1. Path Analysis Application of multiple linear regression.
Special case of Structural Equation Modeling.
Method to summarize and display information about relationships among variables.
6-Sep-19
AGR206

2. Uses of Path Analysis
Good presentation tool for results of multiple linear regression where there are intermediate variables and indirect effects because the causal variables are correlated.
Path analysis reflects part of the collinearity among explanatory variables.
To test how well a priori models are supported by the data. It cannot be used to derive the form of the relationships or of the diagram.
6-Sep-19
AGR206

3. Path analysis is based on MLR
Model:
Y = 0 + 1 X1 + 2 X2 + 
Assumptions:
Same as MLR:
Linearity
Normality of errors
Homogeneity of variance
Independence of errors
No outliers
6-Sep-19
AGR206

4. Example: teaching methods
Students were randomly assigned to two teaching methods.
Scores in the exam and degree of motivation were measured.
Objective performance (scores) is affected both by teaching method and motivation.
The new method can work if the negative link with motivation is changed.
6-Sep-19
AGR206

5. Example: deer bites (on plants!)
Theory indicated that quantity and quality of diet should be negative related.
Study over season with several deer showed no relationship.
Path analysis showed that theory should have been interpreted more carefully, and that relationships were actually present in data.
6-Sep-19
AGR206

6. Bite size and diet quality0!
Day of season
Plant mass
Bite Size
Diet quality
Plant quality
Deer Size + -
6-Sep-19
AGR206

7. Example: yield components
Fertility
Seeds/flower
No. Flowers
Yield
Water
Competitor Density
Seed size
es/f
enf eY
ess
6-Sep-19
AGR206

8. Example: yield or fitness components
A path diagram may have more than one “layer.”
All of the variance and covariance of the endogenous variables is explained by the exogenous variables and the residuals.
6-Sep-19
AGR206

9. Elements of path diagrams
6-Sep-19
AGR206

10. Diagram and models
Approaches = b1’ No. flowers + b2’ nectar p.r. + b3’ n. neighbor d.
fruit set = c1’ approaches + c2’ probes + c3’ n. neighbor d.
probes = d1’ appr. + d2’ No. flowers + d3’ nectar p.r. + d4’ n. neighbor d.
6-Sep-19
AGR206

11. Calculating path values
6-Sep-19
AGR206