Understanding Regression Analysis pp 161-165 | Cite as

# Computing direct and total effects of variables

Chapter

## Abstract

One of the lessons to be drawn from structural equation models and path analysis is that an independent variable can have both direct and indirect effects on a dependent variable. In other words, some of the effects of an independent variable on a dependent variable may be transmitted through intervening variables. Consequently, the partial regression coefficient for an independent variable in a multiple regression equation may not capture all of its effects on the dependent variable. In order to understand the difference between direct and total effects, let us consider the example of the simple structural equation model that explains income in terms of education and occupation. The relationship between these three variables was represented by the following set of structural equations, where the variables are expressed in standard form:

$$
\begin{gathered}
z_2 = {\mathbf{ }}z_3 b_{23}^* {\mathbf{ }} + {\mathbf{ }}e_2 \hfill \\
z_1 = {\mathbf{ }}z_3 b_{13.2}^* {\mathbf{ }} + {\mathbf{ }}z_2 b_{12.3}^* + {\mathbf{ }}e_1 \hfill \\
\end{gathered}
$$

where variable Z_{3} is education, variable Z_{2} is occupation, and variable zi is education. It is evident from these structural equations that a one unit change in variable Z_{3} will produce a change in variable Z_{2} and a change in variable Z_{3}. In turn, the change in variable Z_{2} produced by a change in variable Z_{3} will produce a further change in variable zi.

## Keywords

Indirect Effect Structural Equation Structural Equation Model Total Effect Exogenous Variable
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Plenum Press, New York 1997