled count spatial slopes, and zero-inflated spatial effects outside the exact Poisson `zi`, fixed-`zi` Poisson `mu`, and fixed-`zi` NB2 `mu` gates; both fixed-`zi` routes have no recovery, interval, or coverage promotion |
| Animal-model structure | q=1 univariate `mu` and `sigma` intercepts with optional matching `mu`/`sigma` correlation; one numeric `mu` slope for `pedigree`, `A`, or `Ainv`; the exact A-matrix q1 `sigma` one-slope route; q=2 bivariate `mu1`/`mu2`; constant q=4 location-scale intercept block; ordinary Poisson/NB2 q=1 `mu` intercept-plus-one-slope routes; separate recovery-grade NB2 q1 structured `sigma` intercept-plus-one-slope | `summary()$parameters`, marker-specific `ranef()$terms`, `corpairs(level = "animal")`, `profile_targets()`, `check_drm()`; the Gaussian sigma slope is inference-ready with caveats | pedigree/Ainv bridge marshalling, sparse large-pedigree construction, multiple or labelled Gaussian slopes, slope correlations, predictor-dependent `corpair()` regression, direct-SD grammar, pure, multiple, or labelled count animal slopes, and labelled count covariance |
| `relmat()` known latent relatedness | q=1 univariate `mu` and `sigma` intercepts with optional matching `mu`/`sigma` correlation; one numeric `mu` slope for `K` or `Q`; the exact K/Q q1 `sigma` one-slope route; q=2 bivariate `mu1`/`mu2`; constant q=4 location-scale intercept block; ordinary Poisson/NB2 q=1 `mu` intercept-plus-one-slope routes; separate recovery-grade NB2 q1 structured `sigma` intercept-plus-one-slope | `summary()$parameters`, marker-specific `ranef()$terms`, `corpairs(level = "relmat")`, `profile_targets()`, `check_drm()`; the Gaussian sigma slope is inference-ready with caveats | broader K/Q bridge claims, multiple or labelled Gaussian slopes, slope correlations, predictor-dependent `corpair()` regression, direct-SD grammar, pure, multiple, or labelled count `relmat()` slopes, and labelled count covariance |
| Non-Gaussian ordinary `mu` | Ordinary `mu` intercepts/slopes for every fitted univariate family; Poisson/NB2 q1 single-provider structured `mu`; exact recovery-grade Gamma-phylo, lognormal-phylo/relmat, Gamma-relatedness, Student-spatial, beta-animal, and ordinal-phylo gates; and one crossed NB2 spatial-plus-relatedness route | `summary()$parameters`, marker-specific `ranef()$terms`, direct targets from `profile_targets()`, and `check_drm()` where exposed; crossed NB2 recovery is design-dependent | correlated/labelled non-Gaussian slopes, pure/multiple structured slopes, simultaneous count types beyond the exact crossed NB2 gate, unsupported inflation/hurdle neighbours, and cross-parameter covariance |
| Non-Gaussian scale, shape, zero-inflation, and hurdle | fixed-effect formulas where the family supports the component; ordinary NB2, lognormal, and Gamma log-`sigma` random intercepts; recovery-grade NB2 q=1 structured `sigma` one-slope slices; one diagnostic-only truncated-NB2 q=1 `hu ~ relmat(K/Q)` intercept; and exact point-fit-only zero-one-beta `zoi` and `coi` random-intercept/same-raw-symbol slope gates | fixed-effect coefficient tables and Wald intervals where implemented; named rows in `summary()$parameters` and `profile_targets()`, conditional deviations in `ranef()$terms`, and `check_drm()` for the intercept gates; zero-one-beta direct atom-SD targets remain unavailable to profiling; only the exact lognormal and Gamma (`M >= 32`) ledger domains are inference-ready with caveats | non-Gaussian `sigma` slopes outside exact ledger gates, structured scale routes outside the NB2 q=1 one-slope gate, random effects in `nu`, `zi`, or latent skewness, transformed or mismatched atom slopes, and `hu` random effects beyond the exact q=1 `relmat()` intercept |

