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# Path analysis

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### Path analysis

1. 1. Carlo Magno, PhD<br />Counseling and Educational Psychology Department<br />Path Analysis<br />
2. 2. What is path analysis<br />Uses regression models to test theories of causal relationships among a set of variables.<br />The researcher specify explicitly the presumed causal relationship s among the variables.<br />This technique help logically clear theories of variable relationships. <br />Not only searches association of variable relationships but also for causal relationships.<br />
3. 3. Path models<br />Observed variables are represented in a rectangle (manifest variables).<br />Causality is indicated by a single-headed arrow<br />Correlation is indicated by a bent double-headed arrow<br />Error terms are place at each endogenous variable<br />Parental monitoring<br />e1<br />e2<br />Motivation<br />Achievement<br />Intelligence<br />
4. 4. Variables<br />Explaining variable (independent variable, exogenous variable)<br />Outcome variable (dependent variable, endogenous variable)<br />Intervening variable (mediating)<br />Effects:<br />Direct Effects<br />Indirect effects<br />Type of Variables:<br />Latent (factor)<br />Manifest (observed/subscales) <br />Residual variable (error terms/measurement error)<br />
5. 5. Path coefficients<br />Standardized regression coefficients for the regression equation for the response variable to which the arrows point.<br />Interpretation: .14 path estimate from intelligence to motivation<br />“1 standard deviation increase of intelligence corresponds to a .4 standard deviation increase in motivation, controlling fo other factors in the model.”<br />
6. 6. Residual path<br />Attached to every response variable (endogenous variable).<br />Represents the variation unexplained by the explanatory variable (exogenous variable).<br />Remaining portion of the (1-R2) of the unexplained variation, where R2 is the coefficient of multiple determination for the regression equation.<br />Path coefficient=SQRT(1-R2)<br />
7. 7. Decomposing path diagrams<br />X  Z  Y<br />Parameter of X and Y, controlling for the effects of Z<br />Parameter of X on Y<br />Parameter of Z on Y<br />