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A1
Structural equation modeling
Rex B Kline Concordia University
Montréal
ISTQL Set A Concepts, models, tools
A2
A3
Resources
o Kline, R, B. (2012). Assumptions of structural equation
modeling. In R. Hoyle (Ed.), Handbook of structural
equation modeling (pp. 111–125). New York: Guilford. o Kline, R. B. (2013). Exploratory and confirmatory factor
analysis. In Y. Petscher & C. Schatschneider (Eds.), Applied quantitative analysis in the social sciences (pp. 171–207). New York: Routledge.
o Kline, R. B. (2013). Reverse arrow dynamics: Feedback loops and formative measurement. In G. R. Hancock and R. O. Mueller, (Eds.), Structural equation
modeling: A second course (2nd ed.) (pp. 39–76). Greenwich, CT: IAP.
A4
Topics
o Mon: Concepts, models, tools
o Tues: Data, path models
o Weds: Estimation
A5
Topics
o Thurs: Model testing
o Fri: CFA models
o Sat: SR models
A6
Practice
o Weds: LISREL SIMPLIS syntax
o Thurs: LISREL Path Diagram
o Fri: Ωnyx demo
A7
four-variable example
observed variables
neg_str cur_prob prob_sol depress
covariance matrix
76.913
55.668 249.324
33.757 115.685 478.297
21.775 53.614 60.695 37.700
sample size is 205
relationships
cur_prob = neg_str
prob_sol = neg_str cur_prob
depress = neg_str cur_prob prob_sol
LISREL output: ND = 3 SC RS MI
path diagram
end of problem
A8
A9
A10
A11
A12
exercise, hardy, fitness, stress, illness
4422.250
-75.810 1444.000
477.204 48.944 338.560
-111.388 -292.790 -80.132 1122.250
-332.394 -379.878 -333.393 711.647 3903.750
Exercise
Hardiness
Illness
DIl
1
Stress
1 DSt
Fitness
1 DFi
A13
A14
A15
A16
Worst practices
o MacCallum, R. C., & Austin, J. T. (2000).
Applications of structural equation modeling in psychological research. Annual Review of
Psychology, 51, 201–226.
o Shah, R., & Goldstein, S. M. (2006). Use of structural equation modeling in operations management research: Looking back and forward. Journal of Operations Management, 24, 148–169.
A17
Best practices
1. Justify specifications
2. Report psychometrics
3. Verify assumptions
A18
Best practices
4. Report summary statistics
5. Describe method
6. Model-table-text agree?
A19
Best practices
7. Report unstandardized
8. Describe residuals
9. Equivalent models
A20
Best practices
10. Rethink :
Limited role
Not a criterion
Path to folly
*
A21
A22
Keep your eyes on the prize
1
A23
Any monkey can find a
model that fits the data
2
A24
Closer to fit is not closer to
truth
3
A25
Directionality is assumed, not
tested
4
A26
Never forget equivalent
models
5
A27
Smart modeling
o Know your area
o Simple is good
o Build, not trim
A28
Smart modeling
o Advantages of building:
1. Avoid identification issues
2. Prioritize hypotheses
3. Back-up list
A29
Smart modeling
o Add from list
o Done:
1. List exhausted
2. No citations for rest
A30
2. Identification
3. Data collection
4. Analysis
5. Respecification
6. Reporting
A31
no
yes
4a. Model fit adequate?
6. Report results
4c. Consider equivalent or near-equivalent models
4b. Interpret estimates
yes
Justifiable respecification?
no
5. Respecify model
no yes 2. Model identified?