## Slope coverage at a glance

| Random-effect type | At least one random slope fitted? | Current fitted scope | Not yet fitted |
| --- | --- | --- | --- |
| Ordinary Gaussian `mu` | Yes | independent slopes, one-slope correlated blocks, q > 2 numeric `mu` blocks | routine high-q teaching and direct q > 2 correlation profiles |
| Ordinary Gaussian `sigma` | Yes | independent slopes plus unlabelled correlated intercept-slope and multi-slope blocks | labelled residual-scale and cross-formula `mu`-`sigma` slope covariance |
| Ordinary bivariate Gaussian | Yes | matching slope-only `mu1`/`mu2`, same-response `mu`/`sigma`, and `sigma1`/`sigma2` q=2 blocks plus q4/q6 location blocks and the first q8 all-endpoint diagnostic lane with smoke/recovery artifact routing | broader p8/q8 all-endpoint variants, q8 coverage or power evidence, and slope-level `corpair()` regressions |
| Coordinate spatial | Yes | one univariate Gaussian `mu` slope plus a q1 `sigma` one-slope point-fit/extractor route and constant q=4 bivariate Gaussian location-scale intercepts | spatial sigma-slope intervals, multiple or labelled slopes, slope correlations, and non-Gaussian spatial effects outside the exact ordinary Poisson/NB2 q1 spatial `mu` intercept-plus-one-slope, recovery-grade NB2 q1 spatial `sigma`, Student-t spatial `mu`, Poisson spatial `zi`, fixed-`zi` Poisson spatial `mu`, and fixed-`zi` NB2 spatial `mu` gates |
| Phylogenetic | Yes | one univariate Gaussian `mu` slope plus the exact q1 `sigma` one-slope route, inference-ready with caveats; exact non-Gaussian gates include ordinary Poisson/NB2 q1 phylogenetic `mu` intercept-plus-one-slope, recovery-grade NB2 q1 phylogenetic `sigma`, diagnostic-only Student-t q1 phylogenetic `nu`, and diagnostic-only cumulative-logit q1 phylogenetic `mu` | multiple or labelled slopes, slope correlations, direct-SD formulas combined with structured `sigma`, and non-Gaussian phylogenetic effects outside those exact row-specific gates |
| Animal-model relatedness | Yes | documented Gaussian routes plus exact ordinary Poisson/NB2 q1 animal `mu` intercept-plus-one-slope, NB2 q1 animal `sigma`, and beta animal gates | pedigree/Ainv bridge marshalling, sparse large-pedigree scaling, multiple or labelled slopes, slope correlations, and non-Gaussian animal neighbours outside exact gates |
| `relmat()` known latent relatedness | Yes | documented Gaussian routes plus exact ordinary Poisson/NB2 q1 relmat `mu` intercept-plus-one-slope, NB2 q1 relmat `sigma`, Gamma q1 relmat `mu`, and truncated-NB2 q1 relmat `hu` gates | broader bridge claims, multiple or labelled slopes, slope correlations, direct-SD grammar, and non-Gaussian relmat neighbours outside exact gates |
| Non-Gaussian ordinary `mu` | Yes | Ordinary intercepts/slopes for every fitted univariate family; Poisson/NB2 q1 single-provider structured `mu`; exact non-count gates; one recovery-only crossed NB2 spatial-plus-relatedness `mu` route | correlated slopes, unsupported inflation/hurdle count-`mu` effects, pure/multiple/labelled structured slopes, simultaneous structured types beyond the exact crossed NB2 gate, and broader bounded-response dependence |
| Non-Gaussian scale, shape, `zi`, `hu`, ordinal, or bounded-response components | First NB2/lognormal/Gamma scale-intercept slices; exact q1 NB2 structured `sigma` routes at recovery grade; Poisson `zi ~ spatial()`, truncated-NB2 `hu ~ relmat(K/Q)`, and cumulative-logit `mu ~ phylo()` routes are diagnostic-only | fixed effects where implemented; ordinary NB2, lognormal, and Gamma log-`sigma` random intercepts; exact NB2 `phylo()`/`spatial()`/`animal()`/`relmat()` structured `sigma` intercept-plus-one-slope routes; exact diagnostic-only Poisson q1 spatial-`zi`, truncated-NB2 q1 relatedness-hurdle, and cumulative-logit q1 phylogenetic-`mu` intercepts | ordinary non-Gaussian scale slopes, richer or labelled structured sigma, structured-sigma intervals/coverage, and random effects for shape, inflation beyond the exact spatial-`zi` gate, ordinal routes beyond the exact phylogenetic-`mu` gate, or bounded-response components |

