Statistical Consulting Blog

Path Analysis

Posted August 6, 2009

Path analysis represents an attempt to deal with causal types of relationships. Path analysis was developed by Sewall Wright in 1930 and is very useful in illustrating the number of issues that are involved in causal analysis.

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Path Analysis can be carried out by the researcher diagrammatically or graphically in the form of circles and arrows, which indicate various causation among variables. The ultimate goal is to predict the regression weight.  The regression weight is predicted during path analysis, and then compared to the observed correlation matrix.  This type of analysis is also applicable in cases where the researcher wants to perform a goodness of fit test.

There are certain terminologies that are used in path analysis.

The exogenous variables in path analysis are variables whose causes are outside of the model.
The endogenous variables are variables whose causes are inside the model.

The recursive model in is a causal model that is unidirectional.  In other words, they have one way causal flow.  This model in has neither feedback loops nor any reciprocal effects.  In this type of model in path analysis, the variables cannot be both cause and affect at the same time.

The non recursive model in path analysis is a causal model with feedback loops and reciprocal effects.

The path coefficient is the standardized regression coefficient that predicts one variable from another.

Path analysis is usually conducted with the help of an added module called the analysis of moment structures (AMOS).  Other than the added module of SPSS called the analysis of moment structures (AMOS), there is other statistical software like SAS, LISREL, etc. that can be used to conduct path analysis.  According to a well known researcher named Kline (1998), an adequate sample size should always be 10 times the amount of the parameters in path analysis.

The best sample size should be 20 times the number of parameters in path analysis.

Since path analysis is also a kind of statistical analysis, it also comes with several assumptions.

In path analysis, the association among the model should be linear in nature.  The associations among the models should be additive in nature. In path analysis, the association among the model should be causal in nature.  The data that is used should follow an interval type of scale.  In order to reduce volatilities in the data, it is assumed in the theory of path analysis that all the error terms are not correlated among the various variables. It is also assumed that errors are not correlated among themselves.  In path analysis, it is assumed that there is only one way causal flow.

Path analysis does have some limitations.

Path analysis can very well evaluate, test or compute two or more than two types of causal hypotheses. However, the major limitation is that it cannot establish the direction of causality.

Path analysis is applicable only in those kinds of cases where relatively small numbers of hypotheses can be easily represented by a single path.

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