GPModel_shared_params: Documentation for parameters shared by 'GPModel', 'gpb.cv',...
In gpboost: Combining Tree-Boosting with Gaussian Process and Mixed Effects Models

GPModel_shared_params

R Documentation

Documentation for parameters shared by `GPModel`, `gpb.cv`, and `gpboost`

Description

Documentation for parameters shared by GPModel, gpb.cv, and gpboost

Usage

GPModel_shared_params(likelihood = NULL, likelihood_additional_param = NULL,
  group_data = NULL, group_rand_coef_data = NULL,
  ind_effect_group_rand_coef = NULL,
  drop_intercept_group_rand_effect = NULL, gp_coords = NULL,
  gp_rand_coef_data = NULL, cov_function = NULL, cov_fct_shape = NULL,
  gp_approx = NULL, num_parallel_threads = NULL, GPU_use = NULL,
  cov_fct_taper_range = NULL, cov_fct_taper_shape = NULL,
  num_neighbors = NULL, vecchia_ordering = NULL,
  ind_points_selection = NULL, num_ind_points = NULL,
  cover_tree_radius = NULL, matrix_inversion_method = NULL, seed = NULL,
  vecchia_pred_type = NULL, num_neighbors_pred = NULL,
  cg_delta_conv_pred = NULL, nsim_var_pred = NULL,
  rank_pred_approx_matrix_lanczos = NULL, cluster_ids = NULL,
  weights = NULL, likelihood_learning_rate = NULL, free_raw_data = NULL,
  y = NULL, X = NULL, params = NULL, offset = NULL,
  fixed_effects = NULL, group_data_pred = NULL,
  group_rand_coef_data_pred = NULL, gp_coords_pred = NULL,
  gp_rand_coef_data_pred = NULL, cluster_ids_pred = NULL, X_pred = NULL,
  predict_cov_mat = NULL, predict_var = NULL, sample_posterior = NULL,
  sample_prior = NULL, num_post_samples = NULL, num_prior_samples = NULL,
  std_err = NULL, vecchia_approx = NULL, num_data = NULL)

Arguments

`likelihood`	A `string` specifying the likelihood function (distribution) of the response variable. Available options: "gaussian" "bernoulli_logit": Bernoulli likelihood with a logit link function for binary classification. Aliases: "binary", "binary_logit" "bernoulli_probit": Bernoulli likelihood with a probit link function for binary classification. Aliases: "binary_probit" "quasi_bernoulli_logit": quasi-Bernoulli likelihood with a logit link function for y in [0,1]. Aliases: "quasi_binary", "quasi_binary_logit" "quasi_bernoulli_probit": quasi-Bernoulli likelihood with a probit link function for y in [0,1]. Aliases: "quasi_binary_probit" "binomial_logit": Binomial likelihood with a logit link function. The response variable `y` needs to contain proportions of successes / trials, and the `weights` parameter needs to contain the numbers of trials. Aliases: "binomial" "binomial_probit": Binomial likelihood with a probit link function. The response variable `y` needs to contain proportions of successes / trials, and the `weights` parameter needs to contain the numbers of trials "beta_binomial": Beta-binomial likelihood with a logit link function. The response variable `y` needs to contain proportions of successes / trials, and the `weights` parameter needs to contain the numbers of trials. Aliases: "betabinomial", "beta-binomial" "poisson": Poisson likelihood with a log link function "negative_binomial": negative binomial likelihood with a log link function (aka "nbinom2", "negative_binomial_2"). The variance is mu * (mu + r) / r, mu = mean, r = shape, with this parametrization "negative_binomial_1": Negative binomial 1 (aka "nbinom1") likelihood with a log link function. The variance is mu * (1 + phi), mu = mean, phi = dispersion, with this parametrization "gamma": Gamma likelihood with a log link function "lognormal": Log-normal likelihood with a log link function "beta" : Beta likelihood with a logit link function (parametrization of Ferrari and Cribari-Neto, 2004) "t": t-distribution (e.g., for robust regression) "t_fix_df": t-distribution with the degrees-of-freedom (df) held fixed and not estimated The degrees-of-freedom (df) can be set via the `likelihood_additional_param` parameter. The default is df = 2 "quantile_regression" / "asymmetric_laplace" : an asymmetric Laplace likelihood for quantile regression, aliases: "asymmetric_laplace", "quantile_regression" The quantile can be set via the `likelihood_additional_param` parameter. The default is quantile = 0.5 "zero_inflated_gamma": Zero-inflated gamma likelihood. The log-transformed mean of the response variable equals the sum of fixed and random effects, E(y) = mu = exp(F(X) + Zb), and the rate parameter equals (1-p0) * gamma / mu, where p0 is the zero-inflation probability and gamma the shape parameter. I.e., the rate parameter depends on F(X) + Zb, and p0 and gamma are (univariate auxiliary) parameters that are estimated. Note that E(y) = mu above refers the the mean of the