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2/18/2010
1
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 procedureRequires strong empirical or conceptual
foundation
Input: correlation matrix (all variables
standardized)
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 structureSimple structure is achieved by fixing
(most) indicator cross-loadings to zero
Unique variances / measurement error
uncorrelated
Unique variances / measurement error
can be modelled
Overall, CFA offers more parsimonious solutions and greater modelling flexibility than
EFA
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
Latent Variables
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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 - MplusTitle:
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 ! Item and value labels are automatically
3: Less than usual ! returned if labelled in Stata
4: Much less than usual
ghq02 : Lost sleep N
1: Not at all
2: No more than usual
<SNIP> .......
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=BasicMISSING DATA PATTERNS (x = not missing)
1
ID x
GHQ01 x
GHQ02 x
.
.
.
GHQ12 x
COVARIANCE COVERAGE OF DATA
ID GHQ01 GHQ02
________ ________ ________
ID 1.000
GHQ01 1.000 1.000
GHQ02 1.000 1.000 1.000
.
.
Estimated Sample Statistics (means)
Covariances
Correlations
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 GHQ02
ID 1.000
GHQ01 1.000 1.000
GHQ02 1.000 1.000 1.000
Means
GHQ01 GHQ02 GHQ03 GHQ04 GHQ05
________ ________ ________ ________ ________
2.383 2.161 2.132 2.123 2.424
Covariances
Correlations
GHQ01 GHQ02 GHQ03 GHQ04 GHQ05
________ ________ ________ ________ ________
GHQ01 1.000
GHQ02 0.429 1.000
GHQ03 0.407 0.231 1.000
GHQ04 0.475 0.284 0.528 1.000
GHQ05 0.492 0.526 0.252 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; (! Specify potential number of Factors based on no of items)
Estimator = ml; (! Default is ULS)
Rotation = promax; (! Default is geomin)
Output:
sampstat; ! 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
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
1 2 3 4 5
________ ________ ________ ________ ________
1 6.277 1.072 0.803 0.597 0.565
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
6 7 8 9 10
________ ________ ________ ________ ________
1 0.497 0.460 0.445 0.375 0.365
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
11 12
________ ________
1 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 836.052
Degrees of Freedom 54
P-Value 0.0000 (! sensitive to sample size looking for n/s)
RMSEA (Root Mean Square Error Of Approximation) (< 0.06 good model fit)
Estimate 0.114
90 Percent C.I. 0.107 0.121 ! These do not include 0.06
Probability RMSEA <= .05 0.000
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 1F 2F 3F 4F
Value 836.052 476.506 155.396 87.864
Degrees of Freedom 54 43 33 24
P-Value 0.000 0.000 0.000 0.000
RMSEA
Estimate 0.114 0.095 0.058 0.049
90 Percent C.I. 0.107, 0.121 0.087, 0.103 0.049, 0.067 0.038, 0.060
Probability RMSEA <= .05 0.000 0.000 0.081 0.553
Root Mean Square Residual 0.060 0.039 0.020 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
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
Only 2 items on 3rd factorThis item cross loads
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EFA_1: Factor correlations and determinacies
PROMAX FACTOR CORRELATIONS
2 Factor:
1 2
1 1.000
2 0.668 1.000
3 Factor: 1 2 3
1 1.000
2 0.627 1.000
3 0.551 0.540 1.000
FACTOR DETERMINACIES
2 Factor:
1 2
0.916 0.949
3 Factor:
1 2 3
0.911 0.931 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; ! Changed Estimator
ROTATION = promax;
OUTPUT:
sampstat;
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EFA with categorical variables
Difference from ML (continuous model) – item 07 does not crossload but item 12 does
