mmlt: Multivariate Conditional Transformation Models

Description

Conditional transformation models for multivariate continuous, discrete, or a mix of continuous and discrete outcomes

Usage

mmlt(..., formula = ~ 1, data, conditional = FALSE, theta = NULL, fixed = NULL,
     scale = FALSE, optim = mltoptim(auglag = list(maxtry = 5)), 
     args = list(seed = 1, M = 1000), dofit = TRUE, domargins = TRUE)
# S3 method for cmmlt
coef(object, newdata, 
     type = c("all", "conditional", "Lambdapar", "Lambda", "Lambdainv", 
              "Precision", "PartialCorr", "Sigma", "Corr", 
              "Spearman", "Kendall"), fixed = TRUE, 
     ...)
# S3 method for mmmlt
coef(object, newdata, 
     type = c("all", "marginal", "Lambdapar", "Lambda", "Lambdainv", 
              "Precision", "PartialCorr", "Sigma", "Corr", 
              "Spearman", "Kendall"), fixed = TRUE,
     ...)
# S3 method for mmlt
predict(object, newdata, margins = 1:J, 
        type = c("trafo", "distribution", "survivor", "density", "hazard"), 
                 log = FALSE, args = object$args, ...)
# S3 method for mmlt
simulate(object, nsim = 1L, seed = NULL, newdata, K = 50, ...)

Value

An object of class mmlt with coef and predict

methods.

Arguments

...: marginal transformation models, one for each response, for mmlt. Additional arguments for the methods.
formula: a model formula describing a model for the dependency structure via the lambda parameters. The default is set to ~ 1 for constant lambdas.
data: a data.frame.
conditional: logical; parameters are defined conditionally (only possible when all models are probit models). This is the default as described by Klein et al. (2022). If FALSE, parameters can be directly interpreted marginally, this is explained in Section 2.6 by Klein et al. (2022). Using conditional = FALSE with probit-only models gives the same likelihood but different parameter estimates.
theta: an optional vector of starting values.
fixed: an optional named numeric vector of predefined parameter values or a logical (for coef) indicating to also return fixed parameters (only when type = "all").
scale: a logical indicating if (internal) scaling shall be applied to the model coefficients.
optim: a list of optimisers as returned by mltoptim
args: a list of arguments for lpmvnorm.
dofit: logical; parameters are fitted by default, otherwise a list with log-likelihood and score function is returned.
domargins: logical; all model parameters are fitted by default, including the parameters of marginal models.
object: an object of class mmlt.
newdata: an optional data.frame coefficients and predictions shall be computed for.
type: type of coefficient or prediction to be returned.
margins: indices defining marginal models to be evaluated. Can be single integers giving the marginal distribution of the corresponding variable, or multiple integers (currently only 1:j implemented).
log: logical; return log-probabilities or log-densities if TRUE.
nsim: number of samples to generate.
seed: optional seed for the random number generator.
K: number of grid points to generate.

Details

The function implements core functionality for fitting multivariate conditional transformation models as described by Klein et al (2020).

References

Nadja Klein, Torsten Hothorn, Luisa Barbanti, Thomas Kneib (2022), Multivariate Conditional Transformation Models. Scandinavian Journal of Statistics, 49, 116--142, tools:::Rd_expr_doi("10.1111/sjos.12501").

Torsten Hothorn (2024), On Nonparanormal Likelihoods. tools:::Rd_expr_doi("10.48550/arXiv.2408.17346").