Chapter 16 PATH ANALYSIS

Chapter 16 PATH ANALYSIS

Path Analysis Based on simple regression techniques, but by looking at relationships among a set of independent variables, path analysis takes the researcher a step beyond traditional regression analysis.

Research Questions:  Understanding the relationships within a set of predictors  Testing a theoretical model

Data Requirements: The same as in regression analysis…. What are the requirements for regression analysis?

Assumptions 1. Theoretical 2. Statistical

Theoretical Assumptions Path models are “casual models” but do not always result from cross sectional data. Caution is needed in how one describes his/her results (e.g., IV “causes” vs. “influences” DV).

Kenny’s 3 conditions for causation 1. X and Y must have an observed and measurable relationship. 2. X must precede Y in time. Seems simple, but can be tricky (e.g., Do beliefs cause behavior or does behavior cause beliefs?). Important to use theory and research to guide you in assigning direction to the path.

3. X and Y have a non-spurious relationship. The relationship between X and Y will not disappear when the influence of other variables is controlled for…. To argue that smoking causes cancer is to argue that even when genetics, stress, environmental exposures, etc. are controlled for, the relationship between smoking and cancer remains – it is non-spurious.

Statistical Assumptions A. Multiple regression assumptions B. Assumptions unique to path analysis: 1. Correlations between two variables that have no other variables influencing them cannot be analyzed. The path coefficient is equal to the correlation. 2. Flow of causation is unidirectional. 3. Variables are interval level. 4. All variables are measured without error.

Power  Calculate as you would for regression.  Since there is more than one regression equation used in path analysis, need to calculate power for equation with the smallest effect size.

Terms Recursive (one way) X Y Non-recursive (two way) X Y

Indirect Effect XP Y Direct Effect X Y Both Direct & Indirect Effects XP Y

Endogenous Variable Y Exogenous Variable X

How many endongenous variables are in this model?……How many regression equations are needed to estimate the paths in this model? B Y A C

Labeling Path Coefficients p exogenous, endogenous B Y A C p B,A p Y,B p ?,?

Standardized Path Coefficients 1. All coefficients on the same scale. 2. Coefficients range from -1 to Allows comparisons across variables within the same model. Non-Standardized Path Coefficients 1. Scale varies. 2. Coefficients range from negative to positive infinity. 3. Allows comparison across groups or studies examining same relationships or models.

Identification Overidentified – number of paths is less than the number of variables Just identified – number of paths is equal to the number of variables Underidentified – number of paths is greater than the number of variables

Wright’s Rules for Calculating Direct & Indirect Effects 1. Can’t go thru the same variable more than once. 2. Can’t go forward with the arrow and then backwards. 3. Can’t go thru a curved double headed arrow (correlations are a dead end) more than once.

The three components of the correlation between X and Y Direct effect of x on y Indirect effect of x on y +Non-causal r x,y

Satisfaction With Current Weight Personal Attitudes Frequency of Exercise Overall State of Health FIGURE Final path analysis results for computer example. *Path coefficient is significant at p <.001. p s,f =.32* p f,p =.28* p o,s =.19* p o,p =.37* p o,f =.22* p s,p =.17