chapter 6 examples: growth modeling and survival analysis - Mplus
An Overview of Structural EquationModeling using Mplus · I Mixed e ect models for longitudinal...
Transcript of An Overview of Structural EquationModeling using Mplus · I Mixed e ect models for longitudinal...
Harvard Catalyst Biostatistical Seminar
Neuropsychological Pro�les in Alzheimer's Disease and
Cerebral Infarction: A Longitudinal MIMIC Model
An Overview of Structural EquationModeling using Mplus
Richard N. Jones, Sc.D.
Institute for Aging Research, Hebrew SeniorLife
Beth Israel Deaconess Medical Center, Harvard Medical School
HSPH Kresge G2 October 5, 2011
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Objective Overview of SEM in Cognitive Aging & Health Research
Objective
IntroduceI the concepts and terminology relevant to structural equation modeling
(SEM) as applied to health research
Speci�c ExampleI Cognitive EpidemiologyI Mplus software 1
EmphasisI on a broad survey of applications, results, challenges, and opportunities
1www.statmodel.com
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Introduction Use of Mplus and SEM Applications in Epidemiology
Mplus and SEM Trends in Epidemiology
Relative to the frequency
with which Cox Regression
and Epidemiology appear
in Google Scholar...
Citations matching Mplus
and Epidemiology are
increasing
Although speci�c
applications are decreasing
Mplus use is increasing
and applications are
becoming more diverse
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Introduction What is Mplus, Anyways?
Mplus: General statistical analysis software good for...
Analysis with latent variables
Clustered and correlated dataI Complex sampling, weightingI Repeated measuresI Multicomponent variables (i.e., scales, composite outcomes)I Correlated observations (e.g., twins, families)I Multilevel contexts
Particular strengthsI Missing data modelingI Bayesian data analysisI Complex models
F Joint models of change and event occurrenceF Mixture models (population heterogeneity)F Longitudinal factor analysis
Where Mplus is not strongI Data managementI Graphics
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Introduction SEM in Epidemiologic Research
Structural Equation Modeling in Epidemiologic Research
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Introduction Everything You Need to Know about SEM in 1 Slide
Structural Equation Modeling in Epidemiologic Research
DeStavola et al (2005), bottom panel Figure 3
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Introduction What is SEM?
Structural Equation Modeling (SEM) is
A general multivariate regression modeling frameworkI General - �exible model typesI Multivariate - multiple dependent variablesI Regression - it's just regression. Regression can be viewed as a special
case of SEM
SEMs often include latent variablesI Continuous latent variables (i.e., factors)I Categorical latent variables (i.e., classes, mixtures)
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Introduction Varieties of Covariance Structure Modeling
Continuous Latent Variables
No Yes
Regressions among
No
Regression Factor
Dependent or Latent (Multivari-able\-ate) Analysis
Variables y = ν + ΓX+ ε y = ν + Λη + ε
Yes
Path Structural Equa-
Analysis tion Modeling
y = ν + BY + ΓX+ ε y = ν + Λη +KX+ εη = α+ Bη + ΓX+ ζ
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Introduction Get yourself started
SEM Prerequisites
General linear modelI Linear, logistic, & probit regressionI Multivariable regressionI Mixed e�ect models for longitudinal dataI Survival and event occurrence (Cox, parametric survival)
Missing data theoryI Little and Rubin, Statistical Analysis with Missing Data. 1987
Factor AnalysisI Brown, Con�rmatory Factor Analysis for Applied Research. 2006
Item Response TheoryI Embretson and Reise, Item Response Theory for Psychologists. 2000
Path AnalysisI Kerlinger and Pedhazur, Multiple Regression in Behavioral Research.