3. Select measures, collect data
1. Specify model
A32
Smart modeling
o Goals:
Parsimony
Respect theory
Avoid HARKing
A33
Hello, SEM
A34
SEM
o Family
o Integration of MR, FA
o Flexible, extensible
A35
SEM o Inherits from MR ( ):
Multiple predictors
B, R2 effect sizes
Means, too
A36
SEM
o Inherits from FA ( ):
Observed vs. latent
Latents as predictors
Measurement error
A37
SEM
o Inherits from both ( ):
Capitalizes on chance
Specification error
Misuse through
A38
SEM
o Synergistic ( ):
Latents as outcomes
Means of latents
A39
SEM
o Synergistic ( ):
Indirect effects (mediation)
Error covariance structure
A40
Models
A41
Core models
o PA
o CFA
o SR
A42
Path models
o Structural model
o Observed variables only
o Single indicators only
A43
Path models
o Structural model:
Causal effects
Noncausal associations
A44
Path models
o Causal effects:
Direct
Indirect
A45
Path models
o Indirect effects:
Part of mediation
Indirect ⇒/ mediation
A46
Path models
o Noncausal effects:
Common cause (spurious)
Correlated with cause
A47
CFA models
o Multiple indicators only
o L → M only
o Factors covary only
A48
CFA models
o Classical measurement theory
o Convergent validity
o Discriminant validity
A49
SR models o Single, multiple indicators
o L → M or M → L
o L as predictors, outcomes
A50
SR models o Highest level model
o Advanced = SR variation
o Know and love
A51
Examples
o Roth, D. L., Wiebe, D. J., Fillingim, R. B., & Shay, K. A. (1989).
Life events, fitness, hardiness, and health: A simultaneous analysis of proposed stress-resistance effects. Journal of Personality and Social Psychology,
57, 136–142. o Kaufman, A. S., & Kaufman, N. L. (1983). K-ABC
administration and scoring manual. Circle Pines, MN: American Guidance Service.
o Shen, B.-J., & Takeuchi, D. T. (2001). A structural model of acculturation and mental health status among Chinese Americans. American Journal of Community
Psychology, 29, 387–418.
CFA
SR
PA
A52
Exercise
Hardiness
Fitness
1
DFi
Illness
1
DIl
Stress
1 DSt
A53
1
1 1 1 1 1 1 1 1
1
Sequential
EHM
Hand Movements
Number Recall
ENR
Word Order
EWO
Simultaneous
ETr
Triangles Spatial
Memory
ESM
Matrix Analogies
EMA
Gestalt Closure
EGC
Photo Series
EPS
A54
Acculturation
EGS
1
General Status
1
Acculturation
Scale
EAS
1
Percent Life U.S.
EPL
1
1
Job
EJo
1
Interpersonal
EInt
1
Stress
DSt
1
Depression Scale
DDS
1
SES
1
Education
EEd
1
Income
EInc
1
A55
Tools
A56
Tools
o Commercial vs. free
o Stand-alone vs. environment
o User interface
A57
Interaction modes
Computer tool Free Environment
needed Batch
(syntax) Wizard
(template) Drawing
editor
Stand-alone programs
Amos
EQS
LISREL
Mplus
Ωnyx
Packages, procedures, or commands in larger environments
sem, lavaan, lava,
systemfit R
OpenMx R
CALIS SAS/STAT
Builder, sem, gsem Stata
SEPATH STATISTICA
RAMONA SYSTAT
A58
A59
QQQ
A60
GUI liabilities
o Complex models
o Multiple-samples analysis
o Multi-level analyses
A61
GUI liabilities
o Syntax may be easier, faster
o Diagram as archive
o Publication quality graphic
A62
LISREL
A63
Amos
CurrentProblems
NegativeLife Stress
ProblemSolving
Depression
D_PSD_De
1
1
D_CP
1
A64
EQS
A65
Mplus
A66
Stata
A67
Exercise
Hardiness
Illness
DIl
1
Stress
1 DSt
Fitness
1 DFi
A68
Tool support
o Amos:
Blunch, N. (2013). Introduction to structural equation
modeling using IBM SPSS Statistics and Amos (2nd ed.). Thousand Oaks, CA: Sage.
