Nonconvergence in logistic and poisson models for neural spiking

Area of Science:

• Computational neuroscience
• Statistical modeling

Background:

• Generalized linear models (GLMs) are widely used for analyzing neural spike train data.
• Convergence issues in GLM parameter estimation can arise from specific data configurations.
• Complete and quasi-complete separation are known issues for logistic models.

Purpose of the Study:

• To investigate convergence difficulties in logistic and Poisson generalized linear models for spike train data analysis.
• To identify data configurations causing non-convergence, such as refractory periods, bursting, and binning specifics.
• To propose methods for detecting and addressing these convergence problems.

Main Methods:

• Analysis of logistic and Poisson generalized linear models applied to simulated and real spike train data.
• Characterization of data configurations leading to non-convergence (complete/quasi-complete separation).
• Application of linear programming methods for detecting non-convergent configurations.

Main Results:

• Refractory periods in neurons can cause complete or quasi-complete separation in logistic models, leading to convergence failure.
• Similar convergence issues arise in Poisson models, potentially due to neural bursting or data binning.
• Linear programming effectively detects these problematic data configurations.
• Standard software may struggle with these convergence difficulties.

Conclusions:

• Convergence issues in generalized linear models for spike train data are linked to specific neural data properties.
• Detection of non-convergence is possible using linear programming.
• Remedies for these convergence problems should be considered in statistical analysis of neural data.