2/18/2010
JUMPSTART Mplus
Exploratory and Confirmatory
Factor Analysis
Factor Analysis
Exploratory Factor Analysis (EFA)
A method of data reduction which infers presence of latent
factors which are responsible for the shared variance in a set of
observed variables / items. EFA is by definition ‘exploratory’ - the
user does not specify a structure, and assumes each item/ variable
could be related to each latent factor.
Confirmatory Factor Analysis (CFA)
User defines which observed variables /items are related to the specified
constructs or latent factors – based on a priori theory or the results of
EFA
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EFA vs. CFA
EFA
CFA
Purpose: To identify latent factors that account for variance and covariance among a
set of observed variables (both based on common factor model)
Descriptive / exploratory procedure
Input: correlation matrix (all variables
standardized)
Requires strong empirical or conceptual
foundation
Input: variance-covariance matrix
(standardized and unstandardized
solution)
Factor selection based on eigenvalue
procedures and model fit statistics
Prespecification of number of factors
pattern of factor loadings
Factor rotation to obtain simple structure
Simple structure is achieved by fixing
(most) indicator cross-loadings to zero
Unique variances / measurement error
Unique variances / measurement error
uncorrelated
can be modelled
Overall, CFA offers more parsimonious solutions and greater modelling flexibility than
EFA
Latent Variables
Latent Variables are variables that are not measured directly but
are inferred through the relationships (or shared variance) of a
set of observed (measured) variables.
For example: Depression - measured by a set of questionnaire
items – (i.e. observed variables) or Ability measured by a set of
items designed to tap IQ. This compares with temperature which
is directly measured.
An advantage of using latent variables are that they reduce the
dimensionality of data.
A large number of observable variables can be aggregated to
represent an underlying concept
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EFA/CFA important data considerations
•
•
•
•
•
•
•
Prior to analyses need to check:
Continuous or categorical variables
Normal distribution
Missing data (or partially missing item data)
Sample size
Item endorsement
Theoretical basis of model
Example of EFA using GHQ_12
1. Been able to concentrate on what you’re doing
2. Lost much sleep over worry
3. Felt you were playing a useful part in things
4. Felt capable of making decisions about things
5. Felt constantly under strain
6. Felt you couldn’t overcome your difficulties
7. Been able to enjoy your normal day-to-day activities
8. Been able to face up to your problems
9. Been feeling unhappy and depressed
10. Been losing confidence in yourself
11. Been thinking of yourself as a worthless person.
12. Been feeling reasonably happy, all things considered
1. Not at all
2. No more than usual
3. Rather more than usual
4. Much more than usual
1. More so than usual
2. Same as usual
3. Less useful than usual
4. Much less useful
NB: Mix of positive and negatively worded items
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First Stage - Importing the data into Mplus:
Stata2Mplus
• Stata2mplus using E:\mplus\egoghq12r1.dta
Looks like this was a success.
To convert the file to mplus, start mplus and run
the file E:\mplus\egoghq12r1.dta.inp
(NB: Need to import this program into Stata using findit command)
Stata2Mplus - Mplus
Title:
Stata2Mplus conversion for E:\mplus\egoghq12r1.dta.dta
List of variables converted shown below
id :
ghq01 : Able to concentrate P
1: Better than usual
2: Same as usual
3: Less than usual
4: Much less than usual
ghq02 : Lost sleep N
1: Not at all
2: No more than usual
<SNIP> .......
! Item and value labels are automatically
! returned if labelled in Stata
Data:
File is E:\mplus\egoghq12r1.dta.dat ;
Variable:
Names are
id ghq01 ghq02 ghq03 ghq04 ghq05 ghq06 ghq07 ghq08 ghq09 ghq10 ghq11
ghq12;
Missing are all (-9999) ; ! Note if your missing are coded differently alter this
Analysis:
Type = basic ;
! Can run this initially to check your data and get descriptives
! But at the moment it will include all variables including IQ
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Initially Run Type=Basic
MISSING DATA PATTERNS (x = not missing)
1
ID
x
GHQ01
x
GHQ02
x
.
