Package {colvR}

BIC from the ELBO for PLN-PCA and ZIP-PLN-PCA models

Description

Computes a BIC-like score in which the log-likelihood is replaced by the ELBO of the fitted model (higher is better):

\mathrm{BIC} = \mathrm{ELBO} - \frac{\log(n)}{2}\Big[q\{p - (q-1)/2\} + k\Big],

where q\{p - (q-1)/2\} is the number of free parameters in C (identifiable up to a rotation) and k the number of regression parameters: 2d for the ZIP-PLN-PCA model (\beta and \gamma), d for the PLN-PCA model with a vectorized design ((np) \times d) and pd with a rowwise design (n \times d). n is the number of rows of Y (sites), which are the independent units of the model.

Usage

BIC(Y, X, fit, q, model = c("ZIPLNPCA", "PLNPCA"))

Arguments

Value

A single numeric value, the BIC score.

See Also

ICL

ELBO and parameter gradients (ZIP‑PLN variational objective)

Description

Computes the Evidence Lower Bound (ELBO) and its gradients with respect to the model and variational parameters for a zero‑inflated Poisson log‑normal (ZIP‑PLN) latent factor model. This is a thin R wrapper around a fast C++ implementation, with a small preprocessing step that replaces NA values in Y by zeros before delegation.

Usage

Elbo_grad(data, params, tolxi)

Arguments

Details

This function sets NA entries of data$Y to 0 internally (they are not dropped) before calling the C++ backend Elbo_grad_Rcpp. Ensure the dimensions of X, R and the parameter matrices are compatible with Y.

Value

A list containing at least:

elbo

Scalar numeric, the ELBO value.

grad_B, grad_D, grad_C, grad_M, grad_S

Gradients w.r.t. the corresponding parameters.

See Also

Elbo_grad_Rcpp (backend C++).

Calculate the Elbo with log(S) instead of S and the gradients

Description

Calculate the Elbo with log(S) instead of S and the gradients

Usage

Elbo_grad_logS(data, params)

Arguments

Value

Elbo and gradients

95% interval for a theta 95% confidence interval for theta

Description

Computes the 95% confidence interval for theta.

Usage

IC(theta, var)

Arguments

Value

A numeric vector of length 2: lower and upper bounds.

Examples

IC(1, 0.04)

ICL from the ELBO for PLN-PCA and ZIP-PLN-PCA models

Description

Integrated Completed Likelihood: the BIC minus the entropy of the variational distribution of the latent variables (higher is better):

\mathrm{ICL} = \mathrm{BIC} - \mathcal{H}(W) - \mathcal{H}(U).

• \mathcal{H}(W): entropy of the Gaussian variational distribution of W, \frac{1}{2}\sum_{i,k} \log \sigma^2_{ik} + \frac{nq}{2}\{1 + \log(2\pi)\}, where \sigma^2 = S for the ZIP-PLN-PCA model (S is a variance) and \sigma^2 = S^2 for the PLN-PCA model (S is a standard deviation). Zero when q = 0.

• \mathcal{H}(U): entropy of the Bernoulli variational distribution of U, -\sum_{ij} \{\xi_{ij}\log\xi_{ij} + (1-\xi_{ij})\log(1-\xi_{ij})\} (ZIP-PLN-PCA model only).

Usage

ICL(Y, X, fit, q, model = c("ZIPLNPCA", "PLNPCA"))

Arguments

Value

A single numeric value, the ICL score.

See Also

BIC

Initialize parameters for a PLN-PCA with missing data

Description

Provides a quick, SVD‑based initialization of model and variational parameters from a (possibly sparse) count matrix Y and a design matrix X. The routine fits a (log‑transformed) linear model to obtain regression coefficients and uses the SVD of residuals to initialize the latent structure (loadings and variational means).

Usage

Init(Y, X, q)

Arguments

Details

Missing values in Y are handled via na.exclude in the linear model; residuals at missing entries are then set to zero before the SVD.

Value

A list with elements:

B

Matrix of regression coefficients (dimensions follow the chosen design; typically (1 x d) in the rowwise case).

C

Loadings matrix (p x q) for the latent factors.

M

Variational means of the latent factors (n x q).

S

Variational standard deviations (initialized to a small constant; n x q).

