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Basic Structural Equation Modeling (SEM) concepts
Observed Variable
A variable whose values are observable.
Examples: IQ Test scores (Scores are directly observable), GREV, GREQ, GREA, UGPA,
Minnesota Job Satisfaction Scale, Affective Commitment Scale, Gender, Questionnaire items.
Latent Variable
A variable, i.e., characteristic, presumed to exist, but whose values are NOT observable. A Factor in
Factor Analysis literature. A characteristic of people that is not directly observable.
Intelligence, Depression, Job Satisfaction, Affective Commitment
No direct observation of values of latent variables is possible.
Indicator
An observed variable whose values are assumed to be related to the values of a latent variable.
Reflective Indicator
An observed variable whose values are partially determined by, i.e., are caused by or reflect, the
values of a latent variable. For example, responses to Conscientiousness items are assumed to
reflect a person‟s Conscientiousness.
Formative Indicator
An observed variable whose values partially determine, i.e., cause or form, the values of a latent
variable. Mike – Use the SES example, instead of this.
Exogenous Variable
A variable whose values originate from outside the model, i.e., are not explained within the theory
with which we‟re working. That is, a variable whose variation we don‟t attempt to explain or predict
by whatever theory we‟re working with. Causes of exogenous variable originate outside the model.
Exogenous variables can be observed or latent.
Endogenous variable
A variable whose values are explained within the theory with which we‟re working. We account for
all variation in the values of endogenous variables using the constructs of whatever theory we‟re
working with. Causes of endogenous variables originate within the model.
Intro to SEM - 1 Printed on 6/13/2010
Basic SEM Path Analytic Notation
Observed variables are symbolized by squares or rectangles.
103
84
Observed 121
76
Variable ...
97
81
Latent Variables are symbolized by Circles or ellipses.
106
Latent 78 Values of individuals on
115 latent variables are not
Variable 80 observable, hence the
...
93 dimmed text.
83
Correlations or covariances between variables are represented by double-headed arrows.
"Cor / Cov" "Cor / Cov"
Arrow Arrow
Observed Observed Latent Latent
Variable A Variable B Variable A Variable B
101 106 104
103
90 78 79
84
128 115 114
121
72 80 79
76
... ... ...
...
93 93 92
97
80 83 81
81
"Causal" or "Predictive" or “Regression” relationships between variables are represented by single-headed
arrows
"Causal" "Causal"
Arrow Arrow
Latent Observed Observed Latent
Variable Variable Variable Variable
"Causal"
Arrow "Causal"
Latent Latent Arrow Observed
Observed
Variable Variable Variable
Variable
Intro to SEM - 2 Printed on 6/13/2010
Exogenous Observed Variables
"Correlation"
"Causal" Arrow
Arrow
Observed Observed
Variable Variable
Exogenous variable connect to other variables in the model through either a “causal” arrow or a correlation
Exogenous Latent Variables
"Causal" "Correlation"
Arrow Arrow
Latent
Variable
Latent
Variable
Exogenous latent variables also connect to other variables in the model through either a “causal” arrow or a correlation
Endogenous Observed Variables - Endogenous Latent Variable
"Causal" Random Random
Arrow error
"Causal" error
Observed Arrow
Variable Latent
Variable
Endogenous variables connect to other variables in the model by being on the “receiving” end of one or more “causal”
arrows. Specifically, endogenous variables are typically represented as being “caused” by 1) other variables in the
theory and 2) random error. Thus, 100% of the variation in every endogenous variable is accounted for by either other
variables in the model or random error. This means that random error is an exogenous latent variable in SEM
diagrams.
Values associated with symbols
Mean, Variance Mean, Variance
Observed
Variable Latent
Variable
Our SEM program, Amos, prints means and variances above and to the right. Typically the mean and variance of latent
variables are fixed at 0 and 1 respectively, although there are exceptions to this in advanced applications.
