Structural Equation Modeling Mgmt 291 Lecture 4 Model Specification & Data Preparation Oct. 19,...
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Transcript of Structural Equation Modeling Mgmt 291 Lecture 4 Model Specification & Data Preparation Oct. 19,...
What we have:1) National Level Research Government capability
(Governance) Corruption – Political Instability – Property Right
– Rule Regulation
Foreign Direct Investment
Data – need to merger datasets ?
Shanshan Qiu
2) Firm Level Research 1) Earning
Stock price
??? 2) Football team
Abilities => Score Points
John Bae
Matthew Feldmann
3) Individual Level Research 1) Why starting a businessInterests - Belief => Starting
2) Consuming a green product
WealthValue => Organic Food ConsumptionLife-style
Laura Huang
Hannah Oh
3) Analysts behavior by Joshua
A few issues on first assignment: 1) Theory -> Operationalization need to be completed
Theory & Concepts -> Data & Variables
Questions -> Hypotheses
Concepts and Variables linked
2) Confirmative Approach vs. Exploratory Approach need to be clear
Clear Theory-backed hypotheses
Strictly confirmative ? (maybe some exploratory elements added
later are fine)
Usually start with confirmative if theories are strong.
OR completely exploratory.
3) Clear Strategies Needed Extend Replicate previous research Test some theories empirically
Review literature – some critique – are necessary.
(need to know how important your research is, what your contribution is)
4) Need SEM Type of Questions
(that can NOT be handled by OLS regression) Mediation effects Latent Variables Non-recursive
Correlated Disturbances (Errors or Residuals)
- model comparison (15 fit indexes)
SEM Types ofHypotheses
Or Causality Questions
Time precedence ? Direction – (need SEM to rule out other direction)
Partialed out
(panel studies, disturbance – non-deterministic)
Example of Literature Review Literature review – a lot of research on
determinants of economic growth AND determinants of democracy, a few article starting to argue that DEMOCRACY needs to be treated as latent var.
Lack of empirical study of the feedback loop of economic growth and democracy.
Indirect impacts of determinants are rare.
Example of SEM Questions Democracy is a latent variable with
Freedom House indicator, Polity indicator, Polyarchy Indicator and others (FH, ACLP in our data)
democracy and economic growth may be affected by each other.
The impacts of economic development on democracy may be indirect.
Example of data and variables
D&D Data Description A table to list all the variables.
See http://www.researchmethods.org/sem-data.htm for the data and codebook.
Democracy
FH Freedom House Score
Polity
ACLP
Polyarchy
Eco Dev Econ
Openc
Edu
Gini
ELF60
Riots
ODRP
Bricol
For Second Assignment move to model specification Hypotheses or theories <-> model (to be represented by
diagrams)
An Algorithm 1) Link all vars together 2) Take out links corresponding to in sig partial
correlations Repeat 1-2 to take out as many as possible
3) use theory or common sense to place directions
4) use partial correlation to place more directions Repeat 3-4 to change all un-directional links to
directed links
Specification Issues Avoid Misspecification External (missed variables) Internal (missed links)
Sufficient number of indicators for each latent variable (2 is fine, 3 is better, 4 is the best, …)
Do Your Best to Specify Directions
Parsimony - Important
Misspecification Problems -> Biases
Over-estimationSuppression
(depends on the correlation between vars in the equation and vars omitted
Another Model Specification Issue – interaction terms
Moderated effects
X1
X1*X2
X2Y2
Y1
Z1
Z2
Z5
Z4
