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The General LISREL MODEL
Ulf H. Olsson
Professor of Statistics
Ulf H. Olsson
Making Numbers
1131211 SavingsLoanBranchonSatisfacti
221 onSatisfactiLoyalty
Loyalty
Branch
Loan
Savings
Satisfaction
Ulf H. Olsson
Making Numbers-Econometric Model
2
1
3
2
1
232221
131211
2
1
2221
1211
2
1
Ulf H. Olsson
Making Numbers-Psychometric Model
5
4
3
2
1
2
1
51
41
31
21
11
5
4
3
2
1
0
0
0
0
0
y
y
y
y
y
Ulf H. Olsson
Making Numbers-Psychometric Model
9
8
7
6
5
4
3
2
1
3
2
1
93
83
73
62
52
42
31
21
11
9
8
7
6
5
4
3
2
1
00
00
00
00
00
00
00
00
00
x
x
x
x
x
x
x
x
x
Ulf H. Olsson
Parameter Function
'')'('
')(')')('()()( 1
111
xxyx
xyyy
BI
BIBIBI
Ulf H. Olsson
Making Numbers
))(())'(( 1 sUs
S: sample covariance
θ: parameter vector
σ(θ): model implied covariance
Ulf H. Olsson
Making Numbers
1, ghijOLSU
Ulf H. Olsson
Making Numbers
ghijghijGLS ssU ,
Ulf H. Olsson
Making Numbers
ghijijghghijADF sssU ,
Ulf H. Olsson
Making Numbers
ghijghijMLU
,
Ulf H. Olsson
Making Numbers
MLADFGLSOLS UUUU
MLADFGLSOLS
Generally
Ulf H. Olsson
Making Significance
))(())'(()),(,( 1 sUssT
stochasticT
"_
__")1(
squarechicentralnon
allyasymptoticisTN
Ulf H. Olsson
Making Numbers
1131211 SavingsLoanBranchonSatisfacti
221 onSatisfactiLoyalty
Loyalty
Branch
Loan
Savings
Satisfaction
0.330.330.460.290.170.35 0.80
0.800.830.860.830.84
0.400.390.330.440.370.37
0.260.230.210.280.230.23
•Chi-sq.•1769.36• 925.78•1731.09• 839.83• 518.94• 582.91• df=182
Ulf H. Olsson
Multivariate Normal Distribution
zzzf p 12/12/ '
2
1exp)2()(
Ulf H. Olsson
The Maximum Likelihood Estimator
tSStrTML log)()(log 1
Ulf H. Olsson
Making Significance
TN )1(
0; correctly specified
K ; misspecified
4s
Ulf H. Olsson
Making Significance (Sense)
..........,....)(,........,)(,)(,)(321 iNNNN
123 ,,..,,.............,,........)(
iN
)( 2
1
nO
Ulf H. Olsson
Making Sense
If the model is correctly specified,different estimators shouldhave similar values asymptotically(White, 1994)
If the different estimators do not have similar values asymptotically, the model is misspecified
<=>
1) Use at least two estimators 1 and 2; if they differ the model is misspecified;
2) Across-method variability can be used to assess what parts of the model, if any,are close to the true model??
Ulf H. Olsson
Making Sense
A strong theory will give precise predictions!
Ulf H. Olsson
Making sense is more important than making numbers, it is even more
important than making significance
?
Ulf H. Olsson
Assignment
• 1) Evaluate the nine-psychological test model• 2) Estimate EX32A.Ls8• 3) Estimate Ex32B.ls8• 4) Estimate Ex56.Ls8