entire distribution and not just the positive part "zero_censored_power_transformed_normal": Likelihood of a censored and power-transformed normal variable for modeling data with a point mass at 0 and a continuous distribution for y > 0. The model used is Y = max(0,X)^lambda, X ~ N(mu, sigma^2), where mu = F(X) + Zb, and sigma and lambda are (auxiliary) parameters that are estimated. For more details on this model, see Sigrist et al. (2012, AOAS) "A dynamic nonstationary spatio-temporal model for short term prediction of precipitation" "zoctn": Zero-one censored transformed normal likelihood for modeling data in [0,1] with point masses at 0 and 1 and a continuous distribution on (0,1). The model used is Z ~ N(mu, sigma^2), W = max(min(Z,1),0), and Y = g(W), where g(x) = expit(a + b * logit(x)) for x in (0,1), mu = F(X) + Zb, and sigma, a, and b are (auxiliary) parameters that are estimated. For more details on this model, see Qiang and Sigrist (2026) "zero_one_censored_transformed_beta": Zero-one censored transformed beta likelihood for modeling data in [0,1] with point masses at 0 and 1 and a continuous distribution on (0,1). If T follows a beta distribution with mean mu = expit(F(X) + Zb) and precision phi, the observed response is obtained by applying the linear transformation Y = (1 + 2u) * T - u and censoring the result to [0,1]. The precision phi and shift u are (auxiliary) parameters that are estimated. For more details on this model, see Kosmidis and Zeileis (2025) "zero_one_censored_shifted_gamma": Zero-one censored shifted gamma likelihood for modeling data in [0,1] with point masses at 0 and 1 and a continuous distribution on (0,1). The model used is Y = min(max(Z - xi, 0), 1), where Z follows a gamma distribution with mean mu = exp(F(X) + Zb) and shape k. The shape k and shift xi are (auxiliary) parameters that are estimated. For more details on this model, see Sigrist and Stahel (2011) "gaussian_heteroscedastic_fixed_and_random": Gaussian likelihood where both the mean and the variance are related to fixed and random effects. This is currently only implemented for GPs with a 'vecchia' approximation "gaussian_heteroscedastic": Gaussian likelihood where the mean is related to fixed and random effects and the log-error variance is related to fixed effects only (covariates and / or the GPBoost tree-boosting algorithm; no random effects / GPs for the variance) Note: the first lines in the likelihoods source file contain additional comments on the specific parametrizations used Note: other likelihoods can be implemented upon request
`likelihood_additional_param`	A `numeric` specifying an additional parameter for the `likelihood` which cannot be estimated for this `likelihood` (e.g., degrees of freedom for `likelihood = "t_fix_df"`). This is not to be confused with any auxiliary parameters that can be estimated and accessed through the function `get_aux_pars` after estimation. Note that this `likelihood_additional_param` parameter is irrelevant for many likelihoods. If `likelihood_additional_param = NULL`, the following internal default values are used: df = 2 for likelihood = "t_fix_df" quantile = 0.5 for likelihood = "asymmetric_laplace"
`group_data`	A `vector` or `matrix` whose columns are categorical grouping variables. The elements being group levels defining grouped random effects. The elements of 'group_data' can be integer, double, or character. The number of columns corresponds to the number of grouped (intercept) random effects
`group_rand_coef_data`	A `vector` or `matrix` with numeric covariate data for grouped random coefficients
`ind_effect_group_rand_coef`	A `vector` with `integer` indices that indicate the corresponding categorical grouping variable (=columns) in 'group_data' for every covariate in 'group_rand_coef_data'. Counting starts at 1. The length of this index vector must equal the number of covariates in 'group_rand_coef_data'. For instance, c(1,1,2) means that the first two covariates (=first two columns) in 'group_rand_coef_data' have random coefficients corresponding to the first categorical grouping variable (=first column) in 'group_data', and the third covariate (=third column) in 'group_rand_coef_data' has a random coefficient corresponding to the second grouping variable (=second column) in 'group_data'
`drop_intercept_group_rand_effect`	A `vector` of type `logical` (boolean). Indicates whether intercept random effects are dropped (only for random coefficients). If drop_intercept_group_rand_effect[k] is TRUE, the intercept random effect number k is dropped / not included. Only random effects with random slopes can be dropped.
