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Intro to path analysis—Page 1
Intro to path analysis
Sources
.
This discussion draws heavily from Otis Dudley Duncan’s Introduction to Structural
Equation Models.
Overview.
Our theories often lead us to be interested in how a series of variables are interrelated.
It is therefore often desirable to develop a system of equations, i.e. a model, which specifies all
the causal linkages between variables.For example, status attainment research asks how family
background, educational attainment and other variables produce socioeconomic status in later
life. Here is one of the early status attainment models (see Hauser, Tsai, Sewell 1983 for a
discussion):
Among the many implications of this model are that Parents’ SocioEconomic Status (X7)
indirectly affects the Educational Attainment (X2) and Occupational Aspirations (X3) of
children. These, in turn, directly affect children’s Occupational Attainment (X1). In other words,
higher parental SES helps children to become better educated and gives them higher occupational
aspirations, which in turn leads to greater occupational achievement. Our earlier discussion of the
Logic of Causal Order, combined with the current discussion of Path Analysis, can help us better
understand how models such as the above work.
Review of key lessons from the logic of causal order.
In the logic of causal order, we
learned that the correlation between two variables says little about the causal relationship
between them. This is because the correlation between two variables can be due to
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the direct effect of one variable on another
indirect effects; one variable affects another variable which in turn affects a third
common causes, e.g. X affects both Y and Z. This is spurious association
correlated causes, e.g. X is a cause of Z and X is correlated with Y
reciprocal causation; each variable is a cause of the other
Hence, a correlation can reflect many noncausal influences. Further, a correlation can’t tell you
anything about the direction of causality.
At the same time, only looking at the direct effect of one variable on another may also not be
optimal. Direct effects tell you how a 1 unit change in X will affect Y, holding all other variables
constant. However, it may be that other variables are not likely to remain constant if X changes,
e.g. a change in X can produce a change in Z which in turn produces a change in Y. Put another
way, both the direct and indirect effects of X on Y must be considered if we want to know what
effect a change in X will have on Y, i.e. we want to know the
total effects
(direct + indirect).
We have done all this conceptually. Now, we will see how, using path analysis, this is done
mathematically and statistically. We will show how the correlation between two variables can be
decomposed
into its component parts, i.e. we will show how much of a correlation is due to
direct effects, indirect effects, common causes and correlated causes. We will further show how
each of the
structural effects
in a model affects the correlations in the model.
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 Spring '11
 RichardWilliams

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