Improved random-starting method for the EM algorithm for finite mixtures of regressions

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Finite mixture regression models are widely used for analyzing complex data structures.
• The Expectation-Maximization (EM) algorithm is a common method for estimating parameters in these models.
• The choice of starting values for the EM algorithm can significantly impact the estimation results.

Purpose of the Study:

• To compare two methods for generating random starting values for the EM algorithm in finite mixture regression.
• To evaluate the performance of a standard method versus a novel alternative method.

Main Methods:

• The study employed two simulation studies to assess the performance of the two starting value generation methods.
• An illustrative real-world data set was analyzed to compare the methods' practical implications.
• Maximum likelihood parameter estimates were used as the primary evaluation metric.

Main Results:

• The alternative method consistently produced likelihood values equal to or higher than the standard method.
• Simulation studies demonstrated the superior performance of the alternative starting value generation technique.
• Analysis of the illustrative data revealed that different starting value methods can lead to divergent substantive conclusions.

Conclusions:

• The choice of random starting value generation method is critical for finite mixture regression analyses.
• The proposed alternative method offers a more robust approach for parameter estimation.
• Researchers should carefully consider and potentially adopt the alternative method for improved accuracy and reliability.