Nonlinear Path Models with Continuous Variables

• Activity Number: 153
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section*
• Author(s): Patches Johnson*+ and Randy Carter
• Affiliation(s): University of Florida and University of Florida
• Keywords: calculus of coefficients ; path analysis ; causal modeling ; total effect ; direct effect ; indirect effect

Abstract

The well-known Calculus of Coefficients (COC) is commonly used to estimate and partition direct and indirect effects in recursive path models describing linear causal relationships among continuous endogenous variables. These methods rely on an assumption of independent and normally distributed error terms.

Here, we present an analog to the COC for recursive path models involving nonlinear relationships among endogenous variables. This method, the "Calculus of Effects" (COE), results in partitioning the total effect into sums of an expected direct effect and expectations of all indirect effects included in the causal chain, as is also true in the classical COC.

Techniques for estimation and testing of all effects are given. Estimates of effects are based on Nonlinear Least Squares and may, under certain model specifications, require Monte Carlo estimation. Effect testing is based on Intersection-Union Tests.

An application of the COE to maternal and child health is presented. Direct and indirect effects of mother's age on child's mental development (through child's birth weight and length of stay in the hospital at birth) are estimated and tested.