.
.
GHQ12
x
COVARIANCE COVERAGE OF DATA
ID
________
1.000
1.000
1.000
GHQ01
________
ID
GHQ01
1.000
GHQ02
1.000
.
.
Estimated Sample Statistics (means)
Covariances
Correlations
GHQ02
________
1.000
THIS WILL ALSO GIVE YOU THE NUMBER OF OBSERVATIONS IN THE ANALYSIS (IMPT TO CHECK)
Results from type = Basic
COVARIANCE COVERAGE OF DATA
ID
GHQ01
ID
1.000
GHQ01
1.000
1.000
GHQ02
1.000
1.000
GHQ02
1.000
Means
GHQ01
________
2.383
GHQ02
________
2.161
GHQ03
________
2.132
GHQ04
________
2.123
GHQ05
________
2.424
GHQ01
________
1.000
0.429
0.407
0.475
0.492
GHQ02
________
GHQ03
________
GHQ04
________
GHQ05
________
1.000
0.231
0.284
0.526
1.000
0.528
0.252
Covariances
Correlations
GHQ01
GHQ02
GHQ03
GHQ04
GHQ05
1.000
0.336
1.000
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EFA_1 - GHQ-12 Items as continuous
Title:
Stata2Mplus conversion for E:\mplus\egoghq12r1.dta.dta
! Can change title
Data:
File is E:\mplus\egoghq12r1.dta.dat ;
! Data file from stata so .dta.dat
Variable:
Names are
id ghq01 ghq02 ghq03 ghq04 ghq05 ghq06 ghq07 ghq08 ghq09 ghq10 ghq11
ghq12;
Missing are all (-9999) ;
Usevariables are
! Here we specify which variables to use in the model (not IQ)
ghq01 ghq02 ghq03 ghq04 ghq05 ghq06 ghq07 ghq08 ghq09 ghq10 ghq11
ghq12;
Analysis:
Type = efa 1 4;
Estimator = ml;
Rotation = promax;
Output:
sampstat;
(! Specify potential number of Factors based on no of items)
(! Default is ULS)
(! Default is geomin)
! This will give correlation matrix, means etc
Rotation
• Orthogonal rotation
– factors are constrained to be uncorrelated
– interpretability of orthogonally rotated solutions (i.e.
factors and factor loadings)
– e.g. varimax
• Oblique rotation
– factors are allowed to intercorrelate
– often preferred as it may provide a more realistic
representation of how factors are interrelated
– information on potential higher-order structure
– e.g. promax Mplus V5 wide choice of rotation types
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EFA_1 output - Eigenvalues
RESULTS FOR EXPLORATORY FACTOR ANALYSIS
1
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
1
2
3
________
________
________
6.277
1.072
0.803
4
________
0.597
5
________
0.565
1
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
6
7
8
________
________
________
0.497
0.460
0.445
9
________
0.375
10
________
0.365
1
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
11
12
________
________
0.319
0.225
EFA_1 -Test of model fit
EXPLORATORY FACTOR ANALYSIS WITH 1 FACTOR(S):
! It will return goodness of fit for each
! Of the factors specified
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
Value
Degrees of Freedom
P-Value
836.052
54
0.0000
RMSEA (Root Mean Square Error Of Approximation)
Estimate
90 Percent C.I.
Probability RMSEA <= .05
0.114
0.107
0.000
(! sensitive to sample size looking for n/s)
(< 0.06 good model fit)
0.121
! These do not include 0.06
Root Mean Square Residual
Value
0.060 (< 0.08 good model fit)
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Goodness of Fit EFA 1-4 factors - ML
