Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:09 PM
INPUT INSTRUCTIONS
TITLE: this is an example of an EFA with continuous,
censored, categorical, and count factor indicators
DATA: FILE = ex4.3.dat;
VARIABLE: NAMES = u4-u6 y4-y6 u1-u3 y1-y3;
CENSORED = y4-y6(b);
CATEGORICAL = u1-u3;
COUNT = u4-u6;
ANALYSIS: TYPE = EFA 1 4;
INPUT READING TERMINATED NORMALLY
this is an example of an EFA with continuous,
censored, categorical, and count factor indicators
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 12
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Continuous
Y1 Y2 Y3
Censored
Y4 Y5 Y6
Binary and ordered categorical (ordinal)
U1 U2 U3
Count
U4 U5 U6
Estimator MLR
Rotation GEOMIN
Row standardization CORRELATION
Type of rotation OBLIQUE
Epsilon value Varies
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 100
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Maximum value for logit thresholds 15
Minimum value for logit thresholds -15
Minimum expected cell size for chi-square 0.100D-01
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
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 7
Dimensions of numerical integration 4
Adaptive quadrature OFF
Link LOGIT
Cholesky OFF
Input data file(s)
ex4.3.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.504 252.000
Category 2 0.496 248.000
U2
Category 1 0.472 236.000
Category 2 0.528 264.000
U3
Category 1 0.476 238.000
Category 2 0.524 262.000
SUMMARY OF CENSORED LIMITS
Y4 0.000
Y5 0.000
Y6 0.000
COUNT PROPORTION OF ZERO, MINIMUM AND MAXIMUM VALUES
U4 0.316 0 9
U5 0.372 0 10
U6 0.338 0 9
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
Y1 -0.009 0.067 -2.633 0.20% -0.864 -0.279 -0.007
500.000 0.962 -0.214 3.446 0.20% 0.289 0.824
Y2 0.071 -0.031 -2.611 0.20% -0.809 -0.214 0.046
500.000 1.012 -0.437 2.799 0.20% 0.342 0.919
Y3 0.061 0.083 -3.443 0.20% -0.734 -0.251 0.056
500.000 1.033 0.201 3.254 0.20% 0.279 0.855
PROBLEM OCCURRED IN EXPLORATORY FACTOR ANALYSIS WITH 3 FACTOR(S).
WARNING: THE MODEL ESTIMATION HAS REACHED A SADDLE POINT OR A POINT WHERE THE
OBSERVED AND THE EXPECTED INFORMATION MATRICES DO NOT MATCH.
AN ADJUSTMENT TO THE ESTIMATION OF THE INFORMATION MATRIX HAS BEEN MADE.
THE CONDITION NUMBER IS -0.152D-02.
THE PROBLEM MAY ALSO BE RESOLVED BY DECREASING THE VALUE OF THE
MCONVERGENCE OR LOGCRITERION OPTIONS OR BY CHANGING THE STARTING VALUES
OR BY INCREASING THE NUMBER OF INTEGRATION POINTS OR BY USING THE MLF ESTIMATOR.
PROBLEM OCCURRED IN EXPLORATORY FACTOR ANALYSIS WITH 4 FACTOR(S).
WARNING: THE MODEL ESTIMATION HAS REACHED A SADDLE POINT OR A POINT WHERE THE
OBSERVED AND THE EXPECTED INFORMATION MATRICES DO NOT MATCH.
AN ADJUSTMENT TO THE ESTIMATION OF THE INFORMATION MATRIX HAS BEEN MADE.
THE CONDITION NUMBER IS -0.145D-02.
THE PROBLEM MAY ALSO BE RESOLVED BY DECREASING THE VALUE OF THE
MCONVERGENCE OR LOGCRITERION OPTIONS OR BY CHANGING THE STARTING VALUES
OR BY INCREASING THE NUMBER OF INTEGRATION POINTS OR BY USING THE MLF ESTIMATOR.