`gp_coords`	A `matrix` with numeric coordinates (= inputs / features) for defining Gaussian processes
`gp_rand_coef_data`	A `vector` or `matrix` with numeric covariate data for Gaussian process random coefficients
`cov_function`	A `string` specifying the covariance function for the Gaussian process. Available options: "matern": Matern covariance function with the smoothness specified by the `cov_fct_shape` parameter (using the parametrization of Rasmussen and Williams, 2006) "matern_estimate_shape": same as "matern" but the smoothness parameter is also estimated "matern_space_time": Spatio-temporal Matern covariance function with different range parameters for space and time. Note that the first column in `gp_coords` must correspond to the time dimension "space_time_gneiting": Spatio-temporal covariance function given in Eq. (16) of Gneiting (2002). Note that the first column in `gp_coords` must correspond to the time dimension. This covariance has seven parameters (in the following order: sigma2, a, c, alpha, nu, beta, delta) which are all estimated by default. You can disable the estimation of some of these parameter using the 'estimate_cov_par_index' argument of the `params` argument in either the `fit` function of a `gp_model` object or the `set_optim_params` function prior to estimation. "matern_ard": anisotropic Matern covariance function with Automatic Relevance Determination (ARD), i.e., with a different range parameter for every coordinate of `gp_coords` "matern_ard_estimate_shape": same as "matern_ard" but the smoothness parameter is also estimated "exponential": Exponential covariance function (using the parametrization of Diggle and Ribeiro, 2007) "gaussian": Gaussian, aka squared exponential, covariance function (using the parametrization of Diggle and Ribeiro, 2007) "gaussian_ard": anisotropic Gaussian, aka squared exponential, covariance function with Automatic Relevance Determination (ARD), i.e., with a different range parameter for every coordinate of `gp_coords` "powered_exponential": powered exponential covariance function with the exponent specified by the `cov_fct_shape` parameter (using the parametrization of Diggle and Ribeiro, 2007) "wendland": Compactly supported Wendland covariance function (using the parametrization of Bevilacqua et al., 2019, AOS) "linear": linear covariance function. This corresponds to a Bayesian linear regression model with a Gaussian prior on the coefficients with a constant variance diagonal prior covariance, and the prior variance is estimated using empirical Bayes. "hurst": Hurst covariance function cov(s, s') = (sigma2 / 2) * ( \|\|s\|\|^(2H) + \|\|s'\|\|^(2H) - \|\|s - s'\|\|^(2H) ). For H = 0.5, this corresponds to Brownian motion (-> see the 'estimate_cov_par_index' argument) "hurst_ard": Hurst covariance function with with Automatic Relevance Determination (ARD), i.e., with a different range parameter for every coordinate of “gp_coords“ except for the first coordinate which has a range parameter of 1 due to identifiability with the marginal variance: `cov(s, s') = (\sigma^2/2)\left[ \left(s_1^2 + \sum_{k=2}^d (s_k/l_k)^2\right)^H + \left({s'}_1^2 + \sum_{k=2}^d ({s'}_k/l_k)^2\right)^H - \left((s_1-{s'}_1)^2 + \sum_{k=2}^d ((s_k-{s'}_k)/l_k)^2\right)^H \right]`
`cov_fct_shape`	A `numeric` specifying the shape parameter of the covariance function (e.g., smoothness parameter for Matern and Wendland covariance) This parameter is irrelevant for some covariance functions such as the exponential or Gaussian
`gp_approx`	A `string` specifying the large data approximation for Gaussian processes. Available options: "none": No approximation "vecchia": Vecchia approximation; see Sigrist (2022, JMLR) for more details "full_scale_vecchia": Vecchia-inducing points full-scale (VIF) approximation; see Gyger, Furrer, and Sigrist (2025) for more details "tapering": The covariance function is multiplied by a compactly supported Wendland correlation function "fitc": Fully Independent Training Conditional approximation aka modified predictive process approximation; see Gyger, Furrer, and Sigrist (2024) for more details "full_scale_tapering": Full-scale approximation combining an inducing point / predictive process approximation with tapering on the residual process; see Gyger, Furrer, and Sigrist (2024) for more details "vecchia_latent": similar as "vecchia" but a Vecchia approximation is applied to the latent Gaussian process for likelihood == "gaussian". For likelihood != "gaussian", "vecchia" and "vecchia_latent" are equivalent
`num_parallel_threads`	An `integer` specifying the number of parallel threads for OMP. If num_parallel_threads = NULL, all available threads are used
`GPU_use`	A `boolean`. If TRUE, GPU acceleration will be used if supported
`cov_fct_taper_range`	A `numeric` specifying the range parameter of the Wendland covariance function and Wendland correlation taper function. We follow the notation of Bevilacqua et al. (2019, AOS)