Chi-Square Test of Model Fit
Value
Degrees of Freedom
P-Value
RMSEA
Estimate
90 Percent C.I.
Probability RMSEA <= .05
Root Mean Square Residual
1F
836.052
54
0.000
2F
476.506
43
0.000
3F
155.396
33
0.000
4F
87.864
24
0.000
0.114
0.107, 0.121
0.000
0.060
0.095
0.087, 0.103
0.000
0.039
0.058
0.049, 0.067
0.081
0.020
0.049
0.038, 0.060
0.553
0.014
EFA 1 - Factor loadings
ESTIMATED FACTOR LOADINGS (for 2 or
more factors use rotated loadings)
1
1
2
1
2
3
1
2
3
4
GHQ01
0.68
0.42
0.33
0.49
0.41
-0.13
0.69
0.18
-0.11
0.01
GHQ02
0.61
-0.09
0.72
-0.08
0.74
0.01
0.02
0.72
-0.05
0.03
GHQ03
0.53
0.73
-0.09
0.69
-0.13
0.09
0.45
-0.15
0.18
0.19
GHQ04
0.60
0.82
-0.09
0.76
-0.07
0.05
0.03
0.03
-0.02
1.03
GHQ05
0.67
-0.01
0.71
0.01
0.73
0.01
0.15
0.64
-0.02
0.01
GHQ06
0.75
0.24
0.57
0.21
0.49
0.16
0.17
0.46
0.18
0.09
GHQ07
0.65
0.37
0.35
0.44
0.41
-0.11
0.71
0.16
-0.09
-0.06
GHQ08
0.69
0.49
0.28
0.47
0.22
0.13
0.38
0.15
0.18
0.12
GHQ09
0.81
-0.01
0.87
-0.03
0.69
0.28
0.12
0.60
0.27
-0.05
GHQ10
0.80
0.23
0.63
0.07
0.31
0.61
-0.02
0.32
0.65
0.02
GHQ11
0.73
0.34
0.46
0.17
0.06
0.72
0.03
0.04
0.85
-0.03
GHQ12
0.75
0.36
0.46
0.36
0.35
0.16
0.56
0.14
0.23
-0.09
This item cross loads
Only 2 items on 3rd factor
NB: Use ‘rotated’ loadings from the output as factor loadings i.e. regression coefficients
Factor structure is the correlation between each item and factor.
Items loading < 0.40 are considered poor loadings
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EFA_1: Factor correlations and determinacies
PROMAX FACTOR CORRELATIONS
2 Factor:
1
1.000
0.668
1
2
2
1.000
3 Factor:
1
1.000
0.627
0.551
1
2
3
2
3
1.000
0.540
1.000
FACTOR DETERMINACIES
2 Factor:
1
0.916
2
0.949
3 Factor:
1
0.911
2
0.931
3
0.902
EFA_2 with categorical variables
DATA:
File is E:\mplus\egoghq12r1.dta.dat ;
VARIABLE:
Names are
id ghq01 ghq02 ghq03 ghq04 ghq05 ghq06 ghq07 ghq08 ghq09 ghq10 ghq11 ghq12;
Missing are all (-9999) ;
USEVARIABLES are
ghq01 - ghq12;
CATEGORICAL ARE
ghq01 - ghq12;
!Add in categorical statement
ANALYSIS:
TYPE = efa 1 4;
ESTIMATOR = WLSMV;
ROTATION =
! Changed Estimator
promax;
OUTPUT:
sampstat;
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2/18/2010
EFA with categorical variables
GHQ01
GHQ02
GHQ03
GHQ04
GHQ05
GHQ06
GHQ07
GHQ08
GHQ09
GHQ10
GHQ11
GHQ12
1
0.73
0.66
0.60
0.70
0.72
0.79
0.71
0.73
0.86
0.87
0.83
0.80
1
0.53
-0.05
0.79
0.86
0.05
0.23
0.53
0.53
0.07
0.07
0.09
0.43
2
0.29
0.73
-0.10
-0.06
0.72
0.63
0.27
0.30
0.84
0.84
0.78
0.45
1
0.45
-0.14
0.76
0.80
-0.07
0.16
0.44
0.45
-0.01
0.11
0.16
0.35
2
0.57
0.74
-0.13
-0.05
0.79
0.53
0.53
0.29
0.66
0.28
0.09
0.44
3
-0.19
0.12
0.12
0.11
0.08
0.25
-0.16
0.15
0.36
0.66
0.78
0.16
1
0.71
0.06
0.32
-0.04
0.11
0.01
0.67
0.30
0.25
-0.01
-0.04
0.64
2
0.21
0.69
-0.18
0.06
0.74
0.56
0.19
0.17
0.49
0.27
0.08
0.07
3
0.07
-0.03
0.42
0.99
0.02
0.23
0.06
0.25
-0.14
0.05
0.04
-0.09
4
-0.14
0.04
0.17
-0.03
-0.02
0.18
-0.09
0.17
0.39
0.70
