Path Analysis PDF

In conventional breeding programme, characters are selected for utilization depending up on the influence/effect of the character concerned in improving the response character/variable. As the variables/characters are not only correlated with th...

In conventional breeding programme, characters are selected for utilization depending up on the influence/effect of the character concerned in improving the response character/variable. As the variables/characters are not only correlated with the response variable but also among themselves so, the question arises how to separate the direct influence of a particular variable/character on the response variable/character and the effects of the variable/character through other variables/ characters because, of their interrelationship; possible answer is through the Path Coefficient Analysis. Path coefficient analysis or simply path analysis is special type of multiple regression analysis. In a path coefficient analysis there are at least two groups of variables. Independent variables or the exogenous variables and the dependent variables or the endogenous variables. Path coefficients indicate the direct and indirect effects of the variables on other variable. A path diagram is a flow chart to represent the direction of effects of different variables on the dependent variables. Path coefficients indicate the direct and indirect effects of the variables on other variable. A path diagram is a flow chart to represent the direction of effects of different variables on the dependent variables. Fig. 1. Path diagram with two Independent and three independent variables  In the above diagram Xl, X2, X3 are the exogenous independent variables and X4, X5 are the endogenous dependent variables. Here the variable X5 is not only dependent on X4 but also on the independent variables Xl, X2, X3. Similarly, the dependent variable X4 is dependent on Xl, X2 and X3. Direction of arrows indicates the response variable by the causal variables. It may be noted that there may be both way arrows among the endogenous independent variables but there are one way arrows from the exogenous independent variables and to the endogenous variables Thus for X5, the variable X4 is independent but it is not exogenous. Both way arrows mean the variables are related among themselves.  As because the yield components are correlated among themselves, so the effect of one yield component may be viewed as the resultant effect of its relationship with the response variables (direct effect) and the influence this variable on the ultimate response variables through the other variables (indirect effect). So the correlation between the response variable and any component variable (causal variable) can be looked upon as the additive effect of direct and indirect effects of the causal variables. If ai and bi' (i ≠ i' = 1, 2,….., k) are the direct effect k and indirect effects of the ith variable in a system of (k+1) variables then ai + σ𝑘i ≠ i′ = 1 bi’ = rx y. In the above i relationship ai is the direct effect of the ith causal variable on the response variable y, bi is the indirect effect of ithcausal variable on the response variable via the ithcausal variable (other than the ithvariable).  In this fashion each of the 'k' number of individual correlation coefficients of causal variables with the response variable can be partitioned into the additive effect of the direct effect of the respective variables and the sum of the indirect effects of the other variables. Path analysis is the method of studying the direct and the indirect effects of the variables on the response variables It may be noted emphatically that the path coefficient analysis is not directed towards discovering the causes of a response, rather it is intended to combine the quantitative information from correlation study with qualitative information on different causes to quantify the interpretation. ASSUMPTIONS 1. Path analysis model assumes the linear relationship among the variables. 2. All the effects are additive in nature, there is no interaction effects. 3. Only one-way causation is considered (recursive model) 4. The variables are to be measured in interval scale. If dummy variables are used to code a categorical variable, this must be represented as a block in the path diagram. 5. The residual or unmeasured parts are uncorrelated with any of the variable in the models. 6. Existence of low multi collinearity, otherwise there will be high standard error of the regression coefficients. 7. The model should be correctly specified; specification error arises when a significant causal variable is left out of the model. 8. Adequate sample size is required to asses’ significance; according to Kline (1998), the number of cases should be around 10 times of the parameters in the model. 5 times or less number of cases is insufficient for test of significance of model effect.  The path model can be estimated with standard ordinary least square technique under the above conditions. PATH DIAGRAM The graphical or diagrammatical presentation of path analysis is known as path diagram. Generally, arrows are used to show the relations; a single headed arrow is meant for showing cause to effect. In a path diagram there are two types of variables, the independent variables known as the causal variables and the dependent / response variables known as endogenous variables. A recursive path model is a unidirectional model where the causal flow is in one direction, there is no question of loop or reciprocal causes.