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Exploratory factor analysis is a statistical technique used to identify underlying factors or dimensions within a set of variables. This method is commonly used in social sciences, psychology, and market research. It can also be applied to data sets consisting of both categorical and continuous variables.
To perform an exploratory factor analysis with categorical or mixed data, the first step is to choose an appropriate method based on the nature of the data. This can include principal component analysis, principal axis factoring, or maximum likelihood estimation.
Next, the researcher must decide on the number of factors to be extracted, which can be determined using various techniques such as the Kaiser criterion or scree plot. Once the number of factors is determined, the data is then subjected to rotation, which helps to simplify and interpret the factor structure.
The rotation method can also vary, with options such as Varimax, Promax, and Oblimin. After rotation, the researcher should examine the factor loadings to determine which variables are most strongly associated with each factor.
The final step is to interpret and label the factors based on the variables with high loadings. This process can help to identify underlying themes or concepts within the data and provide valuable insights for further analysis.
Overall, performing an exploratory factor analysis with categorical or mixed data requires careful consideration of the data, appropriate statistical methods, and thorough interpretation of the results to gain a deeper understanding of the underlying factors influencing the variables.
How can I perform an exploratory factor analysis with categorical (or categorical and
continuous) variables? | Mplus FAQ
This page was created using Mplus version 5.2, the output and/or syntax may be different for other versions of Mplus.
This page shows an example exploratory factor analysis in Mplus with both
categorical and continuous variables. The dataset for this example includes data on 1428 college students
and their instructors. You can download the dataset by clicking on
https://stats.idre.ucla.edu/wp-content/uploads/2016/02/fa_categorical.dat. The factor analysis will
include dichotomous variables, including
faculty sex (facsex) and faculty nationality (US citizen or foreign citizen,
facnat); ordered categorical variables, including faculty rank (facrank), student
rank (studrank) and grade (A, B, C, etc., grade);
and the continuous variables faculty salary (salary), years teaching at
the University of Texas (yrsut), and number of students in the class (nstud) in this analysis. These
variables were selected to represent a range of types of variables (i.e. dichotomous, ordered categorical, and continuous),
and do not necessarily form substantively meaningful factors.
Below is the Mplus input file for our model. The categorical variables, both dichotomous and ordered categorical, are
listed in the categorical option of the variable command. Note
that the nominal option is used to specify that variables are unordered
categorical (none of the variables in this model are nominal so that option was
not used). We indicate the type of analysis that we would like to do,
exploratory factor analysis (efa), using the type option of the analysis command. The numbers after
efa indicate the minimum and maximum number of factors to be extracted.
By using 3 3, we indicate that we want only a three-factor solution. We
have done this to save space. We suggest that you use a reasonable range here, and each solution will be shown in the output.
For example, if we had 2 4 at the end of the option, we would see the
two-factor, three-factor and four-factor solution in the output. The missing
option of the variable command informs Mplus that in the data file any missing values are represented by
-9999.
Data::
File is https://stats.idre.ucla.edu/wp-content/uploads/2016/02/fa_categorical.dat ;
Variable:
Names are
facsex facnat facrank salary yrsut nstud studrank grade;
Missing are all (-9999) ;
Categorical are facsex facnat facrank studrank grade;
Analysis: Type = efa 3 3;The output for this model is shown below. The results of this analysis are interpreted in a manner similar to
an exploratory factor analysis with all continuous variables.
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1428
Number of dependent variables 8
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Continuous
SALARY YRSUT NSTUD
Binary and ordered categorical (ordinal)
FACSEX FACNAT FACRANK STUDRANK GRADE
Estimator WLSM
Rotation GEOMIN
Row standardization CORRELATION
Type of rotation OBLIQUE
Epsilon value Varies
Maximum number of iterations 1000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Optimization Specifications for the Exploratory Factor Analysis
Rotation Algorithm
Number of random starts 30
Maximum number of iterations 10000
Derivative convergence criterion 0.100D-04
Input data file(s)
https://stats.idre.ucla.edu/wp-content/uploads/2016/02/fa_categorical.dat
Input data format FREE
SUMMARY OF DATA
Number of missing data patterns 3
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
PROPORTION OF DATA PRESENT
Covariance Coverage
FACSEX FACNAT FACRANK SALARY YRSUT
________ ________ ________ ________ ________
FACSEX 1.000
FACNAT 1.000 1.000