See Also

MatrixToVector, VectorToMatrix

Examples

set.seed(1)
n <- 30; p <- 8; d <- 2; q <- 2
Y <- matrix(rpois(n * p, 2), n, p)
X <- cbind(1, rnorm(n))          # rowwise design
init <- Init(Y, X, q)
str(init)

Initialize parameters for the ZIP case (zero-inflated)

Description

SVD-based initialization of parameters for a zero-inflated Poisson log-normal latent factor model (ZIP-PLN). Regression coefficients for the abundance part (B) are obtained by regressing log(1+vec(Y)) on X; zero-inflation coefficients (D) come from a logistic regression of I(Y>0) on X. The latent structure is initialized from the SVD of the residual matrix.

Usage

Init_ZIP(Y, X, q)

Arguments

Value

A list with elements:

B

Abundance (Poisson) regression coefficients (1 x d).

D

Zero-inflation (logit) regression coefficients (1 x d).

C

Loadings matrix (p x q).

M

Variational means of latent factors (n x q).

S

Variational scale parameters.

See Also

Init for the non-ZI initializer; MatrixToVector, VectorToMatrix

Examples

set.seed(1)
n <- 30; p <- 10; d <- 3; q <- 2
Y <- matrix(rpois(n*p, 2), n, p)
X <- cbind(1, rnorm(n*p), rnorm(n*p))  # (n*p) x d, vectorized design
init <- Init_ZIP(Y, X, q)
str(init)

Init_ZIP_q0

Description

Parameters initialisation in the zero inflated case without the latent factors

Usage

Init_ZIP_q0(Y, X, q)

Arguments

Value

A list with elements:

B

Matrix of Poisson regression coefficients (1 x d).

D

Matrix of logistic regression coefficients (1 x d).

MatrixToVector

Description

Convert a numeric matrix to a numeric vector (column-major order). Implemented in C++ via Rcpp/Armadillo.

Usage

MatrixToVector(matrix)

Arguments

Value

Numeric vector of length n*p.

See Also

VectorToMatrix

PLN-PCA with missing data (variational fit + imputation)

Description

Fits a Poisson log-normal PCA model (PLN-PCA) to a count matrix with missing values, using a variational objective optimized by NLOpt-based routines. The function estimates model/variational parameters and returns expected counts to impute missing entries.

Usage

Miss.PLNPCA(Y, X, q, O = NULL, w = NULL, params = NULL, config = NULL)

Arguments

Details

Two designs for X are supported:

1. Rowwise design (nrow(X) == n): one row per sample.

2. Vectorized design (nrow(X) == n*p): X aligns with vec(Y) (vectorization by columns).

Value

A list with components:

mStep

List with beta (1 x d) and C (p x q).

eStep

List with M (n x q) and S (n x q).

pred

List with A and predicted, both equal to the n x p matrix of expected counts used for imputation:

A = \exp\!\big(O + X B + M C^\top + 0.5\,(S\odot S)\,(C\odot C)^\top\big),

where \odot denotes the Hadamard product and X B is reshaped to n x p when X is vectorized.

iter

Integer, number of iterations.

elboPath

Numeric vector of objective (ELBO) values over iterations.

elbo

Final ELBO value.

params.init

The initial parameters used.

monitoring

Optimizer log/diagnostics as returned by the backend.

See Also

Init, PLNPCA_param MatrixToVector, VectorToMatrix, Elbo_grad

Examples

set.seed(1)
n <- 30; p <- 5; q <- 2
Y <- matrix(rpois(n * p, 2), n, p)
Y[sample(n * p, 20)] <- NA                        # missing entries
X <- cbind(1, rnorm(n))                           # rowwise design, n x d

fit <- Miss.PLNPCA(Y = Y, X = X, q = q)
fit$elbo
str(fit$pred$A)

ZI‑PLN-PCA with missing data (variational fit + imputation)

Description

Fits a zero‑inflated Poisson log‑normal (ZI‑PLN-PCA) latent factor model to a count matrix with missing values. The routine optimizes a variational objective with NLOpt backends and returns parameter estimates, variational parameters and an imputed matrix.

Usage

Miss.ZIPLNPCA(Y, X, q, params = NULL, config = NULL, tolS = NULL, tolxi = NULL)

Arguments

Details

This function supports latent rank q >= 0. When q = 0, it reduces to a ZIP regression (no latent factors). When q > 0, it fits a ZIP‑PLN factor model.

Internally, a binary mask R = 1_{observed}(Y) is created; a copied matrix Y.na sets missing entries to zero for objective evaluation. The optimizer bounds for S are taken from tolS. Ensure that the vectorization and parameter stacking used in the optimizer are consistent with the shapes listed above.

