STATSU webinar:Path Analysis using Mplus

RME—Research, Measurement, and Evaluation

June 2, 2020

Welcome! Path Analysis using Mplus

“If a model is consistent with reality, then the data should beconsistent with the model. But if the data are consistent with the

model, this does not imply the model corresponds to reality”

-K. A. Bollen

Outline

1 Resources

2 Introduction

3 Causation

4 Recap of formulas in statistics

5 Framework for PA/SEM

6 Example 1

7 Examples

Website Links

University of Miami virtual lab for Mplus:https://vlabs.it.miami.edu/

Mplus website:https://www.statmodel.com/

Path Analysis:https://stats.idre.ucla.edu/mplus/seminars/mplus-class-

notes/path/

Names of notation methods in this webinar:linear structual relations (LISREL)reticular action model (RAM)

Resources

Leisure read on causal modeling:The Book of Why: The New Science of Cause and Effectby Judea Pearl and Dana Mackenzie

Structural Equation Text Book:Principles and Practice of Structural Equation Modelingby Rex B. Kline

History

Introduction to path analysis

Formalized approximately around the 1920’s by Sewall Wright.

Kline states the purpose of path analysis is to model thecorrelation among selected variables and to explain the variances inthe specified model.

Path analysis assumes that variables are perfectly measuredwithout error; However, the diagrams in this presentation willinclude error terms.

Introduction to path analysis

One or more independent variables and one or more dependentvariables can be examined through path analysis.

Path analysis (PA) can be considered a special case of structuralequation modeling (SEM) where all variables of interest aremanifest variables.

In other words, all independent variables/predicators for theoutcome can be observed, and measured directly.

correlation 6= causation

Causal inference:1 Association2 Temporal Antecedence

(if A −→ B, A occurs before B in time)3 Ingorability

(i.e., no unknown variables are influencing the model)

The model should be based on researched theory and tenable logic.Counterfactuals1 are important! Substantiated theory necessary...

lemons imported and highway deaths ≈ .9https://www.tylervigen.com/spurious-correlations

1A. person cannot be assigned to 2 conditions; B. the outcome exists underboth conditions

Review

Sample variance:

s2X =

N∑n=1

(X − X )2

n − 1 (1)

Pearson Product Moment Correlation:

rxy =

N∑n=1

(X − X )√√√√( N∑n=1

(X − X )2

)(N∑

n=1(Y − Y )2

) (2)

Review

Sample covariance for variables X an Y:

sXY = σXY = cov(X ,Y ) =

N∑n=1

(X − X )(Y − Y )

n − 1 (3)

Slope:

βxy =

N∑n=1

[(X − X )(Y − Y )

]N∑

n=1X − X

= rxy

(sysx

)(4)

Review

Cov(Row number , Column number)

Variance-Covariance matrix Var(X1) Cov(X1,X2) Cov(X1,X3)Cov(X2,X1) Var(X2) Cov(X2,X3)Cov(X3,X1) Cov(X3,X2) Var(X3)

“Diagional” values:

Off-diagonal values are two symmetrical triangles above and belowthe diagonal line.

Notation-Symbols

Foundations

Influence or cause BA −→ B

X and Y covaryX ←→ Y

Wright’s Path Tracing Rules

1 No looping back through the same variable2 No going backward on any arrow after going through it3 No more than 1 two-headed arrow for each compound path

Path Diagram

IV1 IV2

DV

yx

z

error

Example 1

IV1 IV2

DV

.60.55

.2

error

Wright’s Path Tracing Rules

1 No loops back through thesame variable

2 No going backward3 One two-headed arrow for

each compound path

Process

Kline, R. B. (2015). Principles and practice of structural equationmodeling. Guilford publications

Mplus input

University of Miami virtual lab for Mplus:https://vlabs.it.miami.edu/

In a text editor (i.e., Sublime Text, Vim, Coda, Atom...) or:Windows: NotepadMac OS: TextEdit

Mplus introduction

Thank you!

Questions?