"Correlation"
Arrow "Causal"
r or Covariance
Arrow
B or
Intro to SEM - 3 Printed on 6/13/2010
Path Diagrams of Analyses We‟ve Done Previously
Following is how some of the analyses we‟ve performed previously would be represented using path
diagrams.
1. Simple correlation between two observed variables.
rVQ
GRE-V GRE-Q
2. Simple correlations between three observed variables.
rVA
rVQ rQA
GRE-V GRE-Q GRE-A
3. Simple regression of an observed dependent variable onto one observed independent variable.
GRE-Q B or P511G e
4. Multiple Regression of an observed dependent variable onto three observed independent variables.
GRE-V BV or V
GRE-Q BQ or Q e
P511G
UPGA BU or U
Intro to SEM - 4 Printed on 6/13/2010
ANOVA in SEM Models
Since ANOVA is simply regression analysis, the representation of ANOVA in SEM is merely as a
regression analysis. The key is to represent the differences between groups with group coding
variables, just as we did in 513 and in the beginning of 595 . . .
1) Independent Groups t-test
The two groups are represented by a single, dichotomous observed group-coding variable. It is the
independent variable in the regression analysis.
Dichotomous Dependent
variable representing e
the two groups
Variable
2) One Way ANOVA
The K groups are represented by K-1 group-coding variables created using one of the coding
schemes (although I recommend contrast coding). They are the independent variables in the
regression analysis. If contrast codes are used, the correlations between all the group coding
variables are 0, so no arrows between them need be shown.
1st Group-coding Note: Contrast codes were used so Group-
contrast code coding variables are uncorrelated.
variable
2nd Group-coding Dependent
contrast code e
Variable
variable.
. . . . .
(K-1)th Group-
coding contrast code
variable.
3) Factorial ANOVA.
Each factor is represented by G-1 group-coding variables created using one of the coding schemes.
The interaction(s) is/are represented by products of the group-coding variables representing the
factors. Again, no correlations between coding variables need be shown if contrast codes are used.
1st Factor Note: Contrast codes should be used to make the
group-coding variables uncorrelated.
1st Factor
2st Factor Dependent e
2st Factor Variable
Interaction
Interaction
Interaction
Interaction
Intro to SEM - 5 Printed on 6/13/2010
Path Diagrams representing Exploratory Factor Analysis
1) Single Factor solution.
The factor is represented by a latent variable with three or more observed indicators. (Three is the
generally recommended minimum no. of indicators for a factor.)
Note that with respect to error
1 variables, either
e1
Obs 1 1) Each variance must be set to
1 1, or
1
Obs 2 e2 2) Each regression parameter
F connecting it to the factor must
1 be set to 1.
Obs 3 e3
Note that factors are exogenous. Indicators are endogenous. Since the indicators are endogenous,
all of their variance must be accounted for by the model. Thus, each indicator must have an error
latent variable to account for the variance in it not accounted for by the factor.
The factor analysis model is underidentified. That means that there are more quantities that must be
estimated than there are observed quantitites in the data. So restrictions have to be placed on the
parameters. Typically, one of the paths from the factor to indicators is fixed at 1. In addition,
typically, the paths from latent error variables to indicators are all fixed at 1.
2) Two orthogonal Factor solution.
Each factor is represented by a latent variable with three or more indicators. The orthogonality of
the factors is represented by the fact that there is no arrow connecting the factor symbols.
For exploratory factor analysis, each variable is allowed to load on all factors. Of course, the hope is
that the loadings will be substantial on only some of the factors and will be essentially 0 on the
others.
e4
Obs 1
Obs 2 e5
F1
Obs 3 e6
e7
Obs 4
e8
Obs 5
F2
Obs 6 e9
Orthogonal factors represent uncorrelated aspects of behavior.
Intro to SEM - 6 Printed on 6/13/2010
3) Two oblique factors.