0.88
0.29
Only 2 items on 3rd factor
Difference from ML (continuous model) – item 07 does not crossload but item 12 does
EFA 2 with categorical variables – Goodness of fit
Chi-Square Test of Model Fit
Value
Degrees of
Freedom
P-Value
1F
2F
3F
4F
943.696
556.16
190.307
99.849
33
28
26
20
0.000
0.000
0.000
0.000
0.157
0.13
0.075
0.060
0.075
0.050
0.020
0.015
RMSEA
Estimate
90 Percent C.I.
Probability RMSEA <= .05
Root Mean Square
Residual
Factor determinacies:
2F: 0.935, 0.966
3F: 0.926, 0.948, 0.941
Goodness of fit suggests 3 or 4 factor model, but only 2 items load on 3rd factor
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EFA Summary
EFA is exploratory – requires interpretation
Mplus user can specify if the item responses are continuous (as in
PCA) or binary (categorical) or ordinal
Treatment of variables as binary or ordinal is particularly useful if
item responses are not normally distributed
Mplus can also include missing item level data
Different rotations can be specified
Confirmatory Factor Analysis
in Mplus
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2/18/2010
Alternative model structures for the GHQ_12
from Shevlin/Adamson 2005
Model 2 is the same as suggested by EFA2 – WLSMV with categorical data
CFA_1 GHQ-12 Politi et al, 1994
Squares or rectangles
represent observed variables
01
02
03
Dysphoria
04
05
F1
06
07
08
09
F2
10
11
12
Social dysfunction
Circles represent
latent variables
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2/18/2010
Specifying the model
02
05 06
09 10 11 12
F1 by ghq02* ghq05 ghq06
ghq09 ghq10 ghq11 ghq12;
F1@1;
Dysphoria
01
F1
03 04
07 08
12
F2 by ghq01* ghq03 ghq04
ghq07 ghq08 ghq12;
F2@1;
Social dysfunction
F2
F1
F2
F1 with F2;
Mplus syntax for 2 factor CFA model
VARIABLE:
Names are
id ghq01 ghq02 ghq03 ghq04 ghq05 ghq06
ghq07 ghq08 ghq09 ghq10 ghq11 ghq12;
Missing are all (-9999) ;
usevariables = ghq01-ghq12;
categorical = ghq01-ghq12;
idvariable = id;
ANALYSIS:
estimator = WLSMV;
MODEL:
! (this differs from EFA)
F1 by ghq02* ghq05 ghq06 ghq09 ghq10 ghq11 ghq12; !(1st item freely estimated)
F1@1;
!(fix factor variance to 1)
F2 by ghq01* ghq03 ghq04 ghq07 ghq08 ghq12;
F2@1;
F1 with F2;
!(factors are correlated)
OUTPUT: Sampstat Res
;
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2/18/2010
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
Value
Degrees of Freedom
P-Value
561.922*
32**
0.0000
*
The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used for chi-Square difference
tests. MLM, MLR and WLSM chi-square difference testing is described in the Mplus Technical Appendices at
www.statmodel.com.
See chi-square difference testing in the index of the Mplus User's Guide.
**
The degrees of freedom for MLMV, ULSMV and WLSMV are estimated according to a formula given in the Mplus
Technical Appendices at www.statmodel.com. See degrees of freedom in the index of the Mplus User's Guide.
