An Introduction to Structural Equation Modeling for Survey Researchers

[MUSIC PLAYING][An Introduction to Structural Equation Modelingfor Survey Researchers]

DR. BRADY WEST: Hi, my name is Brady West,and I'm a Research Assistant Professorat the University of Michigan [BRADY WEST, PhD,Research Assistant Professor] Institute for Social Research,specifically in the Survey Research Center.And today in this tutorial, I'll betalking about structural equation modeling.I do research in modeling of survey data.And in this tutorial, we'll be talkingabout major concepts of structural equation modeling,

DR. BRADY WEST [continued]: and then potential applications of structural equation modelingto different research problems in the survey research arena.So in this tutorial, the major learning objectiveswill be to understand the primary conceptsof structural equation modeling and a lotof the important terminology.Think about how one would write down structural equation

DR. BRADY WEST [continued]: models when you're thinking about fitting them to data.Talk about interpretation of structural equation modelingor of models, and the different waysin which structural equation models canbe applied to address specific research questions.And then we're also going to talk about software that can beused to fit structural equation models,and the different state-of-the-art software tools

DR. BRADY WEST [continued]: that are out there today enabling researchers to workwith these kinds of models.And then finally, we'll be talkingabout specialized software enabling researchersto fit structural equation models to datafrom complex samples and some of the underlyingissues with those types of software procedures.[What does the term structural equation model mean?]

DR. BRADY WEST [continued]: So the term "structural equation model"refers to a statistical model thatgenerally combines two different types of models in one.First of all, there's a measurement model,where latent variables or variables thataren't actually observed in a survey data collectionare indicated by other variables that are actuallyobserved in the data set.

DR. BRADY WEST [continued]: And that measurement model defines a seriesof latent traits or constructs that researchers maybe interested in quantifying.And those latent variables are quantified with the observedvariables in the data set.So that's the measurement portionof a structural equation model.The second main portion of the structural equation modelis the structural model.And that's the portion of the model that

DR. BRADY WEST [continued]: relates both latent variables and observed variablesto each other.So the structural model is the partof the model that allows researchers to quantifythe relationships between different latent variablesand different observed variables.So when one fits a structural equation model,one may be interested in these latent variables which,again, aren't actually observed in the data set,

DR. BRADY WEST [continued]: but are still used to quantify unknown traits basedon other observed variables, and then the structural partof the model that allows researchersto quantify relationships of scientific interest.And a key aspect of structural equation modelingis the presence of these latent variables that, again, capturevariables that aren't necessarilymeasured in the data collection, but may be of otherwise

DR. BRADY WEST [continued]: interest.And the structural model generallycould include both latent and observed variablesand the relationship between those,but the structural portion could also just define relationshipsamong observed variables only.One of the really interesting thingsabout structural equation models isthat complex causal relationships

DR. BRADY WEST [continued]: and causal pathways can be studied.And these pathways could involve latent variables,as I mentioned earlier, that are defined in the measurementportion of the model, and then also observed variables.So researchers can test hypothesesabout the possibility or the plausibilityof complex causal pathways when describing the relationshipsbetween variables.

DR. BRADY WEST [continued]: And structural equation modeling allows researchersto do that via the use of latent variables,and then these combinations of measurement structural models.[How would you apply structural equation models to surveyresearch?]In terms of applications of structural equationmodels in the social sciences and in survey research,

DR. BRADY WEST [continued]: there are many different types of applications.Often, structural equation modelsare used to determine whether a series of unobserved variablescan reliably indicate these latent traits that, again, wearen't able to directly observe in a data collection.So in many cases, those measurement modelsare used to determine whether different observed variables

DR. BRADY WEST [continued]: are, in fact, highly correlated with each other,and define reliable indicators of a particular latent trait.So many cases, survey researchersmight be interested in trying to quantify an unobservedtrait like political knowledge or something like that.And they'll use a series of observed variablesto try to get at the level of political knowledgethat an individual may have.

DR. BRADY WEST [continued]: Structural equation models specifically allow researchers,then, to define these unobserved variableslike political knowledge as a function of the observedvariables in the data set.So measurement models are often usedto allow survey researchers to form scales,in many cases, that are indicated

DR. BRADY WEST [continued]: by these different observed variables.So that's one very common application.And along the same line, survey researcherswill also use structural equation modelsto get a sense of possible measurementerror in observed variables.So a particular class of structural equation modeling,known as latent class analysis, canbe used when survey researchers collect

DR. BRADY WEST [continued]: categorical measures of certain behaviorslike drug use or risky behaviors.And in face-to-face interviews, respondentsmay not be truthful about these different kinds of behaviors.So structural equation modeling, and specificallylatent class analysis, can be usedto identify latent classes or groups of individuals based

DR. BRADY WEST [continued]: on their patterns of responses to these different typesof categorical measures.And these latent groups of individualscan then be compared in terms of other observed variablesor other types of outcomes.And a cool part of latent class analysisis that given these latent classes,we can estimate the probability that someonemay be untruthful on one of these observed variables.