Each factor is represented by a latent variable with three or more indicators. The obliqueness of the
factors is represented by the fact that there IS an arrow connecting the factors.
e4
Obs 1
Obs 2 e5
F1
Obs 3 e6
e7
Obs 4
e8
Obs 5
F2
Obs 6 e9
Intro to SEM - 7 Printed on 6/13/2010
Confirmatory vs Exploratory Factor Analysis
In Exploratory Factor Analysis, the loading of every item on every factor is estimated. The analyst
hopes that some of those loadings will be large and some will be small. An EFA two-orthogonal-
factor model is represented by the following diagram.
e4
Obs 1
Obs 2 e5
F1
Obs 3 e6
e7
Obs 4
e8
Obs 5
F2
Obs 6 e9
Note that there are arrows (loadings) connecting each variable to each factor. No EFA programs
allow you to specify or fix loadings to pre-determined values.
A factor analysis in which some loadings are fixed at specific values is called a Confirmatory
Factor Analysis. The analysis is confirming one or more hypotheses about loadings by fixing them
at specific (usually 0) values.
Unfortunately, EFA and CFA cannot be done using the same computer program except MPlus.
The problem is that SPSS won‟t allow some loadings to be fixed at predetermined values. And the
above model canNOT be estimated in Amos. Amos and all SEM programs other than MPlus require
that some of the loadings be fixed.
So, in many instances, you will have to employ both SPSS and AMOS in exploring the interrelations
between variables and factors. Often, analysts will use an EFA program to estimate ALL loadings to
all factors, then use an SEM program to perform a confirmatory factor analysis, fixing those
loadings that were close to 0 in the EFA to 0 in the CFA.
E1
Obs 1
Obs 2 E2
F1
Obs 3 E3
E4
Obs 4
Obs 5 E5
F2
Obs 6 E6
Intro to SEM - 8 Printed on 6/13/2010
Diagrams of analyses we couldn‟t perform previously
1. Simple correlation between two latent variables each with multiple reflective indicators.
We could have approximated this
e GRE-V analysis by computing an
“average” of the ability measures
and an average of the motivation
GRE-Q measures, perhaps after
e standardizing them, and then
correlating the two averages. But
Entering the averaging would have forced
GRE-AW Ability equal weighting of the observed
e
variables. The analysis shown here
estimates the weight of each
e UGPA observed variable.
REA,M
e Volunteering
e Extra- Pre SEM analyses computed the
Motivation
Curricular canonical correlation between the
two sets of observed variables.
Jobs This is a generalization of that
e type of analysis.
2. Simple regression of a dependent latent variable onto an independent latent variable. (With reflective
indicators of both latent variables.)
e GRE-V e
Service to e
program
e GRE-Q B or
Content e
Entering Core Grades
Performance
GRE-AW Ability In Program
e Electives
e
Grades
e UGPA
This analysis could have been approximated by “averaging” the ability measures and the outcome measures. But, as
above, the analysis diagrammed here allows us to estimate the weight of each observed variable in the analysis.
Intro to SEM - 9 Printed on 6/13/2010
3. Combining Formative and reflective indicators.
e
e e
Grade
Genetic Point
Makeup
e
Test
Prenatal Cognitive Academic Scores
Environment Ability Success
School
Family
Recognition e
Environment
Formative indicators are observed variables that, taken together, form the values of a latent variable.
Reflective indicators are observed variables that reflect the values of a latent variable.
Same comments apply here as above.
4. Simultaneous assessment of indirect and direct effects
e e
Study Time
Test
Conscientiousness Performance
Does high performance lead directly to a search for alternative jobs, or is the relationship between performance and
turnover mediated by the perception of perceived alternatives? Using previous methods, we could not simultaneously
estimate both effects.
5. Multistage analyses.
Grade
Point Test
e e Scores
School
Recognition
Genetic e
Makeup
Prenatal Cognitive Academic Career
Environment Ability Success Success
Family
Environment
Position
Salary Power
Up to know, we‟ve been able to analyze only one relationlship at a time. In this analysis, Academic Success is the DV in
one relationship and the IV in another.