SUMMARY OF MODEL FIT INFORMATION
Degrees of
Models Compared Chi-Square Freedom P-Value
1-factor against 2-factor 389.590 11 0.0000
2-factor against 3-factor 325.150 10 0.0000
3-factor against 4-factor 14.974 9 0.0917
RESULTS FOR EXPLORATORY FACTOR ANALYSIS
EXPLORATORY FACTOR ANALYSIS WITH 1 FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 30
Loglikelihood
H0 Value -6933.890
H0 Scaling Correction Factor 1.1536
for MLR
Information Criteria
Akaike (AIC) 13927.780
Bayesian (BIC) 14054.218
Sample-Size Adjusted BIC 13958.996
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 13.296
Degrees of Freedom 1
P-Value 0.000
Likelihood Ratio Chi-Square
Value 12.773
Degrees of Freedom 1
P-Value 0.000
MINIMUM ROTATION FUNCTION VALUE 3.17587
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1
________
U4 1.000*
U5 1.000*
U6 1.000*
Y4 -0.075
Y5 -0.032
Y6 -0.030
U1 0.154*
U2 0.028
U3 0.069
Y1 -0.244
Y2 -0.191
Y3 -0.205
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1
________
1 1.000
ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.994 0.999
ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
0.999 0.976 0.999 0.995 0.941
ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
0.964 0.958
S.E. GEOMIN ROTATED LOADINGS
1
________
U4 0.000
U5 0.000
U6 0.000
Y4 0.108
Y5 0.101
Y6 0.111
U1 0.072
U2 0.069
U3 0.066
Y1 0.127
Y2 0.132
Y3 0.126
S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.016 0.007
S.E. ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
0.007 0.022 0.004 0.009 0.062
S.E. ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
0.050 0.052
Est./S.E. GEOMIN ROTATED LOADINGS
1
________
U4 99999.896
U5 99999.904
U6 99999.875
Y4 -0.688
Y5 -0.322
Y6 -0.274
U1 2.132
U2 0.405
U3 1.058
Y1 -1.911
Y2 -1.449
Y3 -1.621
Est./S.E. GEOMIN FACTOR CORRELATIONS
1
________
1 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.207 0.193 0.249 61.457 152.409
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
147.142 43.683 260.469 109.065 15.154
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
19.177 18.492
EXPLORATORY FACTOR ANALYSIS WITH 2 FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 41
Loglikelihood
H0 Value -6776.779
H0 Scaling Correction Factor 1.0605
for MLR
Information Criteria
Akaike (AIC) 13635.558
Bayesian (BIC) 13808.357
Sample-Size Adjusted BIC 13678.221
(n* = (n + 2) / 24)
MINIMUM ROTATION FUNCTION VALUE 0.20008
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2
________ ________
U4 1.000* -0.001
U5 0.998* -0.020
U6 1.004* 0.077
Y4 -0.023 0.120
Y5 -0.038 -0.046
Y6 0.000 0.053
U1 0.100 -0.158*
U2 -0.007 -0.088
U3 0.063 -0.025
Y1 -0.054 0.641*
Y2 0.030 0.747*
Y3 -0.003 0.683*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2
________ ________
1 1.000
2 -0.094 1.000
ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.984 0.997
ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
0.997 0.962 0.992 0.995 0.579
ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
0.446 0.533
S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U4 0.001 0.008
U5 0.009 0.080
U6 0.008 0.096
Y4 0.124 0.075
Y5 0.115 0.073
Y6 0.125 0.073
U1 0.071 0.060
U2 0.069 0.061
U3 0.069 0.061
Y1 0.058 0.040
Y2 0.061 0.039
Y3 0.004 0.039
S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 0.093 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.018 0.011
S.E. ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
0.007 0.024 0.011 0.009 0.050
S.E. ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
0.058 0.054
Est./S.E. GEOMIN ROTATED LOADINGS
1 2
________ ________
U4 1275.465 -0.153
U5 116.717 -0.246
U6 125.508 0.800
Y4 -0.188 1.602
Y5 -0.330 -0.632
Y6 0.003 0.724
U1 1.415 -2.610