1 1 2 1 2 3 1 2 3 4
GHQ01 0.73 0.53 0.29 0.45 0.57 -0.19 0.71 0.21 0.07 -0.14
GHQ02 0.66 -0.05 0.73 -0.14 0.74 0.12 0.06 0.69 -0.03 0.04
GHQ03 0.60 0.79 -0.10 0.76 -0.13 0.12 0.32 -0.18 0.42 0.17
GHQ04 0.70 0.86 -0.06 0.80 -0.05 0.11 -0.04 0.06 0.99 -0.03
GHQ05 0.72 0.05 0.72 -0.07 0.79 0.08 0.11 0.74 0.02 -0.02
GHQ06 0.79 0.23 0.63 0.16 0.53 0.25 0.01 0.56 0.23 0.18
GHQ07 0.71 0.53 0.27 0.44 0.53 -0.16 0.67 0.19 0.06 -0.09
GHQ08 0.73 0.53 0.30 0.45 0.29 0.15 0.30 0.17 0.25 0.17
GHQ09 0.86 0.07 0.84 -0.01 0.66 0.36 0.25 0.49 -0.14 0.39
GHQ10 0.87 0.07 0.84 0.11 0.28 0.66 -0.01 0.27 0.05 0.70
GHQ11 0.83 0.09 0.78 0.16 0.09 0.78 -0.04 0.08 0.04 0.88
GHQ12 0.80 0.43 0.45 0.35 0.44 0.16 0.64 0.07 -0.09 0.29
Only 2 items on 3rd factor
EFA 2 with categorical variables – Goodness of fit
Chi-Square Test of Model Fit 1F 2F 3F 4F
Value 943.696 556.16 190.307 99.849
Degrees of
Freedom 33 28 26 20
P-Value 0.000 0.000 0.000 0.000
RMSEA
Estimate 0.157 0.13 0.075 0.060
90 Percent C.I.
Probability RMSEA <= .05
Root Mean Square
Residual 0.075 0.050 0.020 0.015
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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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
01 02 03 04 05 06 07 08 09 10 1211
F1 F2Dysphoria Social dysfunction
Circles represent
latent variables
Squares or rectangles
represent observed variables
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Specifying the model
02 05 06 09 10 1211
F1
01 03 04 07 08 12
F2
F1 F2
F1 by ghq02* ghq05 ghq06
ghq09 ghq10 ghq11 ghq12;
F1@1;
F2 by ghq01* ghq03 ghq04
ghq07 ghq08 ghq12;
F2@1;
F1 with F2;
Dysphoria
Social dysfunction
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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TESTS OF MODEL FIT
Chi-Square Test of Model Fit
Value 561.922*
Degrees of Freedom 32**
P-Value 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 9961.631
Degrees of Freedom 13
P-Value 0.0000
CFI/TLI
CFI 0.947
TLI 0.978
Number of Free Parameters 50
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.122
WRMR (Weighted Root Mean Square Residual)
Value 2.067
min=0.90, good 0.95+
< 0.06
< 1.0
Results for CFA_1 (Politi model)MODEL RESULTS
Two-TailedEstimate S.E. Est./S.E. P-Value
F1 BYGHQ02 0.679 0.018 37.113 0.000GHQ05 0.745 0.015 48.738 0.000GHQ06 0.816 0.013 61.601 0.000GHQ09 0.884 0.009 93.445 0.000GHQ10 0.886 0.009 97.383 0.000GHQ11 0.845 0.012 68.721 0.000GHQ12 0.327 0.043 7.516 0.000
F2 BYGHQ01 0.779 0.015 51.337 0.000GHQ03 0.638 0.021 30.899 0.000GHQ04 0.737 0.017 44.364 0.000GHQ07 0.760 0.015 49.694 0.000GHQ08 0.793 0.016 49.767 0.000GHQ12 0.516 0.043 11.967 0.000
F1 WITHF2 0.825 0.012 69.584 0.000
Could try specifying the model without GHQ12 on F1 (same as Andrich pos /neg model)
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THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
Value 605.457*
Degrees of Freedom 33**
P-Value 0.0000
Chi-Square Test of Model Fit for the Baseline Model
Value 9961.631
Degrees of Freedom 13
P-Value 0.0000
CFI/TLI
CFI 0.942
TLI 0.977
Number of Free Parameters 49
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.125
WRMR (Weighted Root Mean Square Residual)
Value 2.149
Results for CFA_2 Positive / Negative (Andrich, 1989)
Removing item 12 from F1
has not made much
difference to model fit if
anything fit indices
slightly worse
This is still high
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
GHQ02 0.678 0.018 37.110 0.000
GHQ05 0.744 0.015 48.716 0.000
GHQ06 0.816 0.013 61.614 0.000
GHQ09 0.885 0.009 93.569 0.000
GHQ10 0.886 0.009 97.448 0.000
GHQ11 0.845 0.012 68.663 0.000
F2 BY
GHQ01 0.764 0.015 50.150 0.000
GHQ03 0.627 0.021 30.457 0.000
GHQ04 0.725 0.017 43.228 0.000
GHQ07 0.745 0.015 48.927 0.000
GHQ08 0.776 0.015 50.181 0.000
GHQ12 0.843 0.012 68.810 0.000
Results for CFA_2 (Pos / Neg model)
Factor structure looks good tho’
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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 to report modind for items)
OUTPUT: Sampstat Res Mod (10) ; ! Specify cut-off 3.84 = sig
Minimum M.I. value for printing the modification index 10.000
M.I. E.P.C. Std E.P.C. StdYX E.P.C.