DR. BRADY WEST [continued]: So latent classes allow us to estimate error ratesin categorical variables.And if we're analyzing continuous variables,we can use those latent measures to basically smooth outany measurement error that may be occurringin the continuous variables.And by analyzing those latent variables, whichessentially aggregate information across thoseobserved variables, we have this nice property

DR. BRADY WEST [continued]: of smoothing out any measurement issues thatmay be occurring in the individual observed variables.So survey researchers like to use these structural equationmodels, because they allow us to study the measurementproperties of particular variablesand particular constructs.And then on top of that, once these measurement modelsare used to refine particular measurements,we look at the relationships, as mentioned earlier,

DR. BRADY WEST [continued]: between these latent constructs and potentially otherobserved variables or other latent variables themselves.And this can be done in longitudinal data collection.So we can study relationships over timebetween different variables.We can study what are potentiallycalled mediating relationships, wherethe relationship between one variable and another

DR. BRADY WEST [continued]: may be carried or mediated by an intermediary variable.And these are different types of causal hypothesesthat define the relationships between variables.So there are a variety of possible applications.These models are quite popular in psychologyand other social sciences, where peopletry to understand the psychometric propertiesof particular measurements and constructs.

DR. BRADY WEST [continued]: And by using this latent variable modeling framework,we can really get a good sense of some of the measurementproperties of the different variablesthat we're trying to collect.And then, again, use the latent variablesthemselves to study the relationshipsbetween these different latent traits.[Why use structural equation models in survey research?]

DR. BRADY WEST [continued]: The primary motivation for fitting structural equationmodels is, again, to try to describethe reliability of different variables or related variablesin indicating these different latent constructs,and then also to describe causal relationshipsbetween variables.So when one decides to fit a structural equation model

DR. BRADY WEST [continued]: there may be a couple of primary objectives-- first of all,to determine whether or not a series of related variablesare reliably indicating a particular latent trait.And a second main objective is to test a hypothesizedcausal relationship between variables,possibly a mediating relationship,or possibly whether relationships between variables

DR. BRADY WEST [continued]: may change across different subgroupsin a population of interest, such as males and females.So there are two really primary motivationsfor fitting these models.It's, again, to study the measurement propertiesof particular observed variables,and seeing whether we can form individual latentvariables using several different observed variables.

DR. BRADY WEST [continued]: And that has the nice property of reducingthe dimensionality of a given modelingproblem from many observed variables down to one single,or maybe a small handful, of latent variables.And then second of all, to test whether hypothesized causalrelationships actually exist.And structural equation models allowus to test more complicated relationships

DR. BRADY WEST [continued]: than one may be able to typically testusing standard linear regression and related types of models.So understanding and testing causal relationshipsis really one of the primary motivationsfor fitting these models, in additionto studying the measurement propertiesof individual variables.[What does structural equation modeling allow you to do?]

DR. BRADY WEST [continued]: So structural equation modeling allowsyou to test these more complicated hypotheses-- firstof all, about whether or not particular variables reliablyindicate a particular latent trait so we can formallytest whether representing a series of unobserved variableswith a single latent variable actually

DR. BRADY WEST [continued]: does a good job of replicating what the available data aretelling us, and replicating the correlations among variablesin the actual data set itself.So can we, again, reduce the dimensionalityof a given problem, and take advantage of the factthat multiple variables are correlated with each other,and essentially combine them into a single latent measure

DR. BRADY WEST [continued]: that can be further analyzed?So that's one cool aspect of structural equation modeling.And second of all, structural equation modeling, again,allows you to study these complex relationshipswhere one may be interested in testing a mediationrelationship or a causal relationshipwith many different steps.For example, variable a predicts variableb, which in turn predicts variable c, which

DR. BRADY WEST [continued]: in turn may predict variable d.We can study these complex causal pathways.And many researchers like fitting structural equationmodels for that purpose, because they can test some veryunique causal hypotheses.And a lot of this is generally facilitatedwith longitudinal data, which allows peopleto test causal hypotheses using datafrom different points in time.

DR. BRADY WEST [continued]: But with structural equation models,we can at least test whether certain causal relationshipsare plausible.And many of these types of complex relationshipscan't be easily tested using more standard techniques--again, like linear and logistic regression modeling.So it's really nice that structural equation modelsallow researchers to test hypothesesabout these complex causal pathways.