Chi-Square Test of Model Fit for the Baseline Model
Value
Degrees of Freedom
P-Value
9961.631
13
0.0000
CFI/TLI
CFI
TLI
min=0.90, good 0.95+
0.947
0.978
Number of Free Parameters
50
RMSEA (Root Mean Square Error Of Approximation)
Estimate
0.122
< 0.06
WRMR (Weighted Root Mean Square Residual)
Value
< 1.0
2.067
Results for CFA_1 (Politi model)
MODEL RESULTS
F1
Two-Tailed
P-Value
Estimate
S.E.
Est./S.E.
0.679
0.745
0.816
0.884
0.886
0.845
0.327
0.018
0.015
0.013
0.009
0.009
0.012
0.043
37.113
48.738
61.601
93.445
97.383
68.721
7.516
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.779
0.638
0.737
0.760
0.793
0.516
0.015
0.021
0.017
0.015
0.016
0.043
51.337
30.899
44.364
49.694
49.767
11.967
0.000
0.000
0.000
0.000
0.000
0.000
0.825
0.012
69.584
0.000
BY
GHQ02
GHQ05
GHQ06
GHQ09
GHQ10
GHQ11
GHQ12
F2
BY
GHQ01
GHQ03
GHQ04
GHQ07
GHQ08
GHQ12
F1
WITH
F2
Could try specifying the model without GHQ12 on F1 (same as Andrich pos /neg model)
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2/18/2010
Results for CFA_2 Positive / Negative (Andrich, 1989)
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
Value
Degrees of Freedom
P-Value
605.457*
33**
0.0000
Chi-Square Test of Model Fit for the Baseline Model
Value
Degrees of Freedom
P-Value
Removing item 12 from F1
has not made much
difference to model fit if
anything fit indices
slightly worse
9961.631
13
0.0000
CFI/TLI
CFI
TLI
0.942
0.977
Number of Free Parameters
49
RMSEA (Root Mean Square Error Of Approximation)
Estimate
0.125
WRMR (Weighted Root Mean Square Residual)
Value
This is still high
2.149
Results for CFA_2 (Pos / Neg model)
MODEL RESULTS
F1
Two-Tailed
P-Value
Estimate
S.E.
Est./S.E.
0.678
0.744
0.816
0.885
0.886
0.845
0.018
0.015
0.013
0.009
0.009
0.012
37.110
48.716
61.614
93.569
97.448
68.663
0.000
0.000
0.000
0.000
0.000
0.000
0.764
0.627
0.725
0.745
0.776
0.843
0.015
0.021
0.017
0.015
0.015
0.012
50.150
30.457
43.228
48.927
50.181
68.810
0.000
0.000
0.000
0.000
0.000
0.000
BY
GHQ02
GHQ05
GHQ06
GHQ09
GHQ10
GHQ11
F2
BY
GHQ01
GHQ03
GHQ04
GHQ07
GHQ08
GHQ12
Factor structure looks good tho’
15
2/18/2010
Mplus syntax for adding Modification Indices
VARIABLE:
Names are
id ghq01 ghq02 ghq03 ghq04 ghq05 ghq06
ghq07 ghq08 ghq09 ghq10 ghq11 ghq12;
Missing are all (-9999) ;
usevariables = ghq01-ghq12;
categorical = ghq01-ghq12;
idvariable = id;
ANALYSIS:
estimator = WLSMV;
MODEL:
F1 by ghq02* ghq05 ghq06 ghq09 ghq10 ghq11 ghq12;
F1@1;
F2 by ghq01* ghq03 ghq04 ghq07 ghq08 ghq12;
F2@1;
F1 with F2;
ghq02 with ghq05;
! (this is needed
OUTPUT: Sampstat Res Mod (10)
;
to report modind for items)
! Specify cut-off 3.84 = sig
Output for Modification Indices
Minimum M.I. value for printing the modification index
Std E.P.C.
10.000
M.I.
