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Cosmic rays measured through neutron monitors on Earth's surface have a strong correlation with the number of sunspots on the solar photosphere. Other indices that affect the dynamics of the heliosphere and distortions in the Earth's geomagnetic field also exhibit significant correlations. Typically, studies focus on these indices individually or combine some into a smaller set of estimators. This study uses Structural Equation Modeling to examine relationships between a broad range of parameters of solar dynamics and cosmic ray intensity (measured by the Moscow neutron monitor) across several solar cycles from 1976 to present day. The study also classifies these indices into three distinct contributions: Photosphere, Solar Wind and Terrestrial Geomagnetic Field Distortions. Regression models were built for all solar cycles and the complete cosmic ray series from 1976 to the present, resulting in good estimators with calculated p-values below 0.05 (95% confidence). Relationships among all contributions were determined using their estimators. [ABSTRACT FROM AUTHOR]