mmlt: Multivariate Conditional Transformation Models

In mlt: Most Likely Transformations

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, scaleparm = FALSE,
     optim = mltoptim(hessian = TRUE),  ### provides hessian
     args = list(seed = 1, M = 1000), 
     dofit = TRUE, domargins = TRUE)
## S3 method for class 'cmmlt'
coef(object, newdata, 
     type = c("all", "conditional",
              "Lambda", "Omega", "Lambdainv", "Omegainv",
              "Precision", "PartialCorr", "Sigma", "Corr", 
              "Spearman", "Kendall"), fixed = TRUE, 
     ...)
## S3 method for class 'mmmlt'
coef(object, newdata, 
     type = c("all", "marginal",
              "Lambda", "Omega", "Lambdainv", "Omegainv",
              "Precision", "PartialCorr", "Sigma", "Corr", 
              "Spearman", "Kendall"), fixed = TRUE,
     ...)
## S3 method for class 'mmlt'
predict(object, newdata, margins = 1:J, 
        type = c("trafo", "distribution", "survivor", "density", "hazard"), 
                 log = FALSE, args = object$args, ...)
## S3 method for class 'mmlt'
simulate(object, nsim = 1L, seed = NULL, newdata, K = 50, ...)
## S3 method for class 'mmlt'
residuals(object, parm = coef(object, fixed = FALSE), 
                         w = NULL, newdata = NULL, ...)

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").
scaleparm	a logical indicating if (internal) scaling shall be applied to the model parameters.
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.
parm	parameter vector.
w	weights.

Details

The function implements core functionality for fitting multivariate conditional transformation models as described by \bibcitetmlt::Klein:Hothorn:Barbanti:2020.

Value

An object of class mmlt with coef and predict methods.

The model is always parameterised in terms of a unit lower-triangular matrix \Lambda. If conditional = FALSE (the default), it is standardised to a lower-triangular matrix \Omega = \Lambda \text{diag}(\Lambda^{-1} \Lambda^{-\top}) such that \Sigma = \Omega^{-1} \Omega^{-\top} is a correlation matrix. Note that Omega = \Lambda when conditional = TRUE was requested. These concepts are explained in \bibcitetmlt::hothorn_2024, Section 2.

References

\bibshow

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mlt documentation built on April 27, 2026, 3:04 a.m.