Path Analysis

Remember What Multiple Regression Tells Us

• How each individual IV is related to the DV

• The total amount of variance explained in a DV

• Multiple regression is VERY DV CENTRIC!!!

• We know NOTHING about how the IV’s are related

What is Path Analysis?

• Another way to do Multiple Regression

• A special case of multiple regression where all the relationships among variables can be estimated simultaneously

What do you mean Simultaneously?

• Estimate correlations among your IV’s• Estimate regression relationships in the

model• You can make all the variables related to

one another and find out what the relationship is exactly!

• All the regression analyses we did in SPSS can be done in path analysis

Example

• Lets say you are interested in the extent to which intellectual activities mediate the relationship between education and cognition

SPSS

• SPSS tells you about mediation• SPSS tells you the relationship between

– Intellectual activities and cognition– Education and cognition

• SPSS doesn’t tell you anything about the relationship between education and intellectual activities

Coefficientsa

.257 .016 16.100 .000

.571 .065 .558 8.822 .000

.163 .049 3.320 .001

.521 .069 .509 7.560 .000

.008 .004 .136 2.016 .045

(Constant)

intell_act

(Constant)

intell_act

education

Model1

2

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: cognitiona.

Path Analysis

Education Activities Cognition

R2 = ?R2 = ?

a b

All these parameters are estimated at the same time!

c

• If we wanted to get the same results in SPSS we would have to do a bunch of different models– Education predicts cognition– Activities predicts cognition– Both Predict cognition

• If we had more than three variables you can see how this could get impossible

A model like this would be impossible in SPSS

DV

Mediator IV

Mediator IV

IV

IV

IV

Benefits of Path Analysis

• Estimate all the relationships among all variables SIMULTANEOUSLY

• Able to test various hypothesis regarding different relationships

• Most programs you do path analysis in having Missing Data Estimation procedures!!!– SPSS uses list-wise deletion

Statistical Packages for Path Analysis

• Path analysis is the precursor to Structural Equation Modeling

• Any SEM program can do path analysis– AMOS– LISREL– EQS

AMOS

• AMOS is now bundled with SPSS

• It is the EASIEST program to use

• It’s ease is based on the fact that you actually DRAW your models right in the program!!!

AMOS Steps

1. Open AMOS

2. Tell AMOS what SPSS data set to use

3. Draw your variables in AMOS

4. Select estimation and output options

5. Draw your model(s)

6. Run your model

(1) Open AMOS

(2) Tell AMOS what SPSS data set to use

• Select FILE on the top tool bar– Select DATA FILE from the drop down menu

Click on File Name and select your SPSS data set

Drawing Tool Bar

(3) Draw your variables in AMOS

Draw Your Variables

Variables are represented by a box

You click on this icon to draw a box in AMOS!

You RIGHT CLICK on your variable box to get the “Object Properties”

You write the NAME of your variable here

(4) Select estimation and output options• Select VIEW on the top tool bar

– Select ANALYSIS PROPERTIES from the drop down menu

(5) Draw your model(s)

Regression PathCorrelations

age memory

DV needs a way indicate variance not explained by AGE

age memory

1

0,

Error_1

AMOS practice

• Education and activity engagement are predictors of cognition. Also allow education and activity to correlate

– EDUCATION (educ), activity (activ), cognition (cog)