## Current future-work lanes

The next implementation work should move only one boundary at a time. The
detailed slice history lives in the contributor design ledgers. This page keeps
only the current user-facing lanes:

| Current lane | Why it helps users | Done when |
| --- | --- | --- |
| Generic `sd*()` direct-SD design | Users should not need separate direct-SD names for phylo, spatial, animal, and `relmat()` routes forever. | The grammar, compatibility route for existing `sd_phylo*()` helpers, examples, tests, and reference-index plan are explicit before parser work. |
| Broader p8/q8 location-scale slope planning | Full individual-difference location-scale slope models are scientifically attractive but weakly identified. | The first q8 diagnostic lane stays separate from coverage and power claims, and any broader p8/q8 variant has endpoint classes, parameterization, diagnostics, sample-size gates, and interval policy written before syntax opens. |
| q=4 interval policy | Users need to know which q=4 rows are point estimates and which have real intervals. | q=4 rows keep `derived_interval_unavailable` until a validated derived-profile or bootstrap route exists. |
| Non-Gaussian structured q1 gate | Count users need realistic structural-dependence paths before broad non-Gaussian parity. | Poisson and NB2 q1 phylogenetic `mu` intercepts are fitted as narrow first slices; broader promotion waits for formal recovery, diagnostics, extractor rows, and interval-status evidence. |
| Route-specific non-Gaussian issues | Developers need a narrow implementation issue before touching code. | The issue names one family, component, layer, q, comparator, extractor contract, diagnostic contract, interval status, simulation artifact, and user fallback. |
| Poisson q1 runner contract | The fitted Poisson phylogenetic q1 route needs schema checks before broader simulation claims. | Direct target, extractor, manifest, warning/error, smoke-grid, formal-grid, malformed-neighbour, diagnostic, and artifact tests are specified before the route is promoted beyond smoke evidence. |
| Map and evidence maintenance | The site should help users fit a supported model rather than read a project diary. | `model-map`, this article, `source-map`, the validation-debt register, and stale scans agree after each substantial feature slice. |

## Common planned requests

Use this table when a desired model is not fitted yet.

