A primer on marginal effects--Part I: Theory and formulae

Area of Science:

• Health Services Research
• Econometrics
• Biostatistics

Background:

• Marginal analysis, a core economic concept, assesses changes in outcomes due to unit variable changes.
• The primary statistic, marginal effect (ME), provides interpretable results in original units (e.g., costs, probabilities).
• ME is underutilized in health services research despite its potential for nuanced patient profile analysis.

Purpose of the Study:

• Introduce and illustrate the calculation of marginal effects (ME) for diverse regression models.
• Expand the application of ME beyond traditional linear and logistic models in health services research.
• Provide a foundation for estimating and interpreting ME in applied health research.

Main Methods:

• Review of existing literature on marginal effects (ME).
• Derivation of ME formulas for linear, logistic, multinomial logit (MLM), generalized linear (GLM) for continuous and count data, two-part, sample selection, and parametric survival models.
• Focus on models relevant to health services research, including cost and utilization studies.

Main Results:

• Formulas for ME calculation are derived for a comprehensive suite of regression models.
• Emphasis is placed on models beyond linear and logistic, including MLM, GLM, two-part, sample selection, and survival models.
• The paper establishes the theoretical groundwork for applying ME to complex health services research questions.

Conclusions:

• Marginal effects (ME) offer a flexible and insightful approach for analyzing health services data.
• This paper provides essential derivations for applying ME across a wider range of statistical models.
• The presented methods support the broader adoption and application of marginal analysis in health services research.