1973
Structural Equation ModelingI Jöreskog and Sörbom, LISREL 8: User's Reference Guide. 1996
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Introduction What you have to look forward to
Mplus Work�ow
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Introduction But life can be better
Mplus Work�ow
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Introduction Weaving with Stata and a good Text Editor is Fun and Easy
Mplus Work�ow - Weaving = Reproducible Research
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Introduction Path Diagrams and Equations - Variables
Multivariate Regression
y = ν + ΓX + ε
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Introduction Path Diagrams and Equations - Variables
Multivariate Regression
Mplus Syntax
TITLE: Multivariate regression
DATA: FILE = data.dat ;
VARIABLE: NAMES = y1 y2 x1 x2 ;
MODEL: y1 y2 on x1 x2 ;
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Introduction Path Diagrams and Equations - Variables
Con�rmatory Factor Analysis
y = ν + Λη + ε
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Introduction Path Diagrams and Equations - Variables
Con�rmatory Factor Analysis
Mplus Syntax
TITLE: Confirmatory Factor Analysis
DATA: FILE = data.dat ;
VARIABLE: NAMES = y1 y2 y3 ;
MODEL: eta by y1 y2 y3 ;
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Introduction Path Diagrams and Equations - Variables
Structural Equation Modeling
y = ν + Λη +KX + ε
η = α +Bη + ΓX + ζ
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Introduction Path Diagrams and Equations - Variables
Structural Equation Modeling
Mplus Syntax
TITLE: Structural Equation Model
DATA: FILE = data.dat ;
VARIABLE: NAMES = y1-y6 x1 ;
MODEL: eta1 by y1-y3 ; ! measurement model for eta1
eta2 by y4-y6 ; ! measurement model for eta2
eta2 on eta1 ; ! a structural regression
eta1 on x1 ; ! an "indirect effect"
y1 on x1 ; ! a "direct effect"
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Introduction Path Diagrams and Equations - Variables
Structural Equation Modeling
Mplus Syntax
. runmplus y1-y6 x1 , model(eta1 by y1-y3 ; eta2 by y4-y6 ; ///eta2 on eta1 ; eta1 on x1 ; y1 on x1 ;)
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Latent Variables What is a Latent Variable?
What Latent Variables Are
Latent variables are mathematical abstractions
that account for covariation among observed
variables
Latent variables may be continuous or
categorical
But what do they mean?
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Latent Variables What is a Latent Variable?
What is the Meaning Behind a Latent Variable?
The answer depends on theI scienti�c questionI philosophical position 2
Two broad classes of latent variable (LV) applicationsI Instrumentalist
F the LV is a mathematical abstraction
I RealistF the LV existsF the LV re�ects some unmeasurable quantity or quality that really exists
in natureF the LV exists independently of our measurement of it
Realist or Instrumentalist interpretations are a matter of statistical
inference
2Borsboom, Mellenbergh et al., 2003 Psychol Rev 110:203-18
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Conclusion
Parting Words
Why use SEM?I More easily specify analysis to answer research questionI Gain statistical power
Not sure if SEM is right for you?I Stata Corp recently added SEM to Stata (version 12)I ... and pitching SEM to EconomistsI http://www.stata.com/news/statanews.26.3.pdf
Why use Mplus?I Regression-based framework for exogenous variablesI Categorical dependent variablesI Categorical latent variablesI Complex sampling weightsI Survival analysisI Bayesian data analysis
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Conclusion Penetrance of SEM Concepts and Software
Google Scholar Hits 1998-2011 (5 Oct 2011)
Keyword phrase NEJM JAMA+ AJE
analysis 10,000 16,000 4,500
logistic regression 1,000 2,000 2,000linear regression 620 1,700 1,700cox proportional 610 760 650random e�ects 100 540 340generalized estimating 110 280 320
factor analysis 90 190 170structural equation 21 25 49pro�le mixture OR latent class 13 12 21item response theory 2 12 3path analysis 5 10 19latent growth curve 0 1 4
SAS Institute 440 2,500 1,400SPSS 210 1,100 240Stata 190 800 590R Foundation OR R Development 36 100 87
Mplus 0 12 15LISREL 1 3 13
Note: Hits include the text matches in the reference list.
Values greater than 100 rounded to two signi�cant digits.
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