CJT 765 CJT 765 Quantitative Quantitative Methods in Methods in

CommunicationCommunicationStructural Equation ModelingStructural Equation Modeling

Class 1: IntroductionClass 1: Introduction

Review syllabusReview syllabus Discuss history of SEMDiscuss history of SEM Discuss issues related to causationDiscuss issues related to causation

Definitions of Structural Definitions of Structural Equation Models/ModelingEquation Models/Modeling

““Structural equation modeling (SEM) does not Structural equation modeling (SEM) does not designate a single statistical technique but designate a single statistical technique but instead refers to a family of related procedures. instead refers to a family of related procedures. Other terms such as covariance structure Other terms such as covariance structure analysis, covariance structural modeling, or analysis, covariance structural modeling, or analysis of covariance structures are essentially analysis of covariance structures are essentially interchangeable. Another term…is causal interchangeable. Another term…is causal modeling, which is used mainly in association modeling, which is used mainly in association with the technique of path analysis. This with the technique of path analysis. This expression may be somewhat dated, however, as expression may be somewhat dated, however, as it seems to appear less often in the literature it seems to appear less often in the literature nowadays.” (Kline, 2005)nowadays.” (Kline, 2005)

History of SEMHistory of SEM

Sewall Wright and Path AnalysisSewall Wright and Path Analysis Duncan and Path AnalysisDuncan and Path Analysis EconometricsEconometrics Joreskog and LISRELJoreskog and LISREL Bentler and EQSBentler and EQS Muthen and MplusMuthen and Mplus

Sewall WrightSewall Wright

GeneticistGeneticist Principle of Path Analysis provides Principle of Path Analysis provides

algorithm for decomposing algorithm for decomposing correlations of 2 variables into correlations of 2 variables into structural relations among a set of structural relations among a set of variablesvariables

Created the path diagramCreated the path diagram Applied path analysis to genetics, Applied path analysis to genetics,

psychology, and economicspsychology, and economics

DuncanDuncan

Applied path analysis methods to the Applied path analysis methods to the area of social stratification area of social stratification (occupational attainment)(occupational attainment)

Key papers by Duncan & Hodge Key papers by Duncan & Hodge (1964) and Blau & Duncan (1967) (1964) and Blau & Duncan (1967)

Developed one of the first texts on Developed one of the first texts on path analysispath analysis

EconometricsEconometrics

Goldberger added the importance of Goldberger added the importance of standard errors and links to statistical standard errors and links to statistical inferenceinference

Showed how ordinary least squares Showed how ordinary least squares estimates of parameters in overidentified estimates of parameters in overidentified systems of equations were more efficient systems of equations were more efficient than averages of multiple estimates of than averages of multiple estimates of parametersparameters

Combined psychometric and Combined psychometric and econometric componentseconometric components

Indirect EffectsIndirect Effects

Duncan (1966, 1975)—applying Duncan (1966, 1975)—applying tracing rulestracing rules

Reduced-form equations (Alwin & Reduced-form equations (Alwin & Hauser, 1975)Hauser, 1975)

Asymptotic distribution of indirect Asymptotic distribution of indirect effects (Sobel, 1982)effects (Sobel, 1982)

JoreskögJoreskög

Maximum Likelihood estimator was Maximum Likelihood estimator was an improvement over 2 and 3 stage an improvement over 2 and 3 stage least squares methodsleast squares methods

Joreskög made structural equation Joreskög made structural equation modeling more accessible (if only modeling more accessible (if only slightly!) with the introduction of slightly!) with the introduction of LISREL, a computer programLISREL, a computer program

Added model fit indicesAdded model fit indices Added multiple-group modelsAdded multiple-group models

BentlerBentler

Refined fit indicesRefined fit indices Added specific effects and brought Added specific effects and brought

SEM into the field of psychology, SEM into the field of psychology, which otherwise was later than which otherwise was later than economics and sociology in its economics and sociology in its introduction to SEMintroduction to SEM

