title: A primer on marginal effects--Part I: Theory and formulae.
abstract: Marginal analysis evaluates changes in an objective function associated with a unit change in a relevant variable. The primary statistic of marginal analysis is the marginal effect (ME). The ME facilitates the examination of outcomes for defined patient profiles while measuring the change in original units (e.g., costs, probabilities). The ME has a long history in economics; however, it is not widely used in health services research despite its flexibility and ability to provide unique insights. This paper, the first in a two-part series, introduces and illustrates the calculation of the ME for a variety of regression models often used in health services research. Part One includes a review of prior studies discussing MEs, followed by derivation of ME formulas for various regression models including linear, logistic, multinomial logit model (MLM), generalized linear model (GLM) for continuous data, GLM for count data, two-part model, sample selection (two-stage) model, and parametric survival model. Prior theoretical papers in health services research reported the derivation and interpretation of ME primarily for the linear and logistic models, with less emphasis on count models, survival models, MLM, two-part models, and sample selection models. These additional models are relevant for health services research studies examining costs and utilization. Part Two of the series will focus on the methods for estimating and interpreting the ME in applied research. The illustration, discussion, and application of ME in this two-part series support the conduct of future studies applying the marginal concept.
authors.affiliation: Department of Pharmaceutical Health Services Research, University of Maryland School of Pharmacy, 220 Arch Street, 12th Floor, Baltimore, MD, 21201, USA, eonukwug@rx.umaryland.edu.
authors.forename: Eberechukwu
authors.initials: E
authors.lastname: Onukwugha
authors.forename: Jason
authors.initials: J
authors.lastname: Bergtold
authors.forename: Rahul
authors.initials: R
authors.lastname: Jain
mesh_terms: D006302:Health Services Research / Q000191:economics*; D006801:Humans; D016014:Linear Models; D016015:Logistic Models; D018803:Models, Economic; D015233:Models, Statistical; D012044:Regression Analysis