An Introduction to Path Analysis and Structural Modeling · PDF fileToday’s Class • An introduction to path analysis • An introduction to structural equation modeling • Information

An Introduction to Path Analysis andStructural Equation ModelingMultivariate Methods in Education

ERSH 8350Lecture #13 (and final)November 30, 2011

ERSH 8350: Lecture 13

Today’s Class

• An introduction to path analysis

• An introduction to structural equation modeling

• Information about the take‐home final exam Drafts for revisions: Due 11:59pm Wednesday, December 7th

Final Drafts: Due 11:59pm, Wednesday December 14th

ERSH 8350: Lecture 13 2

AN INTRODUCTION TO PATH ANALYSIS


Path Analysis

• Path analysis is a statistical technique used to estimate a set of simultaneous regression equations All variables are observed – assumed measured without error

In SEM, we can use a path analysis for latent variables

• Path models are useful for Mediation analyses: the effect of one variable on another is mediated by one or more variables

Simultaneous equations: multiple predictions of multiple variables in a model


Data Example

• Today’s example data come from the UCLA Academic Technology Services website http://www.ats.ucla.edu/stat/mplus/seminars/introMplus_part2/path.htm

• The data file contains four variables collected from 200 respondents: High School GPA (hs) College GPA (col) GRE Score (gre)

Note: GRE scores are not measured perfectly – so this is likely to over‐power this analysis

Graduate School GPA (grad)


Initial Setup: Determining What is Possible

• Much like the other analyses in this class, the number of “paths” in a path analysis is constrained by the number of covariances between the observed variables Here, a path represents a

regression coefficient

• Mplus can give you the descriptive statistics for an analysis with a fairly simple set of commands:


Mplus Output: Descriptive Statistics


Note: Estimates come from ML –with a MVN distribution

Covariances

Means

Variances

Mplus Output: Standardized Coefficients


Correlations

Initial Analysis: A Just Identified Model

• For our first analysis, we will examine the following set of equations:

• GRE score depends on HS (?) and COL GPA• GRAD GPA depends on HS GPA (?), COL GPA, and GRE score

• Note: 6 coefficients We have 6 covariances – so this models is called “just identified” Just identified models give no meaningful fit statistics


A Path Diagram of Path Analysis


Mplus Syntax and Output for Path Model #1


Path Analysis Unstandardized Parameter Output


Path Analysis Standardized Parameter Output


Types of Effects in Path Analysis

• Depending on how a model is set up, there are three types of effects in a path analysis: Direct effects – the influence of one variable directly on another Example: HS GPA on GRE Score

Indirect effects – the influence of one variable on another, as mediated by one or more variables Example: HS GPA on GRAD GPA, through GRE Score

Total effects – The aggregate effect of direct and indirect effects


Mplus Syntax for Indirect and Total Effects


Mplus Unstandardized Indirect Effects Output


Mplus Standardized Indirect Effects Output


Over‐Identified Models

• Over identified path models are models with fewer coefficients than covariances Tests of model fit are available Even if model fit is poor, information may be meaningful

• New model:


Mplus Syntax


Mplus Model Fit Output


Mplus Unstandardized Output


Mplus Standardized Output


Mplus Unstandardized Indirect Effects Output


Mplus Standardized Indirect Effects Output


Path Analysis Wrap‐Up

• Path analysis is a powerful technique for testing multivariate regression models with direct and indirect effects

• The example shown today was meant to provide a basic overview of the technique Many details omitted

• For more information, come to the SEM course next semester


AN INTRODUCTION TO STRUCTURAL EQUATION MODELING


Structural Equation Modeling• Similar to confirmatory factor analysis and path analysis,

structural equation model seeks to describe relationships between latent variables Generally speaking, SEM is for latent variables…path analysis is for

observed variables

• SEM consists of two key elements: Measurement model – typically a confirmatory factor model

The link between the data and the latent variables Structural model – a path model or factor model for the

latent variables Generally uses the covariance matrix between latent factors

• As such, the basic SEM analysis consists of portions you already know


SEM: Example Data

• To demonstrate the structural equation model, we will use data presented in the PCA/EFA lecture Gambling research instrument: 41 items measuring 10 factors

• We will use these data to demonstrate SEM through: A higher order factor model

A path model for the higher order factors

• Before we do either of these, we must first construct a measurement model A CFA model for the data


Pathological Gambling: DSM Definition

• To be diagnosed as a pathological gambler, an individual must meet 5 of 10 defined criteria:

Pathological Gambling 29

1. Is preoccupied with gambling 2. Needs to gamble with increasing

amounts of money in order to achieve the desired excitement

3. Has repeated unsuccessful efforts to control, cut back, or stop gambling

4. Is restless or irritable when attempting to cut down or stop gambling

5. Gambles as a way of escaping from problems or relieving a dysphoricmood

6. After losing money gambling, often returns another day to get even

7. Lies to family members, therapist, or others to conceal the extent of involvement with gambling

8. Has committed illegal acts such as forgery, fraud, theft, or embezzlement to finance gambling

9. Has jeopardized or lost a significant relationship, job, educational, or career opportunity because of gambling

10. Relies on others to provide money to relieve a desperate financial situation caused by gambling

Research on Pathological Gambling

• The Gambling Research Instrument (Feasel, Henson, & Jones, 2002) was created with 41 Likert‐type items Items were developed to measure each criterion

• Example items (ratings: Strongly Disagree to Strongly Agree): I worry that I am spending too much money on gambling (C3) There are few things I would rather do than gamble (C1)

• The instrument was used on a sample of experienced gamblers from a riverboat casino in a Flat Midwestern State Casino patrons were solicited after playing roulette

Pathological Gambling 30

Measurement Model Mplus Syntax


Measurement Model Output


Structural Equation Model #1

• The first model we will estimate attempts to determine if the 10 gambling criteria are all related to a hierarchical factor of gambling:


Gambling

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10

Mplus Syntax


Mplus Output


Mplus Output

• Unstandardized:

• Standardized:



• The DSM suggests the gambling criteria are influenced by three factors: dependency, disruption, and loss of control:


C1 C2 C3C4 C5 C6 C7C8 C9 C10

Dependency Loss of Control

Disruption

Mplus Syntax


Mplus Output


Mplus Output

• Unstandardized:

• Standardized:



• Instead of correlated factors, could we determine if dependency caused loss of control, which caused disruption?


C1 C2 C3C4 C5 C6 C7C8 C9 C10

Dependency Loss of Control

Disruption

Mplus Syntax


Mplus Output


Mplus Output

• Unstandardized:


Mplus Output

• Standardized:


SEM Wrap Up

• Structural equation modeling is a procedure where relationships between latent variables is evaluated and tested statistically Based on covariances of latent variables

• The modeling technique is very powerful: it extends well beyond what was shown today


TAKE HOME FINAL EXAM INFORMATION


Take Home Final Exam Information

• The take home final exam is a two‐week test where you are asked to perform an intricate data analysis using techniques learned in this class

• The final will not be easy – but can be done I would suggest you do not procrastinate

• I am offering you the chance to receive feedback if you submit a draft of your final by next Wednesday Your draft must be an attempted answer, not simply syntax and output


Course Evaluations

• Please complete the course evaluation at:

https://portal.coe.uga.edu/apps/authorize/

• Thank you for a wonderful semester I hope you found this course informative!


Documents

An Introduction to Path Analysis and Structural Modeling · PDF fileToday’s Class • An introduction to path analysis • An introduction to structural equation modeling • Information