Value

A list with components:

mStep

List of model parameters. For q = 0: gamma (d x 1) and beta (d x 1). For q > 0: same plus the loading matrix C (p x q).

eStep

List of variational parameters. For q = 0: only xi (n x p). For q > 0: M (n x q), S (n x q) and xi (n x p).

pred

List with predictors and expected counts: mu (n x p, abundance mean), nu (n x p, zero‑inflation mean), A (n x p, PLN expectation), predicted (n x p, ZIP expectation for all entries: \xi \odot A, with A = \exp( XB + M C^\top + 0.5\, S\, (C\odot C)^\top ), S being the variational variances).

imputed

n x p matrix equal to predicted at missing entries of Y, and Y elsewhere (ZIP expectation).

iter

Integer, number of iterations.

elboPath

Numeric vector of objective (ELBO) values over iterations.

elbo

Final ELBO value.

params.init

Parameters as recorded from the backend call.

monitoring

Optimizer diagnostics/logs from the backend.

gradB, gradD, gradC, gradM, gradS

Gradients of the ELBO with respect to the corresponding parameters, obtained via Elbo_grad.

See Also

Init_ZIP, Init_ZIP_q0, Elbo_grad, VectorToMatrix

Examples

set.seed(1)
n <- 30; p <- 5; d <- 2; q <- 2
X <- cbind(1, rnorm(n * p))                       # (n*p) x d design
theta <- list(B = matrix(c(1, 0.5)), D = matrix(c(1, -0.5)),
              C = matrix(rnorm(p * q, sd = 0.5), p, q))
Y <- Simul(X, theta, list(n = n, p = p, d = d, q = q))$Y
Y[sample(n * p, 20)] <- NA                        # missing entries

fit <- Miss.ZIPLNPCA(Y, X, q)
str(fit$mStep)
fit$imputed[is.na(Y)][1:5]                        # imputed values

ZI‑PLN-PCA with missing data using log(S) parametrization

Description

Fits a zero‑inflated Poisson log‑normal (ZI‑PLN-PCA) latent factor model to a count matrix with missing values, using a variational objective and an alternative parametrization on the variational scales:

\code{log(S)} \text{ instead of } S.

This guarantees positivity of \(S\) and allows simple box constraints on \(log(S) \) via tolLogS.

Usage

Miss.ZIPLNPCA.logS(
  Y,
  X,
  q,
  params = NULL,
  config = NULL,
  tolxi = NULL,
  tolLogS = NULL
)

Arguments

Details

Missing entries are handled by a mask R = 1_{observed}(Y); a working matrix Y.na sets missings to 0 for the objective evaluation. Box constraints are set on logS via config$upper_bounds, using tolLogS. Make sure X matches vec(Y).

Value

A list with components:

mStep

Model parameters: gamma (d x 1), beta (d x 1), and loadings C (p x q).

eStep

Variational parameters: means M (n x q), scales S (n x q), and logistic bound parameters xi (n x p).

pred

List with predictors and expected counts: mu (n x p), nu (n x p), backend Poisson mean A (n x p), and predicted (n x p, ZIP expectation for all entries: \xi \odot A, with A = \exp( XB + M C^\top + 0.5\, S\, (C\odot C)^\top ), S being the variational variances).

imputed

n x p matrix equal to predicted at missing entries of Y, and Y elsewhere.

iter

Number of iterations; elboPath (trajectory of ELBO); elbo (final ELBO).

params.init

Initial parameters passed to the backend (with logS added).

monitoring

Optimizer diagnostics/logs.

gradB, gradD, gradC, gradM, gradS

ELBO gradients w.r.t. corresponding parameters (via Elbo_grad).

See Also

Miss.ZIPLNPCA for the S parametrization, Init_ZIP, Elbo_grad

Examples

set.seed(1)
n <- 30; p <- 5; d <- 2; q <- 2
X <- cbind(1, rnorm(n * p))                       # (n*p) x d design
theta <- list(B = matrix(c(1, 0.5)), D = matrix(c(1, -0.5)),
              C = matrix(rnorm(p * q, sd = 0.5), p, q))
Y <- Simul(X, theta, list(n = n, p = p, d = d, q = q))$Y
Y[sample(n * p, 20)] <- NA                        # missing entries

fit <- Miss.ZIPLNPCA.logS(Y, X, q, tolLogS = 2)   # cap logS
fit$elbo
str(fit$eStep$S)

ZI‑PLN-PCA (missing data) with parameterwise optimization steps

Description

Fits a zero‑inflated Poisson log‑normal (ZI‑PLN-PCA) latent factor model to a count matrix with missing values using a blockwise optimization strategy. At each outer iteration, parameters are updated by activating one block among {B, D, C, M, S} while keeping the others fixed, via an NLOpt backend. The loop stops when both parameter and ELBO changes are below thresholds or when maxiter is reached.

