A flexible statistical framework that generalizes classical regression models to jointly model multiple responses, potentially of different types, while accounting for dependencies between them.
It is particularly useful when you have multiple outcomes (e.g., continuous, binary, count data) that may influence each other.
Handles nonlinear associations between the reponse variables
Packages
{GJRM} - Routines for fitting various joint (and univariate) regression models, with several types of covariate effects, in the presence of equations’ errors association, endogeneity, non-random sample selection or partial observability.
Comparison to a Gaussian Multivariate Regression Model
Allows for more flexible marginal distributions, not limited to normal distributions.
Dependence Structure
Multivariate regression models the correlation between responses using a multivariate normal distribution, which implies a linear association.
GJRM uses copulas to model the dependence structure, allowing for more complex, non-linear associations between responses.
Flexibility
In multivariate regression with splines, the same spline structure is typically applied across all response variables..
In GJRM, each marginal can have its own unique non-linear structure, potentially using different splines or smoothing approaches for each response variable.
GJRM allows different link functions for each marginal distribution, accommodating various types of responses and not just continuous responses
GJRM can handle mixed types of responses (e.g., a combination of continuous, binary, and count data) in a single model.
Steps
First stage: Models each marginal distribution separately, allowing for different distributions and link functions for each response.
Second stage: Combines these marginals using a copula function to create the joint distribution.