# Path Analysis

Posted August 6, 2009

Path analysis is an extended generalized form of the regression model. Path analysis is used for comparing two or more causal models from the correlation matrix. Path analysis is done diagrammatically in the form of circles and arrows that indicate the causation. The task of path analysis is to predict the regression weight. The regression weight predicted during path analysis is then compared to the observed correlation matrix. In path analysis, the goodness of fit test is done in order to show that the model is the best possible fit.

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While conducting path analysis, a researcher comes across some key terminologies used during path analysis. The following terminologies are used during path analysis:

For researchers, the first thing to tackle is the question that they want answered. The question here is what kind of estimation method is to be used in path analysis. Ordinary least squares (OLS) method and maximum likelihood methods are used to estimate the path.

Additionally, there is a term called path model in path analysis. Path model in path analysis is nothing but a diagram that indicates independent variables, intermediate variables and dependent variables. The arrows with a double head indicate that the covariance is being calculated between the two variables in path analysis.

The exogenous variables in path analysis are those variables with no error pointed towards them, except for the measurement error. The endogenous variables in path analysis can have both approaching and withdrawing arrows.

The path coefficient in path analysis is the same as that of the standardized regression coefficient. This coefficient in path analysis indicates the direct effects of an independent variable on the dependent variable.

Since the estimation method is ordinary least squares (OLS), there is a term called disturbance terms in path analysis. These terms in path analysis are nothing but the residual error terms. These terms in path analysis merely indicate the variances which are unexplained and the errors that occurred during measurement (i.e. the measurement errors).

As discussed, goodness of fit test is used in path analysis, and therefore chi square statistics is also used in path analysis. The values that are not significant in path analysis indicate the model with a good fit.

Path analysis is generally conducted with the help of analysis of a moment structures (AMOS), which is an added module in SPSS. Other than the analysis of a moment structures (AMOS), there is other statistical software like SAS, LISREL, etc. that can be used to conduct path analysis. According to Kline (1998), an adequate sample size should be 10 times the cases of parameters in path analysis. The ideal sample size should be 20 times the cases of parameters in path analysis.

Since path analysis is a statistical method, it has assumptions. The following are the assumptions of path analysis:

In path analysis, the relationship between the variables should be linear in nature. The data used in path analysis should have an interval scale. In order to reduce disturbances in the data, the theory of path analysis assumes that the error terms should not be correlated with the variables.

Path Analysis, however, also has some limitations. Although path analysis can evaluate or test two or more causal hypotheses, path analysis cannot establish the direction of causality.

Path analysis is useful only in cases where a small number of hypotheses (that can be represented by a single path) are being tested.