Simultaneous estimation of parameters in the bivariate Emax model.

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Multi-response nonlinear models involve multiple outcome variables and relationships.
• Existing methods often estimate equations individually, potentially ignoring interdependencies.

Purpose of the Study:

• To explore a system estimation approach for simultaneous inference in multi-response nonlinear models.
• To compare system estimation with equation-by-equation estimation for bivariate Emax models.

Main Methods:

• Developed a system estimation approach for joint computation and inference of model and covariance parameters.
• Applied the bivariate Emax model to diabetes dose-response data.
• Conducted a simulation study comparing system estimation to equation-by-equation estimation.

Main Results:

• The system estimation approach demonstrated superior performance for the bivariate Emax model when relations were dependent.
• Increased precision was observed with stronger dependencies between relations using system estimation.
• The approach facilitates simultaneous inference of model and (co)variance parameters.

Conclusions:

• System estimation is a more precise method for multi-response nonlinear models with dependent relations.
• The bivariate Emax model serves as a valid illustration for comparing estimation strategies.
• The findings support the use of system estimation for enhanced accuracy in complex models.