DR. BRADY WEST [continued]: [Examples of Structural Equation Modeling]So one example of structural equation modelingthat's quite common in the literaturein the social sciences is called "confirmatory factor analysis,"where researchers can fit models to confirmthat a factor structure actually exists given the observed data.

DR. BRADY WEST [continued]: So this makes use of the measurement modelsthat we were talking about earlier, wherea series of related variables is represented by a single latentvariable.And when fitting that kind of measurement model,and using a technique known as confirmatory factor analysis,we can confirm, in fact, that that latent factor is reliablyindicated by that series of unobserved variables.

DR. BRADY WEST [continued]: And we can do that using multiple latent variablesindicated by multiple sets of observed variables.And these types of confirmatory factor analysesare widely used to establish the measurementproperties of sets of related variables in a given data set.So there are many examples of papersthat use confirmatory factor analysis to study

DR. BRADY WEST [continued]: the measurement properties of observed variables.Another type of structural equation modelis, again, one that combines both latent variables and thenalso relationships between latent variables.And we'll show some slides that indicatean example of measurement models being used to define latent

DR. BRADY WEST [continued]: variables, and then relationshipsbetween those latent variables being quantified.And we'll see a specific example from the literaturethere, as well.Another type of model that can be fittedin the structural equation modeling frameworkis a multi-level model, and specifically growth curvemodels, that allow us to quantifythe variability among individuals in termsof trajectories over time.

DR. BRADY WEST [continued]: So in that framework, the effectsthat individuals have on particular survey outcomesover time can be quantified as random interceptsand random slopes.And we can estimate the variability in those interceptsand slopes by treating those as latent variablesin a structural equation modeling framework.So many types of multi-level modelsare used in the existing literature.

DR. BRADY WEST [continued]: And we'll see a picture of that in the PowerPoint slides,as well.Another type of structural equation modelthat appears in the literature a lotis a path model, where all the variables are actuallyobserved.So there are no latent variables.But the path model which is oftenfitted to longitudinal data allowsus to quantify complex causal pathways defining relationships

DR. BRADY WEST [continued]: between observed variables that are collected over time.And we'll see a picture of that kind of path model usedto test to mediation as well.And then a final type of model that I want to mention againis latent class analysis, where again, we'retrying to identify latent classes of individuals based

DR. BRADY WEST [continued]: on their responses on a series of categorical variables,and then potentially see how those different classesof individuals might relate to other observed variables.So latent class analysis is quite oftenused in the literature, again, to study measurementproperties, and try to identify latent or unobserved classesof individuals based on their responsesto series of categorical variables.

DR. BRADY WEST [continued]: So there are a number of different examplesof applications of these types of models in the literature,but those are some of the main classes of modelsthat one will generally see when studying structural equationmodeling.[What software can be used in structural equation modeling?]Fortunately, today's survey researchersand social scientists have access

DR. BRADY WEST [continued]: to a variety of powerful software toolsthat enable them to fit structural equation models.Many of the general-purpose softwarepackages like SAS, SPSS, Stata, and so forthhave tools existing allowing researchersto fit these types of models.For example, in SAS, there's a procedure called CALIS,

DR. BRADY WEST [continued]: or C-A-L-I-S that allows researchers to fit thesemodels.SPSS has an add-on module-- or I shouldsay IBM SPSS Statistics has an add-on module knownas AMOS, which allows researchers to actually drawthese models using a point and click interface,and then fit the models and compute estimates.So a lot of researchers like that aspect of AMOS.

DR. BRADY WEST [continued]: Stata has recently developed some very interesting toolsthat allow researchers to either draw the models,or specify the models using syntax.And in Stata, the researchers can draw the models,and then ask for the estimation.And Stata will automatically generate the syntax for themthat corresponds to the model that they just drew.So that's a very cool feature.And a nice thing about Stat as well-- and

DR. BRADY WEST [continued]: we'll talk about this a little bitlater-- is the ability to fit these models to survey data,and survey data with certain complex sampling features.So that's a key aspect of the proceduresthat are available in Stata-- the sem and the gsem commands.R has a couple of contributed packages that allow researchersto fit these models, namely the sem package and the lavaan

DR. BRADY WEST [continued]: package, or L-A-V-A-A-N package.So researchers using R can downloadthese contributed packages, and thenfit sem's using the different functions thatare available within these specific packages.So there are a lot of tools available.And this software has grown by leaps and boundsin recent years in terms of the different options

DR. BRADY WEST [continued]: and modeling features that are available for people fittingthese models and diagnosing the fits of these models,testing hypotheses about these causal relationships.There are many very powerful tools available now.There's also a software package knownas Mplus, which is one of the leaders out therein latent variable modeling, that probably providesresearchers with the most capabilities in terms

DR. BRADY WEST [continued]: of the different types of models that can be fittedand the different options that can be implemented.Mplus is extremely powerful statistical softwarefor latent variable modeling.And it's grown quite a lot in popularity in recent yearsamong social scientists and survey researchers.Then there's also a variety of different standalone packages,like EQS and LISREL.

