Unified Computational Methods for Regression Analysis of Zero-Inflated and Bound-Inflated Data

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Bounded data with boundary excess observations are prevalent in many scientific fields.
• Existing computational methods for bound-inflated mixture models are often model-specific, hindering broad application.
• A unified framework is needed to address diverse inflated mixture models efficiently.

Purpose of the Study:

• To develop a common computational framework for inflated mixture models with lower boundary point inflation.
• To extend the applicability of these models to discrete and semi-continuous data.
• To compare estimation and standard error computation methods within this unified framework.

Main Methods:

• Adaptation and comparison of quasi-Newton and Expectation-Maximization (EM) algorithms for parameter estimation.
• Investigation of numerical Hessian and generalized Louis method for standard error computation.
• Inclusion of correlated data using generalized estimating equations.

Main Results:

• Demonstration of reliable parameter estimation and standard error effectiveness through simulations.
• Successful application to real-world data from an ultrasound bioeffect study.
• Validation of the unified approach for a broad range of inflated mixture models.

Conclusions:

• The unified framework provides reliable and efficient computation for a wide class of inflated mixture models.
• This approach facilitates the comparison of competing models for bound-inflated data.
• The methodology is applicable to both discrete and semi-continuous data with lower boundary inflation.