Usage

Miss.ZIPLNPCA_Steps(Y, X, q, params = NULL, config_vem = NULL, config = NULL)

Arguments

Details

Missing entries are handled through a binary mask and a working copy of Y with zeros at missing locations for the objective evaluation.

A binary mask R = 1_{observed}(Y) is built; a working matrix Y.na replaces missings by 0 for the objective. Box constraints for S are set using config_vem$tolS and injected into config$upper_bounds and config$lower_bounds. Each block update calls the backend nlopt_optimize_ZIP_Steps(data, params, config, tolxi, active_blocks) with a single active block at a time.

Predicted mean: in this implementation, the Poisson mean used for the R‑side recomputation is

\exp\!\big( \mu + M C^\top + 0.5\, S \,(C\odot C)^\top \big),

where \mu = X B reshaped into n x p. Note that other functions in le package emploient 0.5\,(S\odot S)\,(C\odot C)^\top. Vérifie que la paramétrisation voulue est cohérente avec le backend.

Value

A list with components:

mStep

Model parameters: gamma (d x 1), beta (d x 1), loadings C (p x q).

eStep

Variational parameters: M (n x q), S (n x q), logistic bound parameters xi (n x p).

pred

List with predictors and expected counts: mu (n x p), nu (n x p), backend mean A (n x p), and predicted (n x p, ZIP expectation for all entries: \xi \odot A, with A = \exp( XB + M C^\top + 0.5\, S\, (C\odot C)^\top ), S being the variational variances).

imputed

n x p matrix equal to predicted at missing entries of Y, and Y elsewhere.

iter

Number of outer iterations performed.

elboPath

Numeric vector of ELBO values across outer iterations.

elbo

Final ELBO value.

params.init

Parameters used for initialization.

monitoring

List with status (stopping reason) and iterations.

gradB, gradD, gradC, gradM, gradS

ELBO gradients w.r.t. each parameter block (from Elbo_grad) at the solution.

See Also

Miss.ZIPLNPCA, Miss.ZIPLNPCA.logS, Init_ZIP, Elbo_grad

Examples

set.seed(1)
n <- 30; p <- 5; d <- 2; q <- 2
X <- cbind(1, rnorm(n * p))                       # (n*p) x d design
theta <- list(B = matrix(c(1, 0.5)), D = matrix(c(1, -0.5)),
              C = matrix(rnorm(p * q, sd = 0.5), p, q))
Y <- Simul(X, theta, list(n = n, p = p, d = d, q = q))$Y
Y[sample(n * p, 20)] <- NA                        # missing entries

fit <- Miss.ZIPLNPCA_Steps(Y, X, q)
fit$elbo
plot(fit$elboPath, type = "l", xlab = "Outer iteration", ylab = "ELBO")

ZI‑PLN-PCA (missing data) — variational E‑step solver

Description

Fits a zero‑inflated Poisson log‑normal (ZI‑PLN-PCA) latent factor model on a count matrix with missing values using a single call to a variational optimization backend (VE). Returns model/variational parameters and expected Poisson means suitable for imputation and prediction.

Usage

Miss.ZIPLNPCA_VE(Y, X, q, params = NULL, config_vem = NULL, config = NULL)

Arguments

Details

Missing entries are handled via a binary mask R = 1_{observed}(Y), and a working copy Y.na with zeros at missing locations for the objective evaluation. Box constraints on S are injected into config$lower_bounds and config$upper_bounds using config_vem$tolS.

Predicted mean: ici, la recomposition côté R utilise

\exp\!\big( X B + M C^\top + 0.5\, S \,(C\odot C)^\top \big).

D'autres fonctions du package emploient 0.5\,(S\odot S)\,(C\odot C)^\top. Vérifie et harmonise selon la paramétrisation attendue par ton backend.

