January 19 Introduction to SEM

8/7/2019 January 19 Introduction to SEM

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Introduction to

Structural Equation Modeling


2/15

Research Questions & SEM

Confirmatory Factor Analysis.

Path Models with Latent Variables.

Models of Developmental Trajectories.

Model Differences between Groups.


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Anxiety

Not Calm

Tired Out

Effort

Cant Sit Still

Restless

Nervous

Worthless

Depressed

Cant Cheer UpDepression

CFA

Hopeless

r1

r2

r3

r4

r5

r6

r7

r8

r9

r10


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Observer

ChildDepression

Family Conflict

Path Model with Latent Variables

Child

Parent

Child

Parent Observer

Child Age

Child Gender


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TrajectoryChild ASB

Family ConflictWave 1

Latent Growth Curve Model

ASBWave 2

Mother

Father Child

ASBWave 3

ASBWave 4Child Self Esteem

Wave 1

MotherFather

Child


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Think in Terms of Models

Strictly Confirmatory.

Alternative Models.

Model Generation.


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Testing Alternative Models

Romney, Jenkins, & Bynner (1992) Human Relations 45, 165-176


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Model Specification

The researchers hypotheses are expressed in theform of a SEM.

What are the variables that effect a particularphenomenon of interest?

What are the pathways of those effects?

(direct and indirect)


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Equivalent Path Models


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Model Identification

Is it theoretically possible to calculate a unique estimatefor all of the models parameters?

Two key issues

The number of model parameters can not exceed the number of

observations number of degrees of freedom

Over-identified, Just-identified, Under-identified

Every unobserved variable must be assigned a scale.

Observations are the variances and covariances of themeasured variables (correlation matrix).

v(v + 1)/2, where v is the number of observed variables

Have 15 observations in Romney et al.


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Model Estimation

Use a model-fitting program to derive estimates of model

parameters (Amos, EQS, LISREL, Mplus).

Maximum Likelihood (ML) is by far the most widely used

estimation procedure.

However, ML assumes multivariate normality. If the data

are not MVN, then other procedures can be used.


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Assessing Model Fit

Determine how well the model accounts for the

observed variances and covariances of the measured

variables.

Fit Indices: G2, GFI, CFI, TLI, RMSEA, SRMR, and many

others.

These indicate only the overall or average fit of the

model, and do not indicate whether the results are

theoretically meaningful.


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Assumptions within SEM

Large samples: try to obtain a 10:1 ratio of number ofsubjects to number of model parameters.

Variables are typically at interval or ratio level ofmeasurement, although not necessarily.

Mplus program designed to analyze categorical variables

Approximately multivariate normal distribution.

Missing data are MAR.


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Dealing with Missing Data in SEM Listwise deletion: assuming MCAR

EM Algorithm and Multiple Imputation methods are

available in most SEM software programs

Common approach is to use Full Information MaximumLikelihood (FIML) estimation Uses all of the raw data, regardless of the amount of missingness

for any given case. Partitions the sample into subsets of cases having the same

pattern of missingness.

All available statistical information is drawn from each subset; allcases are used in the overall analysis.


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Testing for Moderation in SEM

Interactions between observed variables

Create product terms to include in path model

Interactions between latent variables Kenny-Judd method, need to use nonlinear constraints in

measurement model

Ping method, involves calculation of loadings for productindicators, fixed parameters.

Test group differences in model using G2 differences whenconstraining parameters to be equal across groups.

January 19 Introduction to SEM

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