Path analysis is a technique that uses regression models to test theories of causal relationships among variables. It allows researchers to explicitly specify presumed causal relationships and determine not just associations but also potential causal relationships between variables. Path models represent variables as rectangles or ovals, with causality indicated by single-headed arrows and correlation by double-headed arrows. Path coefficients represent standardized regression weights and can be interpreted as the change in the response variable corresponding to a change in the explanatory variable while controlling for other factors.

1. Carlo Magno, PhD Counseling and Educational Psychology Department Path Analysis

2. What is path analysis Uses regression models to test theories of causal relationships among a set of variables. The researcher specify explicitly the presumed causal relationship s among the variables. This technique help logically clear theories of variable relationships. Not only searches association of variable relationships but also for causal relationships.

3. Path models Observed variables are represented in a rectangle (manifest variables). Causality is indicated by a single-headed arrow Correlation is indicated by a bent double-headed arrow Error terms are place at each endogenous variable Parental monitoring e1 e2 Motivation Achievement Intelligence

4. Variables Explaining variable (independent variable, exogenous variable) Outcome variable (dependent variable, endogenous variable) Intervening variable (mediating) Effects: Direct Effects Indirect effects Type of Variables: Latent (factor) Manifest (observed/subscales) Residual variable (error terms/measurement error)

5. Path coefficients Standardized regression coefficients for the regression equation for the response variable to which the arrows point. Interpretation: .14 path estimate from intelligence to motivation “1 standard deviation increase of intelligence corresponds to a .4 standard deviation increase in motivation, controlling fo other factors in the model.”

6. Residual path Attached to every response variable (endogenous variable). Represents the variation unexplained by the explanatory variable (exogenous variable). Remaining portion of the (1-R2) of the unexplained variation, where R2 is the coefficient of multiple determination for the regression equation. Path coefficient=SQRT(1-R2)

7. Decomposing path diagrams X  Z  Y Parameter of X and Y, controlling for the effects of Z Parameter of X on Y Parameter of Z on Y