E.P.C.
StdYX E.P.C.
27.431
20.801
33.145
23.818
-0.299
-0.262
0.316
0.243
-0.299
-0.262
0.316
0.243
-0.299
-0.262
0.316
0.243
10.770
133.201
30.583
19.834
13.681
24.563
10.709
24.293
24.203
11.508
20.234
16.759
16.467
20.693
15.510
20.555
20.511
15.030
14.038
143.250
13.509
15.710
-0.093
0.231
0.108
-0.118
0.070
0.103
0.069
-0.107
0.089
-0.072
0.094
-0.101
-0.087
-0.087
-0.093
-0.127
-0.112
-0.098
-0.076
0.189
-0.086
0.071
-0.093
0.231
0.108
-0.118
0.070
0.103
0.069
-0.107
0.089
-0.072
0.094
-0.101
-0.087
-0.087
-0.093
-0.127
-0.112
-0.098
-0.076
0.189
-0.086
0.071
-0.161
0.444
0.252
-0.224
0.178
0.254
0.156
-0.280
0.254
-0.183
0.270
-0.321
-0.274
-0.326
-0.280
-0.317
-0.306
-0.284
-0.305
0.767
-0.216
0.257
BY Statements
F1
F1
F1
F2
BY
BY
BY
BY
GHQ03
GHQ04
GHQ08
GHQ06
WITH Statements
GHQ03
WITH GHQ02
GHQ04
WITH GHQ03
GHQ05
WITH GHQ01
GHQ05
WITH GHQ03
GHQ06
WITH GHQ05
GHQ07
WITH GHQ01
GHQ07
WITH GHQ05
GHQ08
WITH GHQ01
GHQ08
WITH GHQ06
GHQ08
WITH GHQ07
GHQ09
WITH GHQ02
GHQ09
WITH GHQ04
GHQ10
WITH GHQ05
GHQ10
WITH GHQ06
GHQ11
WITH GHQ01
GHQ11
WITH GHQ02
GHQ11
WITH GHQ05
GHQ11
WITH GHQ07
GHQ11
WITH GHQ09
GHQ11
WITH GHQ10
GHQ12
WITH GHQ04
GHQ12
WITH GHQ09
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2/18/2010
Mplus syntax for adding residual correlations
VARIABLE:
Names are
id ghq01 ghq02 ghq03 ghq04 ghq05 ghq06
ghq07 ghq08 ghq09 ghq10 ghq11 ghq12;
Missing are all (-9999) ;
usevariables = ghq01-ghq12;
categorical = ghq01-ghq12;
idvariable = id;
! DEFINE:
! IF
(ghq01 EQ 3) THEN ghq01=2;
! CUT ghq03(0 2 );
this is useful if you need to
recode
ANALYSIS:
estimator = WLSMV;
MODEL:
F1 by ghq02* ghq05 ghq06 ghq09 ghq10 ghq11 ghq12;
F1@1;
F2 by ghq01* ghq03 ghq04 ghq07 ghq08 ghq12;
F2@1;
F1 with F2;
ghq03 with ghq04;
ghq10 with ghq11;
OUTPUT: Sampstat Res Mod (10)
;
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
Value
Degrees of Freedom
P-Value
318.808*
32**
0.0000
Chi-Square Test of Model Fit for the Baseline Model
Value
Degrees of Freedom
P-Value
9961.631
13
0.0000
CFI/TLI
CFI
TLI
0.971
0.988
Number of Free Parameters
52
RMSEA (Root Mean Square Error Of Approximation)
Estimate
0.089
WRMR (Weighted Root Mean Square Residual)
Value
1.489
By adding residual correlations
WRMR has reduced
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2/18/2010
Graphs
OUTPUT: Sampstat Res Mod (10)
Plot:
type=plot3;
;
Add plot command after output
Use menu bar to select graph
Select type of plot
Under variable selection scroll
down to find F1 F2 etc
Distribution of factors
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2/18/2010
Scatterplot of factors
Saving Factor Scores
VARIABLE:
Names are
id ghq01 ghq02 ghq03 ghq04 ghq05 ghq06 ghq07 ghq08 ghq09 ghq10 ghq11
ghq12;
Missing are all (-9999) ;
USEVARIABLES are
CATEGORICAL ARE
IDVAR is
ghq01-ghq12;
ghq01-ghq12;
id;
need to specify
id
<SNIP> ……………………………
OUTPUT:
sampstat res
mod (10);
PLOT:
type=plot3;
SAVEDATA: SAVE=FSCORES; FILE=E:\GHQ12score.DAT;
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2/18/2010
Saving Factor Scores
SAVEDATA INFORMATION
This data file can be imported
into SPSS / Excel etc using the
text import wizard and merged
back into your data file.