`cov_fct_taper_shape`	A `numeric` specifying the shape (=smoothness) parameter of the Wendland covariance function and Wendland correlation taper function. We follow the notation of Bevilacqua et al. (2019, AOS)
`num_neighbors`	An `integer` specifying the number of neighbors for the Vecchia and VIF approximations. Internal default values if NULL: 20 for gp_approx = "vecchia" 30 for gp_approx = "full_scale_vecchia" Note: for prediction, the number of neighbors can be set through the 'num_neighbors_pred' parameter in the 'set_prediction_data' function. By default, num_neighbors_pred = 2 * num_neighbors. Further, the type of Vecchia approximation used for making predictions is set through the 'vecchia_pred_type' parameter in the 'set_prediction_data' function
`vecchia_ordering`	A `string` specifying the ordering used in the Vecchia approximation. Available options: "none": the default ordering in the data is used "random": a random ordering "time": ordering accorrding to time (only for space-time models) "time_random_space": ordering according to time and randomly for all spatial points with the same time points (only for space-time models)
`ind_points_selection`	A `string` specifying the method for choosing inducing points Available options: "kmeans++: the k-means++ algorithm "cover_tree": the cover tree algorithm "random": random selection from data points
`num_ind_points`	An `integer` specifying the number of inducing points / knots for FITC, full_scale_tapering, and VIF approximations. Internal default values if NULL: 500 for gp_approx = "FITC" and gp_approx = "full_scale_tapering" 200 for gp_approx = "full_scale_vecchia"
`cover_tree_radius`	A `numeric` specifying the radius (= "spatial resolution") for the cover tree algorithm
`matrix_inversion_method`	A `string` specifying the method used for inverting covariance matrices. Available options: "default": iterative methods where possible, otherwise Cholesky factorization "cholesky": Cholesky factorization "iterative": iterative methods. A combination of the conjugate gradient, the Lanczos algorithm, and other methods. This is currently only supported for the following cases: grouped random effects with more than one level likelihood != "gaussian" and gp_approx == "vecchia" (non-Gaussian likelihoods with a Vecchia-Laplace approximation) likelihood != "gaussian" and gp_approx == "full_scale_vecchia" (non-Gaussian likelihoods with a VIF approximation) likelihood == "gaussian" and gp_approx == "full_scale_tapering" (Gaussian likelihood with a full-scale tapering approximation)
`seed`	An `integer` specifying the seed used for model creation (e.g., random ordering in Vecchia approximation)
`vecchia_pred_type`	A `string` specifying the type of Vecchia approximation used for making predictions. Default value if vecchia_pred_type = NULL: "order_obs_first_cond_obs_only". Available options: "order_obs_first_cond_obs_only": Vecchia approximation for the observable process and observed training data is ordered first and the neighbors are only observed training data points "order_obs_first_cond_all": Vecchia approximation for the observable process and observed training data is ordered first and the neighbors are selected among all points (training + prediction) "latent_order_obs_first_cond_obs_only": Vecchia approximation for the latent process and observed data is ordered first and neighbors are only observed points "latent_order_obs_first_cond_all": Vecchia approximation for the latent process and observed data is ordered first and neighbors are selected among all points "order_pred_first": Vecchia approximation for the observable process and prediction data is ordered first for making predictions. This option is only available for Gaussian likelihoods
`num_neighbors_pred`	an `integer` specifying the number of neighbors for the Vecchia approximation for making predictions. Default value if NULL: num_neighbors_pred = 2 * num_neighbors
`cg_delta_conv_pred`	a `numeric` specifying the tolerance level for L2 norm of residuals for checking convergence in conjugate gradient algorithms when being used for prediction Default value if NULL: 1e-3
`nsim_var_pred`	an `integer` specifying the number of samples when simulation is used for calculating predictive variances Internal default values if NULL: 500 for grouped random effects 1000 for gp_approx = "vecchia" and gp_approx = "full_scale_tapering" 100 for gp_approx = "full_scale_vecchia"
`rank_pred_approx_matrix_lanczos`	an `integer` specifying the rank of the matrix for approximating predictive covariances obtained using the Lanczos algorithm Default value if NULL: 1000
`cluster_ids`	A `vector` with elements indicating independent realizations of random effects / Gaussian processes (same values = same process realization). The elements of 'cluster_ids' can be integer, double, or character.
