Path analysis: An overview and its application in social sciences

Path analysis is a form of multiple regression statistical analysis that is used to evaluate causal models by examining the relationships between a dependent variable and two or more independent variables. It was developed by Geneticist Sewell Wright in the year 1921 and he describes path analysis as a technique based on a series of multiple regressions analysis with the added assumption of a causal relationship. Path analysis and regression analysis have similarities as path analysis is essentially the multiple regression analysis with standardized variables and the ß coefficient in regression analysis is equivalent to the test of significance of path coefficients. Path analysis was first developed as a method to decompose correlation coefficient into different components. Path analysis is mainly composed of five elements namely exogenous variables, endogenous variables, path diagram, path coefficient and effects. Path analysis assumes that there is linear relationship among the variables and all the variables are measured in interval scale. Though the methodology was used by a geneticist at the beginning, later Blalock introduced this concept into social scientific research. The algebra and tracing rules have been simplified in path analysis technique compared to conventional statistical methods so that even people with very little statistical training could perform path analysis.

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Introduction

In agriculture and allied fields including social sciences, response variables are influenced by several other variables. If we consider yield in agricultural crops like Paddy is obvious that the yield component is influenced by many different yield components like the number of hills per square, number of tillers per hill, number of panicle-bearing tillers per hill, length of panicle, number of grains and so on, which all are independent components having an effect on the dependent component. These effects can be identified using path analysis. Path analysis is a form of multiple regression statistical analysis used to evaluate a causal model by examining the relationships between a dependent variable and two or more independent variables. Path analysis can be viewed as a special case of a structural equation model in which only single indicators are employed for each of the variables in the causal model. It is SEM with a structural model, but not a measurement model. Other terms used to refer to path analysis include causal modeling and analysis of covariance structures.

History of Path analysis

Path analysis was developed by an American geneticist Sewall Wright in 1921 to examine the effects of hypothesized models in phylogenetic studies which involved writing a system of equations based on the correlations among the variables influencing the outcome and solving for the unknown parameters. He intended to measure the direct effect along each separate path in such a system and thus to find the degree to which variation of a given effect. He defined it as a technique based on a series of multiple regressions with the added assumption of a causal relationship. It has since been applied to a vast array of complex modeling areas, including biology, psychology, sociology and econometrics.

Path Analysis, Regression and Correlation

Path analysis and regression analysis have similarities as path analysis is essentially the multiple regression analysis with standardized variables and the ß coefficient in regression analysis is equivalent to the test of significance of path coefficients. Contrastingly when we compare them, only the direct effect of independent variables on dependent variables can be estimated but in path analysis, both the direct effect as well as the indirect effect of independent variables on the dependent variable can be estimated. In multiple regression, the partial correlation coefficient can be worked out by keeping other variables constant whereas in path analysis we consider all the variables. Path analysis was first developed as a method to decompose correlation coefficient into different components. The www.extensionjournal.com correlation between the response variable and any causal variable can be looked upon as additive effects of direct and indirect path coefficients. Path analysis differs from correlation as correlation is just a measure of association and is based on variance and covariance whereas path analysis is based on all possible simple correlations. In correlation analysis there is no information about direct and indirect effects but not so in case of the later one. The correlation between variables 1 and 3, it is represented in the form of r 13 =p 31 +p 32 *r 12, where r 13 is the correlation coefficient between them, p 31 is the path coefficient which represents the proportion of the variance accounted for by the direct pathway between 1 and 3 and p 32 *r 12 represents the proportion of the variance accounted for by the pathway includes the segment between 1 and 2 and the segment between 2 and 3. P 3a is the square root of (1-r 2 ), using the unadjusted r-square value from the regression of 3 on variables 1 and 2. While the value of p 4b is the square root of (1-r 2 ), using the unadjusted r-square from the regression of 4 on variables 1,2 and 3.

Elements of Path analysis

Elements of Path analysis

Effects in Path Analysis

The total variance explained by each regression model can be partitioned or decomposed into specific types of effects: Direct, Indirect, Spurious and Unanalyzed effects. Direct effects are the effects that go directly from one variable to another. Indirect effects are the effects that occur when the relationship between the two variables is mediated by one more variable. Spurious effects occur when the relationship between two endogenous variables is influenced by a third variable and the unanalyzed effect is due to multicollinearity.

Main Features of

Main Features of

Calculation of Path coefficient

Path coefficient can be calculated using the path diagram and also from the simultaneous equations formed. Path coefficient can be defined as the ratio of standard deviation due to a given cause to the total standard deviation of the response. Path coefficient = p ij (i denotes the dependent variable and j denotes the independent variable). Let us consider three independent variables X 1 , X 2 and X 3 and one dependent variable.

We can form the equation as

By putting the value of Y in the above equation, we get

Thus, equation (2) becomes: r(x 1 ,Y)=V(x 1 )/V(x 1 )V(Y) 1/2 +r(x 1 x 2 )x 1 x 2 /((V(x 1 )V(Y)) 1/2 + r(x 1 x 3 )x 1 x 3 /((V(x 1 )V(Y)) 1/2 + r (x 1 x 2 ) + r (x 1 x 3 )

Where, as per the definition, the path coefficient can be calculated as = 'py 1 ', the path coefficient from x 1 to Y.

= 'py 2 ', the path coefficient from x 2 to Y.

= 'py 3 ', the path coefficient from x 3 to Y. As path coefficient is derived from the correlation coefficient, if the direct effect path coefficient equals to the correlation coefficient, then it indicates that correlation coefficient presents a true picture of associations between the dependent variable and independent variable. When direct effect is negligible or negative but the correlation coefficient is positive and significant then then indirect effects are the cause of such correlation coefficient. If direct effect is high and positive but the correlation coefficient is negligible or negative, then the indirect effects are the cause of the manifestation of such a correlation. When both the correlation and path coefficient is negligible/negative then it is better to discard such characters or variables. Occupational Structure, they utilized data collected from a sample of adult males and their parents to develop path models of the causal processes underlying educational and occupational outcomes. Social and life course epidemiologists subsequently adopted the method as an effective way to distinguish direct from www.extensionjournal.com indirect effects and to test the strength of hypothesized patterns of causal relationships. During the 1970's path analysis became even more popular and numerous papers were published featuring path analytic methods in sociology, psychology, economics, political science, ecology and other fields. In the social sciences, path analysis has been widely used especially in sociology and psychology, most notably in the areas of child or lifespan development or other longitudinal research (Table 1).

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Application of path analysis in studies related to social sciences

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Conclusion

Path analysis can be used by anyone with minimum statistical skills as the algebra and tracing rules have been simplified in path analysis technique compared to conventional statistical methods so that even people with very little statistical training could perform path analysis. If a large number of variables are involved in research, understanding causal relations among them and their interpretation could become difficult. This method can be used as a basic tool as structural model and further can be applied in further methodologies.

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Path diagram of two independent, one mediating and one dependent variable

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Path diagram of three independent variables and one dependent variable

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