Order and format of variables
GHQ01
GHQ02
GHQ03
GHQ04
GHQ05
GHQ06
GHQ07
GHQ08
GHQ09
GHQ10
GHQ11
GHQ12
ID
F1
F2
F10.3
F10.3
F10.3
F10.3
F10.3
F10.3
F10.3
F10.3
F10.3
F10.3
F10.3
F10.3
I5
F10.3
F10.3
Save file
E:\GHQ12score.DAT
If you need other variables in
the saved file that are not
specified in your model use
the AUXILIARY command in
the variable statement e.g.
AUXILIARY = gender educ;
Factor scores / latent trait
scores for each individual
Save file format
12F10.3 I5 2F10.3
CFA_3 - 2F Schmitz et al model
This model is included to show that CFA is not always straightforward
ANALYSIS:
! F1 - Anxiety Depression (Schmitz et al)
! F2 - Social Performance
ESTIMATOR = WLSMV;
MODEL:
F1 by ghq01* ghq02 ghq03 ghq06 ghq07 ghq10 ghq11;
F1@1;
F2 by ghq03* ghq04 ghq05 ghq08 ghq09 ghq12;
F2@1;
F1 with F2;
OUTPUT:
sampstat res
mod (10) tech1;
PLOT:
type=plot3;
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2/18/2010
Identification Problems
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IS NOT POSITIVE DEFINITE.
THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR AN OBSERVED
VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO OBSERVED
VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO OBSERVED VARIABLES.
CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE GHQ03.
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE
COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL.
PROBLEM INVOLVING PARAMETER 40.
THE CONDITION NUMBER IS
0.893D-16.
FACTOR SCORES WILL NOT BE COMPUTED DUE TO NONCONVERGENCE OR
NONIDENTIFIED MODEL.
Use Tech1 to establish what para-40 is
LAMBDA
GHQ01
GHQ02
GHQ03
GHQ04
GHQ05
GHQ06
GHQ07
GHQ08
GHQ09
GHQ10
GHQ11
GHQ12
F1
________
37
38
39
0
0
43
44
0
0
47
48
0
F2
________
0
0
40
41
42
0
0
45
46
0
0
49
Lambda is the matrix of
factor loadings
There is a problem with
the loading of GHQ03 on
the second factor
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2/18/2010
Problem could also be identified from the output:
MODEL RESULTS
Estimate
F1
BY
GHQ01
GHQ02
GHQ03
GHQ06
GHQ07
GHQ10
GHQ11
F2
0.729
0.660
-7545.363
0.796
0.714
0.868
0.828
BY
GHQ03
GHQ04
GHQ05
GHQ08
GHQ09
GHQ12
F1
7545.965
0.692
0.721
0.732
0.859
0.795
WITH
F2
This problem stems from the fact that the
third item is loading on both factors. This
does not always lead to problems (see other
models fitted here) but in this case it has
done.
It does not appear possible to replicate this
model using the current dataset
If the aim was not replication, but merely to
test one’s own theories, then removing the
loading from one of the factors would solve
the problem. Depending on your theories
on the underlying mechanism, this may or
may not be desirable.
1.000
References
Brown, T (2006) Confirmatory factor analysis for applied research
Guildford Press, New York
22