### Mplus Class Notes Exploratory Factor Analysis

Mplus version 5.2 was used for these examples.

#### 1.0 Exploratory factor analysis

Mplus has many nice features to assist researchers conducting exploratory factor analysis.  In the example below, we use the m255_mplus_notes_efa data set, which contains continuous, dichotomous and ordered categorical variables.  Our data set has missing values on several of the variables that will be used in the analysis.  After declaring the data set, we use the listwise statement.  Unlike many other statistical packages, Mplus does not use listwise deletion by default.  Mplus provides several  methods of handling the missing data:  listwise deletion, full information maximum likelihood (FIML) and FIML with auxiliary variables.  (Mplus can also use multiply imputed data sets, although it will not create multiply imputed data sets.)  In this example, we will use listwise deletion.  If this statement was omitted, Mplus would use FIML to estimate the EFA with all of the information in the data set.  The missing statement is included to show how it would be used, but in this example, it is unnecessary.  On the categorical statement, we declare all of our dichotomous and ordered categorical variables.  On the analysis statement, we indicate that we want to run an EFA.  After that specification, two numbers are needed.  The first number indicates the minimum number of factors to extract, and the second number indicates the maximum number of factors to extract.  Mplus will produce solutions for the number of factors between the minimum and maximum.  In our example, we ask for only three factors (so we have 3 for both the first and the second number).  In the commented out analysis statement, we ask for a minimum of 1 and a maximum of 3 factors; hence, Mplus will produce a 1, 2 and 3 factor solution.  By default, Mplus provides a geomin rotated solution.  (Geomin is an oblique type of rotation, so the correlations between the factors are given in the output.)  Mplus offers 27 different types of rotations, which are described in the Mplus User's Guide.  We have commented out an example of using the rotation statement to request a varimax rotation.  Finally, we request a scree plot on the plot statement using type = plot2.  To see the plots requested, click on Graphs and then View Graphs.

Besides having several options for handling missing data and handling dichotomous and ordered categorical variables, Mplus can also conduct EFAs with survey data (data that contain sampling weights, clustering and/or stratification).  As you can see in the output, standard errors are provided for the factor loadings.

For information on the interpretation of the output, please visit our Annotated Mplus Output:  Exploratory Factor Analysis page.

title:  Exploratory factor analysis with categorical and continuous
variables.
data:  file is "f:\m255_mplus_notes_efa.txt";
listwise is on;
variable:  names are facsex facnat facrank studrnk1 grade
salary yrsteach yrsut nstud sample;
usevar are facsex facnat facrank studrnk1 grade
salary yrsteach yrsut nstud;
missing are all (-9);
categorical are facsex facnat facrank studrnk1 grade;
analysis:  type = efa 3 3;
! analysis:  type = efa 1 3;
! rotation = varimax;
iterations = 100000;
plot: type = plot2;
EXPLORATORY FACTOR ANALYSIS WITH 3 FACTOR(S):

TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value                            184.792*
Degrees of Freedom                    12
P-Value                           0.0000
Scaling Correction Factor          0.424
for MLR

*   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.

Chi-Square Test of Model Fit for the Baseline Model

Value                           3344.873
Degrees of Freedom                    36
P-Value                           0.0000

CFI/TLI

CFI                                0.948
TLI                                0.843

Number of Free Parameters                       28

RMSEA (Root Mean Square Error Of Approximation)

Estimate                           0.117

MINIMUM ROTATION FUNCTION VALUE       0.23719

1             2             3
________      ________      ________
FACSEX         0.002        -0.365         0.379
FACNAT        -0.002         0.167         0.397
FACRANK        0.459         0.690         0.001
STUDRNK1      -0.067         0.165         0.422
SALARY         0.358         0.608        -0.003
YRSTEACH       0.843         0.035        -0.025
YRSUT          0.984        -0.013         0.026
NSTUD         -0.299         0.003        -1.078

GEOMIN FACTOR CORRELATIONS
1             2             3
________      ________      ________
1         1.000
2         0.248         1.000
3         0.020        -0.257         1.000

ESTIMATED RESIDUAL VARIANCES
________      ________      ________      ________      ________
1         0.652         0.849         0.157         0.833         0.965

ESTIMATED RESIDUAL VARIANCES
SALARY        YRSTEACH      YRSUT         NSTUD
________      ________      ________      ________
1         0.393         0.273         0.035        -0.264

1             2             3
________      ________      ________
FACSEX         0.002         0.051         0.065
FACNAT         0.013         0.073         0.106
FACRANK        0.134         0.067         0.015
STUDRNK1       0.100         0.050         0.046
SALARY         0.113         0.052         0.022
YRSTEACH       0.047         0.069         0.031
YRSUT          0.039         0.013         0.019
NSTUD          0.178         0.002         0.092

S.E. GEOMIN FACTOR CORRELATIONS
1             2             3
________      ________      ________
1         0.000
2         0.174         0.000
3         0.151         0.086         0.000

S.E. ESTIMATED RESIDUAL VARIANCES
________      ________      ________      ________      ________
1         0.062         0.077         0.063         0.035         0.014

S.E. ESTIMATED RESIDUAL VARIANCES
SALARY        YRSTEACH      YRSUT         NSTUD
________      ________      ________      ________
1         0.047         0.050         0.076         0.206

1             2             3
________      ________      ________
FACSEX         0.922        -7.144         5.879
FACNAT        -0.145         2.268         3.732
FACRANK        3.425        10.322         0.074
STUDRNK1      -0.672         3.315         9.170
SALARY         3.162        11.765        -0.129
YRSTEACH      17.764         0.514        -0.818
YRSUT         25.214        -0.963         1.411
NSTUD         -1.681         1.184       -11.717

Est./S.E. GEOMIN FACTOR CORRELATIONS
1             2             3
________      ________      ________
1         0.000
2         1.426         0.000
3         0.131        -2.999         0.000

Est./S.E. ESTIMATED RESIDUAL VARIANCES
________      ________      ________      ________      ________
1        10.503        11.031         2.476        23.517        71.234

Est./S.E. ESTIMATED RESIDUAL VARIANCES
SALARY        YRSTEACH      YRSUT         NSTUD
________      ________      ________      ________
1         8.306         5.512         0.462        -1.283

FACTOR STRUCTURE
1             2             3
________      ________      ________
FACSEX        -0.081        -0.462         0.473
FACNAT         0.047         0.064         0.354
FACRANK        0.630         0.803        -0.167
STUDRNK1      -0.018         0.040         0.378
SALARY         0.509         0.697        -0.152
YRSTEACH       0.851         0.251        -0.018
YRSUT          0.982         0.225         0.049
NSTUD         -0.319         0.205        -1.084

FACTOR DETERMINACIES
1             2             3
________      ________      ________
1         0.984         0.901         1.172

PLOT INFORMATION

The following plots are available:

Eigenvalues for exploratory factor analysis

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