Value

A list with components:

mStep

Model parameters: gamma (d x 1), beta (d x 1), loadings C (p x q).

eStep

Variational parameters: M (n x q), S (n x q), xi (n x p).

pred

List with predictors and expected counts: mu (n x p), nu (n x p), backend mean A (n x p), and predicted (n x p, ZIP expectation for all entries: \xi \odot A, with A = \exp( XB + M C^\top + 0.5\, S\, (C\odot C)^\top ), S being the variational variances).

elbo

Final ELBO value.

params.init

Initial parameters used.

monitoring

Backend diagnostics (if provided).

elbo1, elbo2, elbo3, elbo4, elbo5

Decomposition terms of the ELBO (as returned by the backend).

Examples

set.seed(1)
n <- 30; p <- 5; d <- 2; q <- 2
X <- cbind(1, rnorm(n * p))                       # (n*p) x d design
theta <- list(B = matrix(c(1, 0.5)), D = matrix(c(1, -0.5)),
              C = matrix(rnorm(p * q, sd = 0.5), p, q))
Y <- Simul(X, theta, list(n = n, p = p, d = d, q = q))$Y
Y[sample(n * p, 20)] <- NA                        # missing entries

fit <- Miss.ZIPLNPCA_VE(Y, X, q)
fit$elbo
str(fit$eStep)

Predictive simulations and intervals

Description

Draws parameter samples using the sandwich variance V_theta, simulates predictive counts with zero-inflation and returns per-cell prediction intervals. Two types of intervals are available: conditional (latent variables drawn from their variational posterior, after one VE step per draw) and marginal (latent variables drawn from their prior).

Usage

Predictions(
  Y,
  X,
  fit,
  MC,
  type = c("conditional", "marginal"),
  probs = c(0, 0.9),
  output = "intervals",
  cl = NULL,
  verbose = TRUE
)

Arguments

Value

A list with elements:

• lower, upper: n x p matrices of predictive quantiles at levels probs.

• draws (if requested): list with count (Poisson draws) and presence (Bernoulli draws U), arrays n x p x MC. The prediction is count * presence.

• latent (if requested): list with Z, array n x p x MC of Gaussian latent draws, and for the conditional type M, S (arrays n x q x MC) and xi (array n x p x MC) from the VE steps.

• params (if requested): list with gamma, beta (matrices MC x d) and C (matrix MC x (p*q), column-major vectorisation of C).

• settings: list with type, probs and MC.

See Also

V_theta, Miss.ZIPLNPCA_VE

Examples

set.seed(1)
n <- 30; p <- 5; d <- 2; q <- 2
X <- cbind(1, rnorm(n * p))                       # (n*p) x d design
theta <- list(B = matrix(c(1, 0.5)), D = matrix(c(1, -0.5)),
              C = matrix(rnorm(p * q, sd = 0.5), p, q))
Y <- Simul(X, theta, list(n = n, p = p, d = d, q = q))$Y
Y[sample(n * p, 20)] <- NA                        # missing entries
fit <- Miss.ZIPLNPCA(Y, X, q)


# Conditional intervals (default), 90% upper bound
pi_cond <- Predictions(Y, X, fit, MC = 20)
pi_cond$upper[1:3, ]

# Marginal intervals at other levels, with the draws
pi_marg <- Predictions(Y, X, fit, MC = 20, type = "marginal",
                       probs = c(0.05, 0.95), output = "draws")
dim(pi_marg$draws$count)

Simulate zero-inflated Poisson log-normal PCA data

Description

Generates simulated observations Y under a ZIP-LN-PCA structure from parameters in theta and dimensions in dim.

Usage

Simul(X, theta, dim)

Arguments

Details

Relies on VectorToMatrix() being available in the package.

Value

A list with elements:

• Y: simulated counts (n x p)

• W: latent scores (n x q)

• U: zero-inflation indicators (n x p)

• Z: Poisson draws before zero-inflation (n x p)

• Lambda: Poisson intensities (n x p)

• mu: mean matrix (n x p)

Examples

set.seed(1)
n <- 30; p <- 5; d <- 2; q <- 2
X <- cbind(1, rnorm(n * p))                       # (n*p) x d design
theta <- list(B = matrix(c(1, 0.5)), D = matrix(c(1, -0.5)),
              C = matrix(rnorm(p * q, sd = 0.5), p, q))
sim <- Simul(X, theta, list(n = n, p = p, d = d, q = q))
str(sim)
mean(sim$Y == 0)                                  # proportion of zeros

Variance-covariance matrix of theta

Description

Computes V(\hat{\theta}) using a sandwich (robust) variance formula.