Intro to SEM - 10 Printed on 6/13/2010
The Identification Problem
Consider the simple regression model . . . Mean, Variance
E
E->Y
Mean, Variance
X Y
X->Y
Quantities which can be computed from the data . .
Mean of the X variable Variance of the X variable
Mean of the Y variable. Variance of the Y variable.
Correlation of X with Y
Quantities in the diagram .
Remember that in SEM path diagrams, all the variance in every endogenous variable must be accounted for. For that
reason, the path diagram includes a latent “Other factors” variable, labeled “E”.
Mean of X Variance of X Note: Mean and variance of Y are not
Mean of E Variance of E separately identified in the model because
Relationship of X to Y they are assumed to be completely determined
Relationship of E to Y by Y‟s relationship to X and to E.
Whoops! There are too few quantities in the data. There are 5 data quantities but 6 in the model. The model is
underidentified. – not identified enough - there aren't enough quantities from the data to identify each model value.
Solution . .
Fix one of the quantities associated with E - either the variance or the relationship E-Y. In the following, I fixed the
variance of E at 1. So in this regression model, the path diagram will be
Mean, 1
E
E->Y
Mean, Variance
X X->Y Y
In this case, the model is said to be “just identified” or “completely identified”. This means that every estimable quantity
in the model corresponds to one quantity obtained from the data.
In other scenarios, the relationship of error variables to observed variables is set equal to 1. The two methods are
equivalent.
Note that in many analyses, means are not estimated. Unfortunately, the number of means in the model is exactly the
same as the number in the data, so not estimating means does not solve the identification problem.
Intro to SEM - 11 Printed on 6/13/2010
Programming with path diagrams: Introduction to Amos
Amos is an add-on program to SPSS that performs confirmatory factor analysis and structural
equation modeling.
It is designed to emphasize a visual interface and has been written so that virtually all analyses can
be performed by drawing path diagrams.
It also contains a text-based programming language for those who wish to write programs in the
command language.
The Amos drawing toolkit with functions of the most frequently used tools.
Observed variable tool
Tool to draw latent variables
Tool to draw regression arrows
Tool to draw correlation arrows
Tool to put text on the diagram
Tool to select all objects in diagram
Tool to select a single object
Tool to deselect all objects in diagram
Tool to copy an object Tool to erase an object
Tool to move an object
Intro to SEM - 12 Printed on 6/13/2010
Creating an Amos analysis
1. Open Amos Graphics.
2. Files -> Data Files . . .
3. Specify the name of the file that contains the raw or summary data.
a. Click on the [File Name] button.
b. Navigate to the file and double-click on it.
c. Click on the [OK] button.
In this example, I opened a file called IncentiveData080707.sav
4. Draw the desired path diagram using the appropriate drawing tools.
The example below is a simple 5. Name the variables by right-clicking on each object. And
correlation analysis. choosing “Object Properties . . .”
Intro to SEM - 13 Printed on 6/13/2010
Correlation Analysis - SPSS and Amos
The data used for this example are the VALDAT data.
a. SPSS analysis of the correlation of FORMULA with P511G
Correlations
Cor relations
P511G FORMULA
Pearson P511G 1.000 .502**
Correlation FORMULA .502** 1.000
Sig. P511G . .000
(2-tailed) FORMULA .000 .
N P511G 83 79
FORMULA 79 81
**. Correlation is signif ic ant at the 0.01 level
(2-tailed).
b. Amos Input Path Diagram - Input Parameter Values
No parameters must
be specified, since
all variables are
exogenous.
The mean and variance
c. Amos Output Path Diagram - Unstandardized (Raw) coefficient of Formula.
The mean and variance
of p511g.
The covariance of
c. Amos Path Diagram - Standardized coefficient p511g and Formula.