| If you want... | Fit now | Planned boundary |
| --- | --- | --- |
| zero-inflated counts with predictors in the zero process | fixed-effect `zi ~ predictors` in the supported count family; diagnostic-only Poisson `zi ~ spatial(1 | id, coords = coords)` q=1 structured intercept | random effects in `zi`, NB2 `zi` structure, and Poisson `zi` structure beyond the first `spatial()` intercept |
| hurdle counts with a modelled hurdle probability | fixed-effect `hu ~ predictors` in hurdle NB2, or one diagnostic-only q=1 `hu ~ relmat(1 | id, K/Q = ...)` intercept | `hu` random effects or structured dependence beyond the exact relatedness intercept |
| phylogenetic or spatial count dependence | ordinary Poisson/NB2 q1 single-provider `mu`; separate NB2 q1 structured `sigma`; exact crossed NB2 spatial-plus-relatedness `mu` when the crossed design identifies both fields | pure, multiple, or labelled structured count slopes, unsupported zero-inflation, richer NB2 structured `sigma`, simultaneous types beyond the exact crossed gate, and labelled count covariance |
| full individual-difference location-scale slopes | fitted q2 slope-only `mu1`/`mu2` covariance, smaller univariate pieces, or the first ordinary q8 diagnostic artifact lane when all four endpoints use matching `(1 + x | p | id)` terms | q8 coverage or power evidence, broader p8/q8 location-scale slope variants, and interval support for derived q8 correlations |
| structured direct-SD surfaces outside phylogeny | fitted structured intercept/slope SDs and `profile_targets()` where available | generic spatial, animal, or `relmat()` direct-SD regression |
| spatial q4 location-scale covariance | fitted bivariate Gaussian q4 spatial location-scale block when all four endpoints use matching labelled `spatial(1 | p | site, coords = coords)` terms; treat current q4 evidence as extractor/diagnostic smoke; the separate q1 spatial `sigma` one-slope route has point-fit/extractor evidence | mesh/SPDE, spatial sigma-slope intervals, multiple or labelled spatial slopes, direct-SD surfaces, predictor-dependent spatial `corpair()` regression, q4 coverage evidence, and non-Gaussian spatial routes outside the exact ordinary Poisson/NB2 q1 spatial `mu` intercept-plus-one-slope, recovery-grade NB2 q1 spatial `sigma`, Student-t spatial `mu`, Poisson spatial `zi`, fixed-`zi` Poisson spatial `mu`, and fixed-`zi` NB2 spatial `mu` gates |
| NB2 structured count model | single-provider q1 `mu` intercept-plus-one-slope routes, ordinary NB2 `mu`, separate recovery-grade q1 structured `sigma`, or the exact recovery-only crossed spatial-plus-relatedness `mu` route | pure/multiple/labelled structured `mu` slopes, unsupported zero-inflated structure, richer structured `sigma`, simultaneous types beyond the exact crossed gate, and labelled count covariance |
| Poisson structured count slopes | ordinary Poisson/NB2 q=1 unlabelled `phylo()`/`spatial()`/`animal()`/`relmat()` intercept-plus-one-slope terms, or independent numeric `mu` slopes when the grouping is exchangeable | pure, multiple, or labelled structured count slopes need their own recovery and diagnostic evidence |
| Poisson `animal()` or `relmat()` count dependence | ordinary Poisson/NB2 q1 animal/relatedness `mu`, ordinary count `mu`, Gaussian animal/relatedness, or the exact crossed NB2 spatial-plus-relatedness `mu` route | pure/multiple/labelled known-relatedness count slopes, unsupported zero-inflation, and simultaneous types beyond the exact crossed NB2 gate remain planned |
| non-Gaussian structured scale or shape effects | fixed-effect `sigma`, `nu`, `zi`, or `hu` formulas where the family supports them; ordinary NB2, lognormal, and Gamma log-`sigma` random intercepts for plain grouping; separate recovery-grade NB2 q=1 `phylo()`/`spatial()`/`animal()`/`relmat()` structured `sigma` intercept-plus-one-slope routes; one diagnostic-only truncated-NB2 q=1 `hu ~ relmat(K/Q)` intercept | richer or labelled structured scale and shape, zero-inflation, and hurdle random effects beyond the exact relatedness intercept need family-specific likelihood, extractor, diagnostic, and recovery contracts |
| known sampling covariance plus latent relatedness | Gaussian `meta_V(V = V)` for known sampling covariance, or Gaussian `relmat()` for latent relatedness when that is the scientific target | `meta_V()` is implemented/tested but tier-unregistered, with no interval or coverage claim; non-Gaussian known covariance and latent relatedness should stay separate until each has its own issue and simulation gate |
| unsupported structured count syntax | fit the nearest fixed-effect or ordinary random-effect model and read `check_drm()` before interpretation | future error messages should name the unsupported family, component, layer, q, and nearest fitted alternative |