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Conventional Linear Regression
The single-headed arrows represent linear dependencies. For example, the arrow
leading from knowledge to performance indicates that performance scores depend, in
part, on knowledge. The variable error is enclosed in a circle because it is not directly
observed. Error represents much more than random fluctuations in performance scores
due to measurement error. Error also represents a composite of age, socioeconomic
status, verbal ability, and anything else on which performance may depend but which
was not measured in this study. This variable is essential because the path diagram is
supposed to show all variables that affect performance scores. Without the circle, the
path diagram would make the implausible claim that performance is an exact linear
combination of knowledge, value, and satisfaction.
The double-headed arrows in the path diagram connect variables that may be
correlated with each other. The absence of a double-headed arrow connecting error
with any other variable indicates that error is assumed to be uncorrelated with every
other predictor variable—a fundamental assumption in linear regression. Performance
is also not connected to any other variable by a double-headed arrow, but this is for a
different reason. Since performance depends on the other variables, it goes without
saying that it might be correlated with them.
Specifying the Model
Using what you learned in the first three examples, do the following:
E Start a new path diagram.
E Specify that the dataset to be analyzed is in the Excel worksheet Warren5v in the file
UserGuide.xls.
E Draw four rectangles and label them knowledge, value, satisfaction, and performance.
E Draw an ellipse for the error variable.
E Draw single-headed arrows that point from the exogenous, or predictor, variables
(knowledge, value, satisfaction, and error) to the endogenous, or response, variable
(performance).
Note: Endogenous variables have at least one single-headed path pointing toward them.
Exogenous variables, in contrast, send out only single-headed paths but do not receive any.