Generalised Linear Latent Variable Models

Fits multivariate generalised linear latent variable models using either long-format data or a wide data frame. Models support several response distributions and trait covariance structures, and can estimate correlations, shared latent axes, and trait-specific variances. Binary presence-absence data can be used for joint species distribution analyses. Optional animal, phylogenetic, spatial, and kernel covariance components are available. Estimation uses 'Template Model Builder'. Spatial effects can use sparse Gaussian Markov random field constructions. This 0.7.1 release remains experimental: evidence for estimates is model- and regime-specific. Broad interval coverage is not certified; a 0.94 coverage floor is documented only for one two-sided Gaussian total-variance profile setting.

gllvmTMB

[!WARNING] gllvmTMB is experimental; use at your own risk. It is not complete, is not fully human-verified, and needs extensive further validation. CRAN availability is not a statement of scientific maturity. Point estimates are the primary inferential output, but their evidence is route- and regime-specific. Broad package-wide interval coverage is not certified; one narrowly scoped two-sided Gaussian total-variance profile regime has a documented 0.94 coverage floor. This is not nominal 95% certification or a guarantee for an individual fit. Covariance routes otherwise have cell-specific evidence only.

gllvmTMB fits multivariate models for data where each site, individual, species, or study has several responses: body traits, species occurrences, behaviours, outcomes, or similar measurements. The main question is simple:

Which responses vary together, and how much of that variation is shared versus response-specific?

Unlike PCA or NMDS, gllvmTMB estimates latent structure inside a likelihood rather than from a distance matrix or eigen-decomposition. Loadings, correlations, and communalities can be paired with model-based uncertainty where a target-specific route is supported; broad interval calibration remains incomplete.

Start Here

The online articles follow active development. If you use CRAN 0.7.1, follow the release notes and documentation installed with that version.

gllvmTMB is under active development and has lifecycle experimental: the formula grammar, defaults, and extractor output may still change as the API matures. The public path above is deliberately bounded. For Gaussian models, the narrow tested-regime point evidence starts with indep() or dep(); inspect the covariance point estimate. The latent model below remains the clearest way to learn Sigma = Lambda Lambda^T + Psi and interpret covariance point estimates. Bare-bar (1 + x | g) slopes remain reserved.

What the model does

The teaching example uses one ordinary Gaussian latent() model. It splits the trait covariance matrix into shared axes plus trait-specific variance:

$$ \boldsymbol{\Sigma}

\boldsymbol{\Lambda}\boldsymbol{\Lambda}^{\mathsf T} + \boldsymbol{\Psi}, \qquad \boldsymbol{\Psi}

\operatorname{diag}(\psi_1,\ldots,\psi_T). $$

In words: total trait covariance = shared multivariate structure + response-specific variation. Read the equation from left to right:

Use latent(...) for this decomposed model, and indep(...) for a standalone diagonal baseline.

Choose a covariance source and level

The grouping factor says where a component varies; the keyword family says what covariance structure it uses. In older output, B means between-unit (unit) and W means within-unit observations (unit_obs). A unit_obs level must be nested within one unit.

The mode describes covariance among traits: indep() gives separate trait variances with no cross-trait covariance; dep() estimates an unstructured trait covariance; and latent(..., d = K) estimates a rank-K shared component. Ordinary latent() includes its diagonal Psi companion by default. For a source-specific *_latent() term, set unique = TRUE when the source-specific diagonal Psi is intended. The older paired form latent(..., unique = FALSE) + unique(...) remains accepted for compatibility; new ordinary fits can write latent(...) alone. These terms can be combined only in the regimes documented for the selected family and covariance source.

Most readers will start from a wide data frame: one row per unit, one column per trait. Use that shape directly with the traits(...) formula marker. If your data are already stacked long, use the same gllvmTMB() entry point with value ~ ..., trait =, and unit =. Internally, both paths reach the same stacked-trait model.

What "stacked-trait" Means

The user-facing data shape can be wide or long. The model itself is stacked-trait: internally, every fit sees one row per (unit, trait) observation. Five traits on 100 individuals become 500 model rows. The wide traits(...) interface does that stacking for you; the long interface lets you supply the stacked table yourself.

Install

Once the first CRAN release has been accepted and published, install the released package with:

install.packages("gllvmTMB")

To install the unreleased development build from GitHub, use pak:

install.packages("pak")
pak::pak("itchyshin/gllvmTMB")

The online site documents the current development branch and may describe features absent from 0.7.1. For this release, use the help pages and vignette installed with the package.

Then load the package and run a small smoke test:

library(gllvmTMB)

set.seed(1)
n_ind <- 30
n_rep <- 3
individual <- factor(rep(seq_len(n_ind), each = n_rep))

z <- rnorm(n_ind)[individual]
u <- matrix(rnorm(n_ind * 3, sd = 0.35), n_ind, 3)[individual, ]

df_wide <- data.frame(
  individual = individual,
  visit = rep(seq_len(n_rep), times = n_ind),
  bill_length = 0.8 * z + u[, 1] + rnorm(n_ind * n_rep, sd = 0.5),
  body_mass = 0.5 * z + u[, 2] + rnorm(n_ind * n_rep, sd = 0.5),
  wing_length = -0.3 * z + u[, 3] + rnorm(n_ind * n_rep, sd = 0.5)
)

fit <- gllvmTMB(
  traits(bill_length, body_mass, wing_length) ~ 1 +
    latent(1 | individual, d = 1),
  data = df_wide,
  unit = "individual"
)

fit
extract_communality(fit, level = "unit")
extract_Sigma_table(fit, level = "unit")

You need R 4.1.0 or newer and a working compiler toolchain because TMB models are compiled during installation. If installation fails while compiling C++, install the usual R build tools for your platform: Rtools on Windows, Xcode Command Line Tools on macOS, or the R development toolchain on Linux.