The correlation of p511g
and Formula.
Means and variances of
standardized variables are
not displayed, since they
0 and 1 respectively.
Intro to SEM - 14 Printed on 6/13/2010
Simple Regression Analysis: SPSS and Amos
The data used here are the VALDAT data.
a. SPSS Version 10 output
GET FILE='E:\MdbT\P595\Amos\valdatnm.sav'.
.
REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA
/CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT p511g
/METHOD=ENTER formula .
Regression
Variables Enter ed/Re m ovebd
Variables Variables
Model Entered Remov ed Method
1 FORMULAa . Enter
a. All requested variables entered.
b. Dependent Variable: P511G
Model Sum m ary
Adjusted Std. Error of
Model R R Square R Square the Estimate
1 .480 a .230 .220 4.725E-02
a. Predictors: (Constant), FORMULA
ANOVAb
Sum of
Model Squares df Mean Square F Sig.
1 Regression 5.005E-02 1 5.005E-02 22.420 .000 a
Residual .167 75 2.233E-03
Total .217 76
a. Predictors: (Constant), FORMULA
b. Dependent Variable: P511G
a
Coe fficients
Standardi
zed
Unstandardiz ed Coef f icien
Coef f icients ts
Model B Std. Error Beta t Sig.
1 (Cons tant) .496 .078 6.361 .000
FORMULA 3.004E-04 .000 .480 4.735 .000
a. Dependent Variable: P511G
Intro to SEM - 15 Printed on 6/13/2010
b. Amos Input Path Diagram - Input parameter values
1
The model is underidentified
unless you fix the value of one
error parameter. It's common to fix the
variance of the latent error variable
to 1 or the regression weight to 1.
Here, the variance has been fixed.
formula p511g
c. Amos Output Path Diagram - Unstandardized (Raw) coefficients
Variance
Mean of X of The estimated
Variance of X 1.00 Note that the fixed
Formula. unstandardized (raw parameter values were
score) relationship of error not changed.
p511g .to Formula -
the slope, to2 decimal
places. For what it's worth, the
estimated
.05 unstandardized (raw
score) relationship of
p511g to the “other
7203.60 factors” latent variable.
.00
formula p511g
d. Amos Output Path Diagram - Standardized coefficients
(View/Set -> Analysis Properties -> Output to get Amos to print Standardized estimates what a pain!!)
Correlation of p511g Correlation of p511g with
with Formula.
error latent “other factors”..
R2 for the model. You may
.88 have to pull down [View/Set] ->
Analysis Properties -> Output to
ask for this to be printed.
.23
No variances are represented in the
.48 standardized output since they're always
formula p511g 0 and 1 respectively.
Intro to SEM - 16 Printed on 6/13/2010
Two IV Regression Example - SPSS and Amos
The data here are the VALDAT data. UGPA and GREQ are predictors of P511G.
a. SPSS output.
GET
FILE='G:\MdbT\P595\P595AL09-Amos\valdatnm.sav'.
DATASET NAME DataSet1 WINDOW=FRONT.
REGRESSION /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE
/STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN
/DEPENDENT p511g /METHOD=ENTER ugpa greq .
Regression
[DataSet1] G:\MdbT\P595\P595AL09-Amos\valdatnm.sav
Correlations
p511g ugpa greq
Pearson p511g 1.000 .225 .322
Correlation ugpa .225 1.000 -.262
greq .322 -.262 1.000
Sig. (1-tailed) p511g . .025 .002
ugpa .025 . .011
greq .002 .011 .
N p511g 77 77 77
ugpa 77 77 77
greq 77 77 77
Variables Entered/Remov ed b
Variables
Model Variables Entered Remov ed Method
1 greq, ugpa a . Enter
a. All requested variables entered.
b. Dependent Variable: p511g
Model Summary
Std. Error of
Model R R Square Adjusted R Square the Estimate
1 .455a .207 .185 .04828
a. Predictors: (Constant), greq, ugpa
Coefficients a
Standardized
Unstandardized Coefficients Coefficients
Model B Std. Error Beta t Sig.