DR. BRADY WEST [continued]: These packages are designed specificallyto fit structural equation models.They don't have the same capabilitiesin terms of data management that the other general purposestatistical software packages would have,but tools like LISREL as standalone packagesare very powerful for fitting structural equation models.So those are some of the examplesof widely used software tools.

DR. BRADY WEST [continued]: But it's very fortunate that researchers nowadayshave access to so many powerful tools thatallow them to very quickly fit these models,and then test the hypotheses that they're truly interestedin.[What are the most exciting developments in structuralequation modeling and survey methodology?]So the most exciting developmentsin structural equation modeling, I think,

DR. BRADY WEST [continued]: as it relates to survey methodologyis the ability of software to fit these different typesof models to data sets that arise from complex samples.So in many cases, when large national samples are selected,these samples are selected using a complex design,where cases may have different weights dependingon their probabilities of selection and the samples

DR. BRADY WEST [continued]: themselves may be stratified, or cluster samples may be drawn.All these features need to be taken into account whenfitting models to make sure that estimates from those modelsare unbiased and representative of the populations of interest.Recent developments in software for fitting structural equationmodels have allowed researchers to account

DR. BRADY WEST [continued]: for these complex design features.The theory to do this was first developed in the mid 1990sby one of the developers of the Mplus package.And since then, software is taken stridesto incorporate these modeling featuresin these different procedures.And nowadays, for example in Stata,individuals can fit structural equation models

DR. BRADY WEST [continued]: to complex sample survey data, and come upwith weighted estimates of relationshipsbetween different latent variables, relationshipsof latent variables with observed variables,all in a way that takes these weights into accountin the estimation, and ensures that the resultingestimates are unbiased and describing

DR. BRADY WEST [continued]: the target population of interest without any bias.So in my view, that's one of the exciting thingsabout fitting these models, whether they'relatent class models, or path models,or whatever the case may be-- is nowwe can make inference about these causal relationshipsin larger populations using software that has implementedthese different features for analyzing data

DR. BRADY WEST [continued]: from complex sample surveys.So that's one of the exciting areas.I mean, survey researchers have beenusing these models for a long time,but the fact we can now use advanced modeling techniquesaccounting for these complex sample design featuresis very, very cool.[Summary]

DR. BRADY WEST [continued]: OK, so to summarize, some key takeaway pointsfrom this particular tutorial for structural equationmodeling are the key terminology and key concepts--ideas of latent variables-- again,variables that we don't actually observe in a data setbut instead are indicated by other observed variables.And the idea that we can see if a series

DR. BRADY WEST [continued]: of correlated variables are reliably indicatinga particular latent trait.So that's a key aspect of structural equation modeling.And then this notion of the structural portion of a modelthat allows us to specify a very complex causalor potentially very complex causal relationshipbetween either observed variables,or latent variables, or any combination of those two

DR. BRADY WEST [continued]: different types of variables, allowing researchersto test hypotheses about how these latent traits may relateto other observed variables, and again, testingcomplex causal hypotheses about the relationshipsbetween variables.It's a key feature of structural equation modeling.There's a variety of different softwareout there nowadays that allows researchers

DR. BRADY WEST [continued]: to fit structural equation modelsin general-purpose packages, or whatI would call boutique packages, or standalone packages.And very cool recent advances in the technology underlyingthat software allow researchers to use those softwareprocedures to fit these models to data from complex samplesurveys.And with all the different types of models

DR. BRADY WEST [continued]: that can be fitted within the structural equation modelingframework, the fact that we can now fit these modelsand make unbiased inferences about larger targetpopulations-- whether it's a latent classanalysis, or a full structural equationmodel, or a multi-level model, or a path model-- whateverthe case may be, with all these different subclasses of models,the fact that we can now make unbiased inferences

DR. BRADY WEST [continued]: about relationships in a larger population of interestis a very nice feature.So researchers have very powerful softwareat their fingertips that can allowthem to test these complex causal hypotheses.And so structural equation modelsallow researchers to do many different things-- test

DR. BRADY WEST [continued]: measurement properties, test causal relationships.And they extend what researchers cando with traditional types of statistical modelslike linear regression and logistic regressioninto a much more causal modeling framework.And for that reason, survey researchersand social scientists have found these modelsto be very useful in their work for a number of years now.

DR. BRADY WEST [continued]: [MUSIC PLAYING]