Data shapes: wide or long, one entry point

One entry point handles both shapes. Start with wide data if that is what you have on disk; use long data when your workflow already stores one response per row.

• Wide data frame -- one row per unit, one column per trait. The traits(...) LHS marker names the response columns and the RHS uses compact wide shorthand (no trait = argument needed -- the LHS is the trait spec):

  gllvmTMB(traits(t1, t2, t3) ~ 1 + latent(1 | unit, d = 2),
           data = df_wide, unit = "unit")
  

• Long data frame -- one row per (unit, trait) observation, one value column for the response:

  gllvmTMB(value ~ 0 + trait + latent(0 + trait | unit, d = 2),
           data = df_long, trait = "trait", unit = "unit")
  

Predictors go into the formula in either form, and both forms describe the same stacked-trait model. The Get started vignette fits one example both ways and checks that the log-likelihoods agree.

Missing response cells are allowed. In a wide traits(...) data frame, an NA trait value can be treated as an unobserved unit-trait cell; in long data, an NA in the response column is treated the same way. The other observed traits for that unit stay in the likelihood, and predict_missing() reconstructs masked response cells when missing = miss_control(response = "include") is used. Missing predictors default to fail-loud, but one explicitly modelled mi() predictor is supported through missing = miss_control(predictor = "model") and impute = list(...) for the covered native-Laplace Gaussian, grouped, phylogenetic, binary, ordered, and unordered fixed-effect routes. VA refuses modelled mi() predictors. Do not treat parser support as an NB2 reliability claim: the frozen NB2 latent missing-response cell produced catastrophic dispersion failures that ordinary fit diagnostics often missed; that route is not recommended for dependable inference. Ordinary missing grouping variables, offsets, weights, or design-matrix values still error because the model cannot build that row.

Current support boundary

The online Current limitations and boundaries page is supplementary and may change with the development version. For the scope and restrictions of version 0.7.1, use the 0.7.1 release notes and the help and vignettes installed with that release. In brief:

• start from an ordinary native-Laplace model and inspect fit health;
• interpret rotation-invariant Sigma, correlations, and communality before raw loading columns;
• treat structured sources, slopes, alternative integration engines, and most non-Gaussian combinations as experimental or partial unless their guide names the evidence regime;
• do not infer interval calibration from the availability of Wald, bootstrap, or profile bounds.

The first-fit correlation example reports point estimates only; profile intervals for correlations are unavailable. The separate profile_ci_total_variance() route targets diagonal per-trait total variance, not correlation. Open its installed help with ?profile_ci_total_variance for the returned lower, upper, and interval_status columns. Its certified-0.94 label marks membership in one simulated regime; it is not nominal 95% coverage or a guarantee for an individual fit. Other computed rows are labelled route-only and do not carry that coverage evidence.

gllvmTMB is for stacked-trait multivariate models. Use glmmTMB for a single-response GLMM, sdmTMB for a single-response spatial model, and drmTMB for one- or two-response distributional regression.

Citation and acknowledgements

If you use gllvmTMB, please cite the package and its TMB engine. Run citation("gllvmTMB") for formatted entries:

• gllvmTMB: Nakagawa S (2026). gllvmTMB: Generalised Linear Latent Variable Models with TMB. R package version 0.7.1. https://itchyshin.github.io/gllvmTMB/
• TMB engine: Kristensen K, Nielsen A, Berg CW, Skaug H, Bell BM (2016). TMB: Automatic Differentiation and Laplace Approximation. Journal of Statistical Software, 70(5), 1-21. https://doi.org/10.18637/jss.v070.i05 The current spatial helpers were substantially rewritten in gllvmTMB against the published SPDE/GMRF construction and public fmesher API after an earlier implementation derived from the GPL-3 sdmTMB helpers. We retain sdmTMB attribution in inst/COPYRIGHTS; the current implementation is covered by focused tests, while the broader spatial family remains partial. TMB itself is a runtime dependency rather than included code. Most of the gllvmTMB C++ engine in src/gllvmTMB.cpp is original package code written against the TMB API; inst/COPYRIGHTS separately records the same-author GPL-3 numerical and missing-predictor code reused from drmTMB. See the spatial-model guide for the public provenance, acknowledgement, and GPL-3 explanation.

Sister packages

• drmTMB fits univariate and bivariate distributional regression, including location-scale and bivariate residual-correlation models.
• glmmTMB fits single-response GLMMs.
• sdmTMB fits spatial single-response models; gllvmTMB fits multivariate stacked-trait spatial models through its own spatial_*() helper layer.
• gllvm (Niku et al. 2019; Korhonen et al. 2025 for gllvm 2.0) is the established multivariate GLLVM / ordination package, with variational, extended-variational, and Laplace approximation paths plus a matrix-in API; gllvmTMB is the TMB-Laplace alternative with stacked-trait formula grammar and the three-mode covariance-keyword grid plus common and unique modifiers.
• MCMCglmm and brms are Bayesian alternatives for multivariate phylogenetic / multi-response models; gllvmTMB returns ML point estimates with profile, Wald, or bootstrap routes where supported. Method availability does not establish calibrated interval coverage; follow the boundary in the relevant guide before reporting uncertainty.

A full scope comparison and decision matrix lives in docs/design/04-sister-package-scope.md on GitHub.

Support boundary

For version 0.7.1, the installed help, vignettes, and release notes define the documented scope. Online guides can change with development and may describe features added after this release. A formula being accepted by the parser does not guarantee that its covariance parameters are estimable from a particular data set; check fit health and follow the guidance installed with this version.