1 (Constan
.571 .069 8.228 .000
t)
ugpa .048 .016 .332 3.098 .003
greq .000 .000 .410 3.817 .000
a. Dependent Variable: p511g
Intro to SEM - 17 Printed on 6/13/2010
b. Amos Input Path Diagram - Input parameters.
1
The variance of the
(unobserved) error latent
variable must be specified at 1.
error
ugpa
Note that if the IVs are correlated, you
must specify that they are correlated.
Otherwise, Amos will perform the
analysis assuming they're
uncorrelated.
p511g
greq
c. Amos Output Path Diagram - Unstandardized (Raw) coefficients
Variance of ugpa Raw
regression
coefficient
relating p511g 1.00
Covariance of ugpa and greq.
to ugpa
Raw
error Regression
.13 coefficient
relating
p511g to
ugpa .05 residual
effects.
.05
-8.54
p511g
7897.62
.00
Raw regression
greq coefficient relating
p511g to GREQ to 2
decimal places.
Intro to SEM - 18 Printed on 6/13/2010
d. Amos Output Path Diagram - Standardized coefficients.
Correlation of ugpa Standardized
and greq. partial regression
coefficients.
error SQRT(1-R2)
ugpa .89
.33 .21
-.26
p511g
.41
Multiple R2.
greq
e. Amos Text Output - Details of input and minimization
Chi-square = 0.000
Degrees of freedom = 0
Probability level cannot be computed
Maximum Likelihood Estimates
----------------------------
Regression Weights: Estimate S.E. C.R. Label
------------------- -------- ------- ------- -------
p511g <----- ugpa 0.048 0.015 3.140
p511g <---- error 0.047 0.004 12.329
p511g <----- greq 0.000 0.000 3.869
Standardized Regression Weights: Estimate
-------------------------------- --------
p511g <----- ugpa 0.332
p511g <---- error 0.891
p511g <----- greq 0.410
Covariances: Estimate S.E. C.R. Label
------------ -------- ------- ------- -------
ugpa <-----> greq -8.537 3.861 -2.211
Correlations: Estimate
------------- --------
ugpa <-----> greq -0.262
Variances: Estimate S.E. C.R. Label
---------- -------- ------- ------- -------
error 1.000
ugpa 0.134 0.022 6.164
greq 7897.622 1281.163 6.164
Squared Multiple Correlations: Estimate
------------------------------ --------
Note – No overall test of significance of R2.
p511g 0.207
Intro to SEM - 19 Printed on 6/13/2010
Oneway Analysis of Variance Example - SPSS and Amos
The data for this example follow. They're used to introduce the 595 students to contrast coding. The
dependent variable is Job Satisfaction (JS). The research factor is Job, with three levels. It is
contrast coded by CC1 and CC2.
The data for this example are in „MdbT\P595\Amos\ OnewayegData.sav‟
ID JS JOB CC1 CC2
1 6 1 .667 .000 The rule for forming a contrast variable between two sets
2 7 1 .667 .000 of groups is
3 8 1 .667 .000
4 11 1 .667 .000 1st Value = No. of groups in 2nd set / Total no. of groups.
5 9 1 .667 .000
6 7 1 .667 .000 2nd Value= - No. of groups in 1st set / Total no. of groups.
7 7 1 .667 .000
8 5 2 -.333 .500 3rd Value = 0 for all groups to be excluded.
9 7 2 -.333 .500
10 8 2 -.333 .500 So, 1st Value of CC1 = 2 / 3 = .667.
