l62 - Intro to path analysis Sources. This discussion draws...

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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 socio-economic 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’ Socio-Economic 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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Intro to path analysis—Page 2 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 non-causal 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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l62 - Intro to path analysis Sources. This discussion draws...

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