`weights`	A `vector` with sample weights. For a Gaussian likelihood, the error variance ("nugget") for observation `i` is divided by `weights[i]`. For non-Gaussian likelihoods, the conditional log-likelihood contribution of observation `i` is multiplied by `weights[i]`. Consequently, weights affect the estimation of both random and fixed effects.
`likelihood_learning_rate`	A `numeric` with a learning rate for the likelihood for generalized Bayesian inference (only non-Gaussian likelihoods)
`free_raw_data`	A `boolean`. If TRUE, the data (groups, coordinates, covariate data for random coefficients) is freed in R after initialization
`y`	A `vector` with response variable data
`X`	A `matrix` with numeric covariate data for the fixed effects linear regression term (if there is one)
`params`	A `list` with parameters for the estimation / optimization trace: `boolean` (default = FALSE). If TRUE, information on the progress of the parameter optimization is printed init_cov_pars: `vector` with `numeric` elements (default = NULL). Initial values for covariance parameters of Gaussian process and random effects (can be NULL). The order is same as the order of the parameters in the summary function: first is the error variance (only for "gaussian" likelihood), next follow the variances of the grouped random effects (if there are any, in the order provided in 'group_data'), and then follow the marginal variance and the ranges of the Gaussian process. If there are multiple Gaussian processes, then the variances and ranges follow alternatingly. If 'init_cov_pars = NULL', an internal choice is used that depends on the likelihood and the random effects type and covariance function. If you select the option 'trace = TRUE' in the 'params' argument, you will see the first initial covariance parameters in iteration 0. init_coef: `vector` with `numeric` elements (default = NULL). Initial values for the regression coefficients (if there are any, can be NULL) init_aux_pars: `vector` with `numeric` elements (default = NULL). Initial values for additional parameters for non-Gaussian likelihoods (e.g., shape parameter of a gamma or negative_binomial likelihood) init_coef_aux_pars_from_iid_model: `boolean` (default = TRUE). If TRUE, regression coefficients and auxiliary parameters are initialized from an iid model (only for models with a linear regression term). This option is ignored if init_coef is provided. If init_aux_pars is provided but init_coef is not, only regression coefficients are initialized from an iid model. estimate_cov_par_index: `vector` with `integer` (default = -1). This allows for disabling the estimation of some (or all) covariance parameters. If 'estimate_cov_par_index' = -1, all covariance parameters are estimated. If estimate_cov_par_index != -1, this should be a vector with length equal to the number of covariance parameters, and estimate_cov_par_index[i] should be of bool type indicating whether parameter number i is estimated or not. For instance, estimate_cov_par_index = c(1,1,0) means that the first two covariance parameters are estimated and the last one not. Parameters that are not estimated are kept at their initial values (see 'init_cov_pars'). estimate_aux_pars: `boolean` (default = TRUE). If TRUE, additional parameters for non-Gaussian likelihoods are also estimated (e.g., shape parameter of a gamma or negative_binomial likelihood) optimizer_cov: `string` (default = "lbfgs"). Optimizer used for estimating covariance parameters. Options: "lbfgs", "gradient_descent", "fisher_scoring", "newton", "nelder_mead". If there are additional auxiliary parameters for non-Gaussian likelihoods, 'optimizer_cov' is also used for those optimizer_coef: `string` (default = "wls" for Gaussian likelihoods and "lbfgs" for other likelihoods). Optimizer used for estimating linear regression coefficients, if there are any (for the GPBoost algorithm there are usually none). Options: "gradient_descent", "lbfgs", "wls", "nelder_mead". Gradient descent steps are done simultaneously with gradient descent steps for the covariance parameters. "wls" refers to doing coordinate descent for the regression coefficients using weighted least squares. If 