11 9 2 -.333 .500
12 10 2 -.333 .500 2nd Value of CC1 = - 1 / 3
13 8 2 -.333 .500
14 9 2 -.333 .500 1st Value of CC2 = 1 / 2 = .5
15 4 3 -.333 -.500
16 3 3 -.333 -.500 2nd Value of CC2 = -1 / 2 = -..5
17 6 3 -.333 -.500
18 5 3 -.333 -.500 3rd Value of CC2 = 0 to exclude Job 1.
19 7 3 -.333 -.500
20 8 3 -.333 -.500
21 2 3 -.333 -.500
a. SPSS Oneway output.
Oneway
ANOVA
JS
Sum of
Squares df Mean Square F Sig.
Between
40.095 2 20.048 5.930 .011
Groups
Within Groups 60.857 18 3.381
Total 100.952 20
Intro to SEM - 20 Printed on 6/13/2010
b. SPSS Regression Output.
regression variables = js cc1 cc2
/dependent = js /enter.
Regression
b
Variables Entered/Removed
Variables Variables
Model Entered Remov ed Method
1 CC2, CC1 a . Enter
a. All requested variables entered.
b. Dependent Variable: JS
Model Summary
Adjusted R Std. Error of
Model R R Square Square the Estimate
1 .630a .397 .330 1.8387
a. Predictors: (Constant), CC2, CC1
ANOVA b
Sum of
Model Squares df Mean Square F Sig.
1 Regressio a
40.095 2 20.048 5.930 .011
n
Residual 60.857 18 3.381
Total 100.952 20
a. Predictors: (Constant), CC2, CC1
b. Dependent Variable: JS
Coefficients a
Standardized
Unstandardized Coefficients Coefficients
Model B Std. Error Beta t Sig.
1 (Constan
6.952 .401 17.326 .000
t)
CC1 1.357 .851 .292 1.594 .128
CC2 3.000 .983 .559 3.052 .007
a. Dependent Variable: JS
Intro to SEM - 21 Printed on 6/13/2010
This was prepared using Amos 3.6. I chose the "Estimate
c. Amos Input Path Diagram. means" option. This was not required, but it caused means to
be displayed.
d. Amos Output Path Diagram - Unstandardized (Raw) Coefficients
e. Amos Output Path Diagram - Standardized Coefficients
Note that the correlation between group
coding variables must be estimated. It's
zero here because they're contrast codes.
Intro to SEM - 22 Printed on 6/13/2010
f. Amos Text Output - Results
Result (Default model)
Minimum was achieved
Chi-square = .00000
Degrees of freedom = 0
Probability level cannot be computed
Maximum Likelihood Estimates
Regression Weights: (Group number 1 - Default model)
Estimate S.E. C.R. P Label
JS <--- CC1 1.35714 .80749 1.68069 .09282
JS <--- CC2 3.00000 .93241 3.21747 .00129
Standardized Regression Weights: (Group number 1 - Default model)
Estimate
JS <--- CC1 .29179
JS <--- CC2 .55859
Means: (Group number 1 - Default model)
Estimate S.E. C.R. P Label
CC1 .00033 .10541 .00316 .99748
CC2 .00000 .09129 .00000 1.00000
Intercepts: (Group number 1 - Default model)
Estimate S.E. C.R. P Label
JS 6.95193 .38065 18.26308 ***
Covariances: (Group number 1 - Default model)
Estimate S.E. C.R. P Label
CC1 <--> CC2 .00000 .04303 .00000 1.00000
Correlations: (Group number 1 - Default model)
Estimate
CC1 <--> CC2 .00000
Variances: (Group number 1 - Default model)
Estimate S.E. C.R. P Label
CC1 .22222 .07027 3.16228 .00157
CC2 .16667 .05270 3.16228 .00157
resid 2.89796 .91642 3.16228 .00157
Squared Multiple Correlations: (Group number 1 - Default model)
Estimate Note that AMOS does not provide a test of
JS .39717 the null hypothesis that in the population, the
multiple R = 0. This test is provided in the
ANOVA box in SPSS.
Intro to SEM - 23 Printed on 6/13/2010
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