MuthénMuthén

Added latent growth curve analysisAdded latent growth curve analysis Added hierarchical (multi-level) Added hierarchical (multi-level)

modelingmodeling

Other DevelopmentsOther Developments

Models for dichotomous and ordinal Models for dichotomous and ordinal variablesvariables

Various combinations of hierarchical Various combinations of hierarchical (multi-level) modeling, latent growth (multi-level) modeling, latent growth curve analysis, multiple-group curve analysis, multiple-group analysesanalyses

Use of interaction termsUse of interaction terms

Quips and Quotes Quips and Quotes (Wolfle, 2003)(Wolfle, 2003)

““Here I was doing elaborate, cross-lagged, multiple-Here I was doing elaborate, cross-lagged, multiple-partial canonical correlations involving dozens of partial canonical correlations involving dozens of variables, and that eminent sociologist [Paul variables, and that eminent sociologist [Paul Lazarsfeld] was still messing around with chi square Lazarsfeld] was still messing around with chi square tables! What I did not appreciate was that his little tables! What I did not appreciate was that his little analyses were generally more informative than my analyses were generally more informative than my elaborate ones, because he had the ‘right’ variables. elaborate ones, because he had the ‘right’ variables. He knew his subject matter. He was aware of the He knew his subject matter. He was aware of the major alternative explanations that had to be major alternative explanations that had to be guarded against and took that into account when he guarded against and took that into account when he decided upon the four or five variables that were decided upon the four or five variables that were crucial to include. His work represented the state of crucial to include. His work represented the state of the art in model building, while my work represented the art in model building, while my work represented the state of the art in number crunching.” (Cooley, the state of the art in number crunching.” (Cooley, 1978)1978)

Quips and Quotes (cont.)Quips and Quotes (cont.)

““All models are wrong, but some are All models are wrong, but some are useful.” (Box, 1979)useful.” (Box, 1979)

““Analysis of covariance structures…is Analysis of covariance structures…is explicitly aimed at complex testing of explicitly aimed at complex testing of theory, and superbly combines methods theory, and superbly combines methods hitherto considered and used separately. hitherto considered and used separately. It also makes possible the rigorous It also makes possible the rigorous testing of theories that have until now testing of theories that have until now been very difficult to test adequately.” been very difficult to test adequately.” (Kerlinger, 1977)(Kerlinger, 1977)

Quips and Quotes (cont.)Quips and Quotes (cont.)

““The government are very keen on The government are very keen on amassing statistics. They collect them, amassing statistics. They collect them, add them, raise them to the nth power, add them, raise them to the nth power, take the cube root and prepare take the cube root and prepare wonderful diagrams. But you must wonderful diagrams. But you must never forget that every one of these never forget that every one of these figures come in the first instance from figures come in the first instance from the village watchman, who just puts the village watchman, who just puts down what he damn pleases.” (Sir J. down what he damn pleases.” (Sir J. Stamp, 1929)Stamp, 1929)

Family Tree of SEMFamily Tree of SEM

T -te s t

L a ten tG row thC urv eAna lys is

ANOVA

M ulti-w ayANOVA Repea ted

M easureD es ign s

G row thC urv eAna lys is

B iv aria teC orre la tion

M ultip leRegre s s ion

P a thAna lys is

S truc tura lE qua tio nM ode ling

F ac torAna lys is

C on firm a toryF ac to rAna lys is

E xp lo ra to ryF ac to rAna lys is

Types of SEM ModelsTypes of SEM Models

Path Analysis ModelsPath Analysis Models Confirmatory factory analysis Confirmatory factory analysis

modelsmodels Structural regression modelsStructural regression models Latent change modelsLatent change models

Causation/CausalityCausation/Causality

David HumeDavid Hume John Stuart MillJohn Stuart Mill More Contemporary PerspectivesMore Contemporary Perspectives

HumeHume Three Principles of Connexion:Three Principles of Connexion:

Resemblance, continguity, and cause and effectResemblance, continguity, and cause and effect Causation takes us beyond evidence of memory and Causation takes us beyond evidence of memory and

sensessenses Must first show that alternative accounts of our Must first show that alternative accounts of our

causal reasonings are inadequatecausal reasonings are inadequate Then must show necessary connection for cause—Then must show necessary connection for cause—