Byrne, B. M. (2010). Structural equation modeling
with Amos: Basic concepts, applications, and
programming (2nd ed.). New York: Routledge.
A69
Tool support
o EQS:
Byrne, B. M. (2006). Structural equation
modeling with EQS: Basic concepts,
applications, and programming (2nd ed.). New York: Routledge.
A70
Tool support
o lavaan:
Beaujean, A. A. (2014). Latent variable
modeling using R: A step-by-step guide. New York: Routledge.
http://lavaan.ugent.be/
A71
Tool support
o LISREL:
Vieira, A. L. (2011). Interactive LISREL in
practice: Getting started with a SIMPLIS
approach. New York: Springer.
A72
Tool support
o Mplus:
Geiser, C. (2013). Data analysis with Mplus. New York: Guilford.
Wang, J., & Wang, X. (2012). Structural equation
modeling: Applications using Mplus. Chichester, UK: Wiley.
A73
Tool support
o Stata:
Acock, A. C. (2013). Discovering structural
equation modeling using Stata 13. College Station, TX: Stata Press.
A74
Statistics
A75
Continuous
o Theoretically infinite scores
o In practice, range > 15
o Symmetrical distribution
A76
Likert scale
o Items
o E.g., 1 = disagree, 2 = not sure 3 = agree
o Ordinal, ordered-categorical
A77
Scales vs. items
o Scale: Σ score, continuous
o Item: Noncontinuous
o Proper method
A78
Other outcomes
o Dichotomous (binary), k = 2
o Nominal, k > 2
o Logit or probit link function
A79
Other outcomes
o Agresti, A. (2007). An
introduction to categorical
data analysis. Hoboken, NJ: Wiley.
A80
Other outcomes
o Count variables
o Poisson distribution
o Mean ≈ variance
A81
A82
Covariance
o Continuous only
o Linear only
o covXY = rXY SDX SDY
A83
rXY = .55, SDX = 3.5, SDY = 2.0
covXY = .55 (3.5) (2.0) = 8.1
A84
Raw data
Case X W Y
A 3 65 24
B 8 50 20
C 10 40 22
D 15 70 32
E 19 75 27
A85
Covariance matrix
38.500
42.500 212.500
17.500 51.250 22.000
A86
Correlation matrix + SDs
1.000
.470 1.000
.601 .750 1 .000
6.205 14.577 4.690
A87
Raw data not needed
comment spss, y on x, w, matrix input.
matrix data variables=x w y/contents=mean sd n corr
/format=lower nodiagonal.
begin data
11.000 60.000 25.000
6.205 14.577 4.690
5 5 5
.470
.601 .750
end data.
regression matrix=in(*)/variables=x w y/dependent=y
/enter.
A88
MR
o Y, X1, X2
o 1 1 2 2Y B X B X A= + +
o ˆYYR r=
A89
Coefficients
B1 = 2.30, B2 = 6.35, A = 10.50
b1 = .65, b2 = .30
Capitalization on chance
A90
Comparisons
Predictors Samples B b
A91
MR assumptions
o Y is continuous
o Linear only
o No interactions
A92
MR assumptions
o r11 = r22 =1.00
o No indirect effects
o No specification error
A93
No specification error
No irrelevant predictors
No omitted predictors that covary with measured predictors
Correct functional form
A94
Heartbreak of L.O.V.E
Y = suicide attempts
X1 Therapy
X2 Depression
rY1 = .19 rY2 = .49 r12 = .70
A95
Heartbreak of L.O.V.E
Y = suicide attempts
X1 Therapy
X2 Depression
rY1 = .19 rY2 = .49 r12 = .70
b1 = −.30 b2 = .70 R = .54
A96
Results depend on
What is measured (data)
What is not (omitted variables)
A97
Predictor entry
Rational (e.g., HMR)
Statistical (e.g., stepwise)
A98
Stepwise flaws
Results are wrong
Will not replicate
Banned
A99
SEM version
MIs only
Same problems
Think for yourself