BY Statements
F1 BY GHQ03 27.431 -0.299 -0.299 -0.299
F1 BY GHQ04 20.801 -0.262 -0.262 -0.262
F1 BY GHQ08 33.145 0.316 0.316 0.316
F2 BY GHQ06 23.818 0.243 0.243 0.243
WITH Statements
GHQ03 WITH GHQ02 10.770 -0.093 -0.093 -0.161
GHQ04 WITH GHQ03 133.201 0.231 0.231 0.444
GHQ05 WITH GHQ01 30.583 0.108 0.108 0.252
GHQ05 WITH GHQ03 19.834 -0.118 -0.118 -0.224
GHQ06 WITH GHQ05 13.681 0.070 0.070 0.178
GHQ07 WITH GHQ01 24.563 0.103 0.103 0.254
GHQ07 WITH GHQ05 10.709 0.069 0.069 0.156
GHQ08 WITH GHQ01 24.293 -0.107 -0.107 -0.280
GHQ08 WITH GHQ06 24.203 0.089 0.089 0.254
GHQ08 WITH GHQ07 11.508 -0.072 -0.072 -0.183
GHQ09 WITH GHQ02 20.234 0.094 0.094 0.270
GHQ09 WITH GHQ04 16.759 -0.101 -0.101 -0.321
GHQ10 WITH GHQ05 16.467 -0.087 -0.087 -0.274
GHQ10 WITH GHQ06 20.693 -0.087 -0.087 -0.326
GHQ11 WITH GHQ01 15.510 -0.093 -0.093 -0.280
GHQ11 WITH GHQ02 20.555 -0.127 -0.127 -0.317
GHQ11 WITH GHQ05 20.511 -0.112 -0.112 -0.306
GHQ11 WITH GHQ07 15.030 -0.098 -0.098 -0.284
GHQ11 WITH GHQ09 14.038 -0.076 -0.076 -0.305
GHQ11 WITH GHQ10 143.250 0.189 0.189 0.767
GHQ12 WITH GHQ04 13.509 -0.086 -0.086 -0.216
GHQ12 WITH GHQ09 15.710 0.071 0.071 0.257
Output for Modification Indices
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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; this is useful if you need to ! CUT ghq03(0 2 ); 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 318.808*
Degrees of Freedom 32**
P-Value 0.0000
Chi-Square Test of Model Fit for the Baseline Model
Value 9961.631
Degrees of Freedom 13
P-Value 0.0000
CFI/TLI
CFI 0.971
TLI 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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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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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 ghq01-ghq12;
CATEGORICAL ARE ghq01-ghq12;
IDVAR is 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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Saving Factor ScoresSAVEDATA INFORMATION
Order and format of variables
GHQ01 F10.3
GHQ02 F10.3
GHQ03 F10.3
GHQ04 F10.3
GHQ05 F10.3
GHQ06 F10.3
GHQ07 F10.3
GHQ08 F10.3
GHQ09 F10.3
GHQ10 F10.3
GHQ11 F10.3
GHQ12 F10.3
ID I5
F1 F10.3
F2 F10.3
Save file
E:\GHQ12score.DAT
Save file format
12F10.3 I5 2F10.3
This data file can be imported
into SPSS / Excel etc using the
text import wizard and merged
back into your data file.
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
CFA_3 - 2F Schmitz et al model
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;
This model is included to show that CFA is not always straightforward
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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
F1 F2
________ ________
GHQ01 37 0
GHQ02 38 0
GHQ03 39 40
GHQ04 0 41
GHQ05 0 42
GHQ06 43 0
GHQ07 44 0
GHQ08 0 45
GHQ09 0 46
GHQ10 47 0
GHQ11 48 0
GHQ12 0 49
Lambda is the matrix of
factor loadings
There is a problem with
the loading of GHQ03 on
the second factor
2/18/2010
22
Problem could also be identified from the output:
MODEL RESULTS
Estimate
F1 BYGHQ01 0.729GHQ02 0.660GHQ03 -7545.363GHQ06 0.796GHQ07 0.714GHQ10 0.868GHQ11 0.828
F2 BYGHQ03 7545.965GHQ04 0.692GHQ05 0.721GHQ08 0.732GHQ09 0.859GHQ12 0.795
F1 WITHF2 1.000
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.
References
Brown, T (2006) Confirmatory factor analysis for applied research
Guildford Press, New York