'optimizer_cov' is set to "nelder_mead" or "lbfgs", 'optimizer_coef' is automatically also set to the same value. maxit: `integer` (default = 1000). Maximal number of iterations for optimization algorithm. If maxit = -999, internal default values are used delta_rel_conv: `numeric` (default = 1E-6 except for "nelder_mead" for which the default is 1E-8). Convergence tolerance. The algorithm stops if the relative change in either the (approximate) log-likelihood or the parameters is below this value. If delta_rel_conv = -999, internal default values are used cg_max_num_it: `integer` (default = 1000). Maximal number of iterations for conjugate gradient algorithms. If cg_max_num_it = -999, internal default values are used cg_max_num_it_tridiag: `integer` (default = 1000). Maximal number of iterations for conjugate gradient algorithm when being run as Lanczos algorithm for tridiagonalization. If cg_max_num_it_tridiag = -999, internal default values are used cg_delta_conv: `numeric` (default = 1E-2). Tolerance level for L2 norm of residuals for checking convergence in conjugate gradient algorithm when being used for parameter estimation. If cg_delta_conv = -999, internal default values are used num_rand_vec_trace: `integer` (default = 50). Number of random vectors (e.g., Rademacher) for stochastic approximation of the trace of a matrix. If num_rand_vec_trace = -999, internal default values are used reuse_rand_vec_trace: `boolean` (default = TRUE). If true, random vectors (e.g., Rademacher) for stochastic approximations of the trace of a matrix are sampled only once at the beginning of the parameter estimation and reused in later trace approximations. Otherwise they are sampled every time a trace is calculated seed_rand_vec_trace: `integer` (default = 1). Seed number to generate random vectors (e.g., Rademacher) cg_preconditioner_type (`string`): Type of preconditioner used for conjugate gradient algorithms. Options for grouped random effects: "ssor" (= default): SSOR preconditioner "incomplete_cholesky": zero fill-in incomplete Cholesky factorization Options for likelihood != "gaussian" and gp_approx == "vecchia" or likelihood == "gaussian" and gp_approx == "vecchia_latent": "vadu" (= default): (B^T * (D^-1 + W) * B) as preconditioner for inverting (B^T * D^-1 * B + W), where B^T * D^-1 * B approx= Sigma^-1 "fitc": FITC / modified predictive process preconditioner for inverting (B^-1 * D * B^-T + W^-1) "pivoted_cholesky": (Lk * Lk^T + W^-1) as preconditioner for inverting (B^-1 * D * B^-T + W^-1), where Lk is a low-rank pivoted Cholesky approximation for Sigma and B^-1 * D * B^-T approx= Sigma "incomplete_cholesky": zero fill-in incomplete (reverse) Cholesky factorization of (B^T * D^-1 * B + W) using the sparsity pattern of B^T * D^-1 * B approx= Sigma^-1 Options for likelihood != "gaussian" and gp_approx == "full_scale_vecchia": "fitc" ( = default): FITC / modified predictive process preconditioner "vifdu": VIF with diagonal update preconditioner Options for likelihood == "gaussian" and gp_approx == "full_scale_tapering": "fitc" (= default): modified predictive process preconditioner "none": no preconditioner fitc_piv_chol_preconditioner_rank (`integer` ): Rank of the FITC and pivoted Cholesky decomposition preconditioners for iterative methods for Vecchia and VIF approximations (for full_scale_tapering, the same inducing points as in the approximation as used). If fitc_piv_chol_preconditioner_rank = -999, internal default values are used: 200 for the FITC preconditioner 50 for the pivoted Cholesky decomposition preconditioner convergence_criterion: `string` (default = "relative_change_in_log_likelihood", only relevant for "gradient_descent", "fisher_scoring", and "newton"). The convergence criterion used for terminating the optimization algorithm. Options: "relative_change_in_log_likelihood" or "relative_change_in_parameters". If convergence_criterion = "default", internal default values are used lr_cov: `numeric` (default = 0.1 for "gradient_descent" and 1. otherwise, only relevant for "gradient_descent", "fisher_scoring", and "newton"). Initial learning rate for covariance parameters if a gradient-based optimization method