““an object, followed by another, and where all objects an object, followed by another, and where all objects similar to the first are followed by objects similar to the similar to the first are followed by objects similar to the second”second”

An object followed by another, and whose appearance An object followed by another, and whose appearance always conveys the thought to that other”always conveys the thought to that other”

MillMill

Five canons on which causation may Five canons on which causation may be established or proven:be established or proven: 1. If 2 or more instances of the 1. If 2 or more instances of the

phenomenon under investigation phenomenon under investigation have only one circumstance in have only one circumstance in common, the circumstance in common, the circumstance in which alone all the instances agree which alone all the instances agree is the cause or effect of the given is the cause or effect of the given phenomenon.phenomenon.

MillMill

2. If the phenomenon under 2. If the phenomenon under investigation occurs, and an instance investigation occurs, and an instance in which it does not occur, have every in which it does not occur, have every circumstance in common save one, circumstance in common save one, and that one occurring only in the and that one occurring only in the former, the circumstance in which former, the circumstance in which alone the two instances differ is the alone the two instances differ is the effect or the cause, or a necessary effect or the cause, or a necessary part of the cause, of the part of the cause, of the phenomenon.phenomenon.

Mill (cont.)Mill (cont.)

3. If two or more instances in which the 3. If two or more instances in which the phenomenon occurs have only one phenomenon occurs have only one circumstance in common, while two or circumstance in common, while two or more instances in which it does not more instances in which it does not occur have nothing in common save the occur have nothing in common save the absence of that phenomenon, the absence of that phenomenon, the circumstance in which alone the two circumstance in which alone the two sets of instances differ is the effect or sets of instances differ is the effect or cause, or a necessary part of the cause, cause, or a necessary part of the cause, of the phenomenon.of the phenomenon.

Mill (cont.)Mill (cont.)

4. Subduct from any 4. Subduct from any phenomenon such part as is phenomenon such part as is known by previous inductions known by previous inductions to be the effect of certain to be the effect of certain antecedents, and the residue of antecedents, and the residue of the phenomenon is the effect of the phenomenon is the effect of the remaining antecedents.the remaining antecedents.

Mill (cont.)Mill (cont.)

5. Whatever phenomenon varies in any 5. Whatever phenomenon varies in any manner whenever another phenomenon manner whenever another phenomenon varies in some particular manner is varies in some particular manner is either a cause or an effect of that either a cause or an effect of that phenomenon, or is connected with it phenomenon, or is connected with it through some fact of causation. The through some fact of causation. The difficulty of discovering causation is difficulty of discovering causation is greatly increased by the fact that in greatly increased by the fact that in many cases there are plurality of causes many cases there are plurality of causes and intermixture of effects.and intermixture of effects.

Other ViewsOther Views

SalmonSalmon Statistics and relations among variables are Statistics and relations among variables are

probabilistic rather than wholly probabilistic rather than wholly deterministicdeterministic

PearlsPearls D-separataionD-separataion CounterfactualsCounterfactuals SurgeriesSurgeries Bayesian EstimatesBayesian Estimates The importance of diagrams as The importance of diagrams as

mathematical modelmathematical model

Ways to Increase Ways to Increase Confidence in Causal Confidence in Causal

ExplanationsExplanations Conduct experiment if possibleConduct experiment if possible If not:If not:

Control for additional potential confounding Control for additional potential confounding (independent or mediating) variables(independent or mediating) variables

Control for measurement error (as in SEM)Control for measurement error (as in SEM) Make sure statistical power is adequate to Make sure statistical power is adequate to

detect effects or test modeldetect effects or test model Use theory, carefully conceptualize variables, Use theory, carefully conceptualize variables,

and carefully select variables for inclusionand carefully select variables for inclusion Compare models rather than merely assessing Compare models rather than merely assessing

one modelone model Collect data longitudinally if possibleCollect data longitudinally if possible