Creates an additive Gaussian process model using create_model and fits it using sample_model. See the Mathematical description of lgpr models vignette for more information about the connection between different options and the created statistical model.

lgp(
formula,
data,
likelihood = "gaussian",
prior = NULL,
c_hat = NULL,
num_trials = NULL,
options = NULL,
prior_only = FALSE,
verbose = FALSE,
sample_f = !(likelihood == "gaussian"),
quiet = FALSE,
skip_postproc = sample_f,
...
)

## Arguments

formula The model formula, where it must contain exatly one tilde (~), with response variable on the left-hand side and model terms on the right-hand side terms are be separated by a plus (+) sign all variables appearing in formula must be found in data See the "Model formula syntax" section below (lgp) for instructions on how to specify the model terms. A data.frame where each column corresponds to one variable, and each row is one observation. Continuous covariates and the response variable must have type "numeric" and categorical covariates must have type "factor". Missing values should be indicated with NaN or NA. The response variable cannot contain missing values. Column names should not contain trailing or leading underscores. Determines the observation model. Must be either "gaussian" (default), "poisson", "nb" (negative binomial), "binomial" or "bb" (beta binomial). A named list, defining the prior distribution of model (hyper)parameters. See the "Defining priors" section below (lgp). The GP mean. This should only be given if sample_f is TRUE, otherwise the GP will always have zero mean. If sample_f is TRUE, the given c_hat can be a vector of length dim(data)[1], or a real number defining a constant GP mean. If not specified and sample_f is TRUE, c_hat is set to c_hat = mean(y), if likelihood is "gaussian", c_hat =  log(mean(y)) if likelihood is "poisson" or "nb", c_hat =  log(p/(1-p)), where p = mean(y/num_trials) if likelihood is "binomial" or "bb", where y denotes the response variable measurements. This argument (number of trials) is only needed when likelihood is "binomial" or "bb". Must have length one or equal to the number of data points. Setting num_trials=1 and likelihood="binomial" corresponds to Bernoulli observation model. A named list with the following possible fields: delta Amount of added jitter to ensure positive definite covariance matrices. vm_params Variance mask function parameters (numeric vector of length 2). If options is NULL, default options are used. The defaults are equivalent to options = list(delta = 1e-8, vm_params = c(0.025, 1)). Should likelihood be ignored? See also sample_param_prior which can be used for any lgpmodel, and whose runtime is independent of the number of observations. Can messages be printed during model creation? Has no effect if quiet=TRUE. Determines if the latent function values are sampled (must be TRUE if likelihood is not "gaussian"). If this is TRUE, the response variable will be normalized to have zero mean and unit variance. Should all output messages be suppressed? You need to set also refresh=0 if you want to suppress also the progress update messages from sampling. Should all postprocessing be skipped? If this is TRUE, the returned lgpfit object will likely be much smaller (if sample_f=FALSE). Optional arguments passed to sampling or optimizing.

## Value

Returns an object of the S4 class lgpfit.

## Model formula syntax

There are two ways to define the model formula:

1. Using a common formula-like syntax, like in y ~ age + age|id  + sex. Terms can consist of a single variable, such as age, or an interaction of two variables, such as age|id. In single-variable terms, the variable can be either continuous (numeric) or categorical (factor), whereas in interaction terms the variable on the left-hand side of the vertical bar (|) has to be continuous and the one on the right-hand side has to be categorical. Formulae specified using this syntax are translated to the advanced format so that

• single-variable terms become gp(x) if variable x is numeric and zs(x) if x is a factor

• interaction terms x|z become gp(x)*zs(z)

2. Using the advanced syntax, like in y ~ gp(age) + gp(age)*zs(id) + het(id)*gp_vm(disAge). This creates lgprhs objects, which consist of lgpterms, which consist of lgpexprs. This approach must be used if creating nonstationary, heterogeneous or temporally uncertain components.

Either one of the approaches should be used and they should not be mixed.

## Defining priors

The prior argument must be a named list, like list(alpha=student_t(4), wrp=igam(30,10)). See examples in tutorials. Possible allowed names are

• "alpha" = component magnitude parameters

• "ell" = component lengthscale parameters

• "wrp" = input warping steepness parameters

• "sigma" = noise magnitude (Gaussian obs. model)

• "phi" = inv. overdispersion (negative binomial obs. model)

• "gamma" = overdispersion (beta-binomial obs. model)

• "beta" = heterogeneity parameters

• "effect_time" = uncertain effect time parameters

• "effect_time_info" = additional options for the above

See priors for functions that can be used to define the list elements. If a parameter of a model is not given in this list, a default prior will be used for it.

## When to not use default priors

It is not recommended to use default priors blindly. Rather, priors should be specified according to the knowledge about the problem at hand, as in any Bayesian analysis. In lgpr this is especially important when

1. Using a non-Gaussian likelihood or otherwise setting sample_f = TRUE. In this case the response variable is not normalized, so the scale on which the data varies must be taken into account when defining priors of the signal magnitude parameters alpha and possible noise parameters (sigma, phi, gamma). Also it should be checked if c_hat is set in a sensible way.

2. Using a model that contains a gp_ns(x) or gp_vm(x) expression in its formula. In this case the corresponding covariate x is not normalized, and the prior for the input warping steepness parameter wrp must be set according to the expected width of the window in which the nonstationary effect of x occurs. By default, the width of this window is about 36, which has been set assuming that the unit of x is months.

Other main functions: create_model(), draw_pred(), get_draws(), pred(), prior_pred(), sample_model()