FACRANK 1.000 1.000 1.000
SALARY 1.000 1.000 1.000 1.000
YRSUT 0.945 0.945 0.945 0.945 0.945
NSTUD 1.000 1.000 1.000 1.000 0.945
STUDRANK 0.992 0.992 0.992 0.992 0.937
GRADE 1.000 1.000 1.000 1.000 0.945
Covariance Coverage
NSTUD STUDRANK GRADE
________ ________ ________
NSTUD 1.000
STUDRANK 0.992 0.992
GRADE 1.000 0.992 1.000
SUMMARY OF CATEGORICAL DATA PROPORTIONS
FACSEX
Category 1 0.595
Category 2 0.405
FACNAT
Category 1 0.840
Category 2 0.160
FACRANK
Category 1 0.230
Category 2 0.270
Category 3 0.343
Category 4 0.156
STUDRANK
Category 1 0.171
Category 2 0.212
Category 3 0.250
Category 4 0.242
Category 5 0.125
GRADE
Category 1 0.005
Category 2 0.023
Category 3 0.204
Category 4 0.476
Category 5 0.291
RESULTS FOR EXPLORATORY FACTOR ANALYSIS
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
1 2 3 4 5
________ ________ ________ ________ ________
1 2.821 1.763 1.107 0.809 0.590
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
6 7 8
________ ________ ________
1 0.448 0.329 0.135
EXPLORATORY FACTOR ANALYSIS WITH 3 FACTOR(S):
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
Value 64.604*
Degrees of Freedom 7
P-Value 0.0000
Scaling Correction Factor 0.373
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 3734.662
Degrees of Freedom 28
P-Value 0.0000
CFI/TLI
CFI 0.984
TLI 0.938
Number of Free Parameters 24
RMSEA (Root Mean Square Error Of Approximation)
Estimate 0.076
MINIMUM ROTATION FUNCTION VALUE 0.22117
GEOMIN ROTATED LOADINGS
1 2 3
________ ________ ________
FACSEX -0.447 -0.655 0.004
FACNAT -0.457 0.374 -0.007
FACRANK 1.009 -0.016 0.069
SALARY 0.756 0.067 0.114
YRSUT 0.668 -0.324 -0.029
NSTUD -0.002 0.650 -0.289
STUDRANK -0.005 -0.007 0.767
GRADE 0.007 -0.001 0.274
GEOMIN FACTOR CORRELATIONS
1 2 3
________ ________ ________
1 1.000
2 -0.121 1.000
3 -0.023 -0.207 1.000
ESTIMATED RESIDUAL VARIANCES
FACSEX FACNAT FACRANK SALARY YRSUT
________ ________ ________ ________ ________
1 0.440 0.609 -0.024 0.430 0.398
ESTIMATED RESIDUAL VARIANCES
NSTUD STUDRANK GRADE
________ ________ ________
1 0.417 0.409 0.925
S.E. GEOMIN ROTATED LOADINGS
1 2 3
________ ________ ________
FACSEX 0.043 0.064 0.002
FACNAT 0.030 0.040 0.021
FACRANK 0.013 0.005 0.066
SALARY 0.016 0.028 0.058
YRSUT 0.021 0.038 0.050
NSTUD 0.001 0.049 0.062
STUDRANK 0.006 0.012 0.110
GRADE 0.028 0.045 0.050
S.E. GEOMIN FACTOR CORRELATIONS
1 2 3
________ ________ ________
1 0.000
2 0.054 0.000
3 0.063 0.063 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
FACSEX FACNAT FACRANK SALARY YRSUT
________ ________ ________ ________ ________
1 0.083 0.034 0.025 0.021 0.027
S.E. ESTIMATED RESIDUAL VARIANCES
NSTUD STUDRANK GRADE
________ ________ ________
1 0.076 0.166 0.025
Est./S.E. GEOMIN ROTATED LOADINGS
1 2 3
________ ________ ________
FACSEX -10.394 -10.166 1.969
FACNAT -15.178 9.421 -0.350
FACRANK 77.424 -2.962 1.054
SALARY 48.518 2.412 1.979
YRSUT 31.658 -8.535 -0.590
NSTUD -2.271 13.136 -4.637
STUDRANK -0.859 -0.609 6.961
GRADE 0.253 -0.012 5.434
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2 3
________ ________ ________
1 0.000
2 -2.260 0.000
3 -0.365 -3.308 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
FACSEX FACNAT FACRANK SALARY YRSUT
________ ________ ________ ________ ________
1 5.331 17.653 -0.952 20.375 14.900
Est./S.E. ESTIMATED RESIDUAL VARIANCES
NSTUD STUDRANK GRADE
________ ________ ________
1 5.487 2.458 37.379
FACTOR STRUCTURE
1 2 3
________ ________ ________
FACSEX -0.368 -0.602 0.150
FACNAT -0.502 0.431 -0.074
FACRANK 1.009 -0.153 0.049
SALARY 0.745 -0.049 0.083
YRSUT 0.708 -0.399 0.022
NSTUD -0.074 0.710 -0.423
STUDRANK -0.022 -0.165 0.769
GRADE 0.001 -0.058 0.274
FACTOR DETERMINACIES
1 2 3
________ ________ ________
1 1.012 0.847 0.800See Also
Mplus Annotated Output: Factor Analysis
Cite this article
stats writer (2024). How can I perform an exploratory factor analysis with categorical (or categorical and continuous) variables?. PSYCHOLOGICAL SCALES. Retrieved from https://scales.arabpsychology.com/stats/how-can-i-perform-an-exploratory-factor-analysis-with-categorical-or-categorical-and-continuous-variables/
stats writer. "How can I perform an exploratory factor analysis with categorical (or categorical and continuous) variables?." PSYCHOLOGICAL SCALES, 1 Jul. 2024, https://scales.arabpsychology.com/stats/how-can-i-perform-an-exploratory-factor-analysis-with-categorical-or-categorical-and-continuous-variables/.
stats writer. "How can I perform an exploratory factor analysis with categorical (or categorical and continuous) variables?." PSYCHOLOGICAL SCALES, 2024. https://scales.arabpsychology.com/stats/how-can-i-perform-an-exploratory-factor-analysis-with-categorical-or-categorical-and-continuous-variables/.
stats writer (2024) 'How can I perform an exploratory factor analysis with categorical (or categorical and continuous) variables?', PSYCHOLOGICAL SCALES. Available at: https://scales.arabpsychology.com/stats/how-can-i-perform-an-exploratory-factor-analysis-with-categorical-or-categorical-and-continuous-variables/.
[1] stats writer, "How can I perform an exploratory factor analysis with categorical (or categorical and continuous) variables?," PSYCHOLOGICAL SCALES, vol. X, no. Y, ص Z-Z, July, 2024.
stats writer. How can I perform an exploratory factor analysis with categorical (or categorical and continuous) variables?. PSYCHOLOGICAL SCALES. 2024;vol(issue):pages.