Usage

V_theta(Y, X, fit, ginv_tol = 1e-12, verbose = TRUE)

Arguments

Value

A symmetric variance-covariance matrix for theta.

VectorToMatrix

Description

Convert a numeric vector to a numeric matrix (column-major order). Implemented in C++ via Rcpp/Armadillo.

Usage

VectorToMatrix(vector, n, p)

Arguments

Value

Numeric matrix (n x p).

See Also

MatrixToVector

Wrapper for 'lori::covmat'

Description

Thin helper that calls lori::covmat() without requiring users to attach the lori package. It constructs the block-structured covariate matrix X (with n \times p rows) from site-level covariates R, year-level covariates C, and optional site–year covariates E. Any of R, C, or E can be NULL to omit that block.

Usage

covmat(n, p, R = NULL, C = NULL, E = NULL, center = FALSE)

Arguments

Value

A numeric matrix with n \times p rows and d = d_R + d_C + d_E columns (when present), identical to the value returned by lori::covmat().

See Also

covmat

Examples

if (requireNamespace("lori", quietly = TRUE)) {
  set.seed(1)
  n <- 3; p <- 2
  R <- matrix(rnorm(n * 2), nrow = n, ncol = 2)  # site-level (d_R = 2)
  C <- matrix(rnorm(p * 2), nrow = p, ncol = 2)  # year-level (d_C = 2)
  X <- covmat(n, p, R = R, C = C)
  dim(X)  # 6 x 4
}

Model selection over candidate latent dimensions (BIC or ICL)

Description

For each value in latents, fits a model with fun and computes the chosen criterion (BIC or ICL). Returns the criterion values, the latent dimension that maximizes the criterion and the corresponding fit.

Usage

select_model_bic(
  Y,
  X,
  fun,
  latents,
  model = c("ZIPLNPCA", "PLNPCA"),
  criterion = c("BIC", "ICL")
)

Arguments

Details

A progress bar is displayed via pbapply. The function checks that model matches the fits returned by fun: a ZIP-PLN-PCA fit contains mStep$gamma, a PLN-PCA fit does not.

Value

A list with elements:

• criterion: the criterion used.

• values: numeric vector of criterion values, named by latents.

• q_star: the latent dimension maximizing the criterion.

• fit_star: the fit obtained with q_star.

See Also

BIC, ICL

Examples

set.seed(1)
n <- 30; p <- 5; d <- 2; q <- 2
X <- cbind(1, rnorm(n * p))                       # (n*p) x d design
theta <- list(B = matrix(c(1, 0.5)), D = matrix(c(1, -0.5)),
              C = matrix(rnorm(p * q, sd = 0.5), p, q))
Y <- Simul(X, theta, list(n = n, p = p, d = d, q = q))$Y
Y[sample(n * p, 20)] <- NA                        # missing entries


sel <- select_model_bic(Y, X, Miss.ZIPLNPCA, latents = 1:3)
sel$values
sel$q_star
fit <- sel$fit_star

sel_icl <- select_model_bic(Y, X, Miss.ZIPLNPCA, latents = 1:3,
                            criterion = "ICL")
sel_icl$q_star

Waterbird count data

Description

Counts of a waterbird species from a multi-year, multi-site monitoring program. The data are incomplete: many site-year combinations were not surveyed and are recorded as missing values. Counts also contain a large proportion of zeros, which makes the data a suitable example for the zero-inflated Poisson log-normal model implemented in the package. Sites and years are anonymized.

Usage

data(waterbird)

Format

A named list with two elements:

Y

Numeric count matrix with 419 rows (sites, site_001 to site_419) and 17 columns (years, year_01 to year_17). Unobserved site-year combinations are NA.

X

Numeric design matrix with 419 \times 17 = 7123 rows (site-year combinations, stacked year by year, i.e. by blocks of 419 sites) and 7 columns: intercept (column of ones), and the standardized covariates dist_coast (distance to the coast), dist_city (distance to the nearest city), elevation, year (linear time trend), spring_temp_anomaly (spring temperature anomaly) and agricultural_land (percentage of agricultural land).

Source

Anonymized data from a waterbird monitoring program.

Examples

data(waterbird, package = "colvR")
str(waterbird, max.level = 1)
mean(is.na(waterbird$Y))                # proportion of missing entries
mean(waterbird$Y == 0, na.rm = TRUE)    # proportion of zeros