Z3
4 more matrixY3
Z6 Z7
e1
e2
e3
Model Specification Example
DemocracyEdu
Openc
Gini
Econ
ODRPRiotsELF60Bricol
FH Polity ACLP Polyarchy
Error terms needed
2 Step Approach for Model Identification
Democracy
Edu Openc
Gini
Econ
ODRPRiotsELF60Bricol
FH Polity ACLP Polyarchy
Democracy
Measurement Model
Structure Model
2 Step Approach
e
Model Identification 2-step Example
Democracy
Edu Openc
Gini
Econ
ODRPRiotsELF60Bricol
FH Polity ACLP Polyarchy
Democracy
Measurement Model
Structure Model
2 Step Approach
e
Missing Values Statistics
BRITCOL8 ELF80 LEVEL80ODRP80 RIOTS80 CCODE80CIVLIB90 POLLIB90 REG90
Missing 7 7 7 7 7 7 23 23 23
Edt & Ginisignificant
PairwiseListwise
Normality
Normal Q-Q Plot of FH90
Observed Value
1614121086420
Exp
ect
ed
No
rma
l Va
lue
16
14
12
10
8
6
4
2
0Detrended Normal Q-Q Plot of FH90
Observed Value
1614121086420
De
via
tion
fro
m N
orm
al
1.0
.5
0.0
-.5
-1.0
-1.5
Descriptive Statistics
112 .167 .228 -1.316 .453
112
FH90
Valid N (listwise)
Statistic Statistic Std. Error Statistic Std. Error
N Skewness Kurtosis
FH90
14.012.010.08.06.04.02.0
30
20
10
0
Std. Dev = 3.77
Mean = 6.9
N = 112.00
Multicollinearity
Correlations
1 .006 -.141 -.239** .042
. .950 .111 .007 .634
128 128 128 128 128
.006 1 .030 .253** .105
.950 . .739 .004 .237
128 128 128 128 128
-.141 .030 1 .760** -.080
.111 .739 . .000 .370
128 128 128 128 128
-.239** .253** .760** 1 -.057
.007 .004 .000 . .522
128 128 128 128 128
.042 .105 -.080 -.057 1
.634 .237 .370 .522 .
128 128 128 128 128
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
BRITCOL8
ELF80
LEVEL80
ODRP80
RIOTS80
BRITCOL8 ELF80 LEVEL80 ODRP80 RIOTS80
Correlation is significant at the 0.01 level (2-tailed).**.
Correlations
1 .383** .417** .397** .028
. .000 .000 .000 .748
135 135 135 135 135
.383** 1 .347** .422** .038
.000 . .000 .000 .662
135 135 135 135 135
.417** .347** 1 .687** .167
.000 .000 . .000 .053
135 135 135 135 135
.397** .422** .687** 1 .063
.000 .000 .000 . .471
135 135 135 135 135
.028 .038 .167 .063 1
.748 .662 .053 .471 .
135 135 135 135 135
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
EDT85
GINI85
LEVEL85
ODRP85
OPENC85
EDT85 GINI85 LEVEL85 ODRP85 OPENC85
Correlation is significant at the 0.01 level (2-tailed).**.
>.90 results 1s or Os Making matrix calculationimpossible
Corr > .85Tolerance (1-R2) < .10VIF (1/ 1-R2) > 10
Linearity
LEVEL80
1600014000120001000080006000400020000
FH90
16
14
12
10
8
6
4
2
0
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111116N =
LEVEL80
12447
11333
10364
7390
5565
4458
3731
3341
2872
2344
1916
1647
1195
1021
940
817
534
Missing
FH
90
16
14
12
10
8
6
4
2
0
Start Thinking about programming Β - beta
η - etaξ - xiζ - zetaΓ - gammaΛ - lambda (upper case)λ - lambda (lower case)δ - deltaε - epsilon
NYNXNKNE
Introducing R R is FREE at www.r-project.org
R is very popular and powerful (see the NY Times article)
SEM in R example
> sem1 <- matrix(c( + + 1.0, 0, 0, 0, 0, + + .516, 1.0, 0, 0, 0, + + .453, .438, 1.0, 0, 0, + + .332, .417, .538, 1.0, 0, + + .322, .405, .596, .541, 1.0), + + 5, 5, byrow=TRUE) > rownames(sem1) <- colnames(sem1) <- c("FatherEd", "FatherOcc",
"Education", "FirstJob", "1962Job") > library(sem) > model.sem1 <- specify.model() FatherEd -> Education, gamma31, NA FatherOcc -> Education, gamma32, NA FatherOcc -> FirstJob, gamma42, NA Education -> FirstJob, beta43, NA FatherOcc -> 1962Job, gamma52, NA Education -> 1962Job, beta53, NA FirstJob -> 1962Job, beta54, NA Education <-> Education, sigma66, NA FirstJob <-> FirstJob, sigma77, NA 1962Job <-> 1962Job, sigma88, NA > sem.1 <- sem(model.sem1, sem1, 20700 , fixed.x=c("FatherEd",
"FatherOcc")) > summary(sem.1) > path.diagram(sem.1)