## Path Analysis

Path analysis is an extension of multiple regression analysis, used to test the fit of the correlation matrix against two or more causal models which are being compared by the researchers. It was developed by Sewal Wrigth in the 1930’s and is useful in illustrating a number of issues in causal analysis. In general, path diagrams are used to display a priori hypothesized structure among the variables in the models. Four possible relationships can be thought of for any two variables *X and Y*. These along with their diagrammatical relationship are given below.

v *X -> Y *implies that *X *might structurally influence *Y* but not vice versa

v *X* *<- Y * implies that *Y* might be structurally influence *X* but not vice versa.

v *X * *<=> Y *implies that both *X *and *Y *might structurally influencing each other, and finally,

v *X * *<->Y* implies that no relationship can be hypothesised between X and Y.

Structures that include the first two and/or the last relations are called recursive models, while those that involved the third relation are called non-recursive models

Since this is an extension of regression analysis, it equally has some assumptions which are:

v Relations among the variables are linear, additive, and causal. Curvilinear, multiplicative, or interaction relations are not inclusive.

v Residuals are uncorrelated with all other variables and residuals in the model.

v There is one-way causal flow.

v The variables are measured on interval scale.

One major advantage of the path analysis is that it allows testing hypothesized multivariate linear causal models. Other advantages are that; it provides a breakdown of the covariance between variables into direct, indirect and spurious or joint effects; it equally allows for the explanation of intervening variables as well as the terminal variables and finally gives a parsimonious diagram of causal links with parameters that indicate the relationship between determined and determining variables.

References:

1. Carey, G. (1998). Path Analysis Using Proc Calis. http://psych.colorado.edu/~carey/Courses/PSYC7291/ExampleCode.htm (assessed on 12-02-07)

2. Shkedy Z. (no date). Structural Equation Modeling, an Introduction: Path Analysis and Confirmatory Factor Analysis. Hasselt University, Diepenbeek.

3. Johnson, R.A., Wichern, D.W. (2002). Applied Multivariate Statistical Analysis. Fifth edition. Prentice Hall.