Structural Equation Models: Complex Models for Complex Questions - - PowerPoint PPT Presentation

Structural Equation Models: Complex Models for Complex Questions

Adam C. Carle, MA, PhD Joe J. Sudano, PhD Adam T. Perzynski, PhD

Today

• Brief introduction to structural equation modeling

concepts.

• Two detailed presentations.

– Drs. Sudano and Perzynski.

• Time for questions.

A Bit About Me

Introduction

• The success of health services research depends
• n the measures and methods used.
• Structural equation models

– SEM.

• Use a set of equations to model the relationships

among a set of variables.

Why SEM?

• How might one test this entire model?

Why SEM?

• Ability to study complex relationships among

multiple variables.

– Some directly observed. – Others indirectly observed. – None measured without error.

• Simultaneously examine the relationships among

several variables.

– Test directionality. – Test timing of effects.

Why SEM?

• Ability to more accurately study and include

indirectly observed variables in analyses.

– Use a series of questions to measure an indirectly

• bserved variable.
• No single question perfectly measures a construct.

– Using a set of questions increases the accuracy with which one estimates individuals’ levels of the variable.

Measurement Model

Measurement Model

• SEM “partials out” random measurement error

and allows for more accurate estimation of relationships among variables.

– Random measurement error typically attenuates the true size of correlations.

• Effect sizes often small in social sciences.

– Attenuation makes it more difficult to observe and understand true effects. – SEM increases study’s power.

• SEM can model more complex forms of

measurement error too.

Measurement and Structure

“Structure”

• Structure is (in essence) specifying how the

variables in the model relate to one another.

• One can test and compare the fit of competing

models.

– Also called causal modeling (partly) because of this.

• Example:

– Hospital level factors predict patients’ outcomes. – Nurse level factors predict patients’ outcomes.

• Hospital level factors are limited by nurse level.

– Patient level factors predict patients’ outcomes.

• Hospital and nurse level factors are

limited by patient level factors.

Measurement and Structure

i i i i  

    η α Γ x Β η ζ

* i y i y i i

    Y υ Λ η Γ x ε

Hold the Horses…..

You promised no equations!

Measurement & Structure

An Alternate Specification

Longitudinal Research

• SEM offers tremendous advantages in

longitudinal research.

• Trajectories of change.

– How do one or more variables change across time?

• Mediation is a critical topic in HSR.

– What is the mechanism that causes a relationship between two variables? – To answer fully, one needs longitudinal data.

Mediation

• Simplified diagram of mediation in SEM.

Longitudinal Growth Models

• Simplified path model of longitudinal growth

analysis in SEM.

Multilevel SEM

• Much of the data in HSR is clustered data.

– Patients clustered within providers. – Providers clustered within centers. – Centers clustered within geographic areas.

• The concepts discussed so far remain relevant, but

now can be considered at all levels.

– A set of items may measure constructs differently across levels. – Growth can occur at both levels.

• And differentially.

Multilevel SEM

County-Level

Average individual response.

Individual-Level

y1

y2 y3 y4 y5 Individual Access y1 y2 y3 y4 y5 County Access Average county response.

y2 y3 y4 y5 y5 y2 y3 y2 y1

Categorical Latent Variables?

• So far, we have only discussed continuous latent

variables.

• Recent advances in SEM have combined mixture

models and structural equation models.

– Second generation SEM.

• Recent advances in SEM have combined mixture

models and structural equation models.

– Second generation SEM.

Factor Mixture Model

Factor Mixture Model

C F

Categorical Latent Variables?

• Growth mixture models.

– Combine growth model

• Trajectory.

– With mixture model

• Categorical latent variable.

– Model different growth trajectories across latent subgroups.

Conclusions

Conclusions

• SEM offers the HSR a tremendous tool to more

accurately, powerfully, and fully investigate key research questions.

– Opportunity to shed the untenable assumptions underlying the use of only directly observed data. – Flexible framework. – Ability to more powerfully evaluate complex questions and data.

• We’ve barely scratched surface of SEM’s potential.
• Drs. Sudano and Perzynski will present two

detailed examples.