is used If lr_cov = -999, internal default values are used (0.1 for "gradient_descent" and 1. otherwise) If there are additional auxiliary parameters for non-Gaussian likelihoods, 'lr_cov' is also used for those For "lbfgs", this is divided by the norm of the gradient in the first iteration lr_coef: `numeric` (default = 0.1, only relevant for "gradient_descent", "fisher_scoring", and "newton"). Learning rate for fixed effect regression coefficients if gradient descent is used. If lr_coef = -999, internal default values are used use_nesterov_acc: `boolean` (default = TRUE, only relevant for "gradient_descent"). If TRUE Nesterov acceleration is used. This is used only for gradient descent nesterov_schedule_version: `integer` (Default = 0, only relevant for "gradient_descent"). Which version of Nesterov schedule should be used. If nesterov_schedule_version = -999, internal default values are used. acc_rate_coef: `numeric` (default = 0.5, only relevant for "gradient_descent"). Acceleration rate for regression coefficients (if there are any) for Nesterov acceleration. If acc_rate_coef = -999, internal default values are used acc_rate_cov: `numeric` (default = 0.5, only relevant for "gradient_descent"). Acceleration rate for covariance parameters for Nesterov acceleration. If acc_rate_cov = -999, internal default values are used momentum_offset: `integer` (Default = 2, only relevant for "gradient_descent"). Number of iterations for which no momentum is applied in the beginning. If momentum_offset = -999, internal default values are used. m_lbfgs: `integer` (Default = 6). Number of corrections to approximate the inverse Hessian matrix for the "lbfgs" optimizer. If m_lbfgs = -999, internal default values are used delta_conv_mode_finding: `numeric` (Default = 1E-8). Convergence tolerance in mode finding algorithm for Laplace approximation for non-Gaussian likelihoods. If delta_conv_mode_finding = -999, internal default values are used
`offset`	A `numeric` `vector` with additional fixed effects contributions that are added to the linear predictor (= offset). The length of this vector needs to equal the number of training data points times the number of fixed-effect sets.
`fixed_effects`	This is discontinued. Use the renamed equivalent argument `offset` instead
`group_data_pred`	A `vector` or `matrix` with elements being group levels for which predictions are made (if there are grouped random effects in the `GPModel`)
`group_rand_coef_data_pred`	A `vector` or `matrix` with covariate data for grouped random coefficients (if there are some in the `GPModel`)
`gp_coords_pred`	A `matrix` with prediction coordinates (=features) for Gaussian process (if there is a GP in the `GPModel`)
`gp_rand_coef_data_pred`	A `vector` or `matrix` with covariate data for Gaussian process random coefficients (if there are some in the `GPModel`)
`cluster_ids_pred`	A `vector` with elements indicating the realizations of random effects / Gaussian processes for which predictions are made (set to NULL if you have not specified this when creating the `GPModel`)
`X_pred`	A `matrix` with prediction covariate data for the fixed effects linear regression term (if there is one in the `GPModel`)
`predict_cov_mat`	A `boolean`. If TRUE, the (posterior) predictive covariance is calculated in addition to the (posterior) predictive mean
`predict_var`	A `boolean`. If TRUE, the (posterior) predictive variances are calculated
`sample_posterior`	A `boolean`. If TRUE, samples from the posterior are drawn
`sample_prior`	A `boolean`. If TRUE, samples from the prior are drawn
`num_post_samples`	A `numeric` with the number of posterior samples to draw if 'sample_posterior=TRUE'
`num_prior_samples`	A `numeric` with the number of prior samples to draw if 'sample_prior=TRUE'
`std_err`	A `boolean`. If TRUE, (approximate) standard errors are calculated (= square root of diagonal of the inverse Fisher information for Gaussian likelihoods and square root of diagonal of a numerically approximated inverse Hessian for non-Gaussian likelihoods)
`vecchia_approx`	Discontinued. Use the argument `gp_approx` instead
`num_data`	A `numeric` with the number of samples. This is only used for iid models