U2 -0.100 -1.424
U3 0.913 -0.404
Y1 -0.943 15.883
Y2 0.496 19.162
Y3 -0.611 17.331
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2
________ ________
1 0.000
2 -1.019 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.203 0.191 0.236 56.074 88.836
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
134.099 40.681 93.105 109.453 11.562
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
7.670 9.903
FACTOR STRUCTURE
1 2
________ ________
U4 1.000 -0.096
U5 1.000 -0.114
U6 0.997 -0.018
Y4 -0.035 0.123
Y5 -0.033 -0.043
Y6 -0.005 0.052
U1 0.115 -0.167
U2 0.001 -0.087
U3 0.065 -0.031
Y1 -0.115 0.646
Y2 -0.040 0.744
Y3 -0.067 0.683
EXPLORATORY FACTOR ANALYSIS WITH 3 FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 51
Loglikelihood
H0 Value -6668.060
H0 Scaling Correction Factor 0.9837
for MLR
Information Criteria
Akaike (AIC) 13438.120
Bayesian (BIC) 13653.065
Sample-Size Adjusted BIC 13491.188
(n* = (n + 2) / 24)
MINIMUM ROTATION FUNCTION VALUE 0.14989
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2 3
________ ________ ________
U4 0.997* -0.022 -0.029
U5 0.998* -0.011 -0.023
U6 1.002* 0.073 0.054
Y4 0.000 0.655* 0.073
Y5 -0.017 0.620* -0.101
Y6 0.034 0.792* -0.004
U1 0.097 -0.061 -0.157*
U2 -0.007 -0.019 -0.084
U3 0.065 0.059 -0.027
Y1 -0.053 0.004 0.643*
Y2 0.029 0.007 0.740*
Y3 -0.003 -0.064 0.695*
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2 3
________ ________ ________
1 1.000
2 -0.029 1.000
3 -0.071 0.072 1.000
ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.559 0.613
ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
0.374 0.958 0.992 0.992 0.578
ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
0.454 0.519
S.E. GEOMIN ROTATED LOADINGS
1 2 3
________ ________ ________
U4 0.006 0.076 0.078
U5 0.007 0.057 0.087
U6 0.010 0.134 0.145
Y4 0.028 0.053 0.063
Y5 0.041 0.052 0.057
Y6 0.062 0.054 0.010
U1 0.066 0.064 0.061
U2 0.069 0.066 0.061
U3 0.068 0.064 0.062
Y1 0.055 0.029 0.039
Y2 0.053 0.030 0.038
Y3 0.012 0.054 0.038
S.E. GEOMIN FACTOR CORRELATIONS
1 2 3
________ ________ ________
1 0.000
2 0.109 0.000
3 0.111 0.073 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.069 0.064
S.E. ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
0.084 0.025 0.011 0.012 0.049
S.E. ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
0.056 0.053
Est./S.E. GEOMIN ROTATED LOADINGS
1 2 3
________ ________ ________
U4 155.098 -0.295 -0.371
U5 149.081 -0.199 -0.263
U6 98.355 0.541 0.372
Y4 0.006 12.453 1.158
Y5 -0.406 11.949 -1.780
Y6 0.543 14.697 -0.401
U1 1.461 -0.956 -2.565
U2 -0.096 -0.292 -1.372
U3 0.959 0.921 -0.438
Y1 -0.962 0.131 16.658
Y2 0.559 0.227 19.584
Y3 -0.271 -1.182 18.095
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2 3
________ ________ ________
1 0.000
2 -0.262 0.000
3 -0.642 0.986 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.201 0.190 0.234 8.156 9.636
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
4.462 38.948 92.525 83.068 11.820
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
8.106 9.747
FACTOR STRUCTURE
1 2 3
________ ________ ________
U4 0.999 -0.053 -0.102
U5 1.000 -0.042 -0.095
U6 0.996 0.048 -0.012
Y4 -0.024 0.660 0.120
Y5 -0.027 0.614 -0.055
Y6 0.011 0.790 0.051
U1 0.110 -0.075 -0.168
U2 0.000 -0.025 -0.085
U3 0.066 0.055 -0.027
Y1 -0.099 0.052 0.647
Y2 -0.023 0.059 0.738
Y3 -0.051 -0.014 0.690
EXPLORATORY FACTOR ANALYSIS WITH 4 FACTOR(S):
MODEL FIT INFORMATION
Number of Free Parameters 60
Loglikelihood
H0 Value -6657.882
H0 Scaling Correction Factor 1.0400
for MLR
Information Criteria
Akaike (AIC) 13435.765
Bayesian (BIC) 13688.641
Sample-Size Adjusted BIC 13498.198
(n* = (n + 2) / 24)
MINIMUM ROTATION FUNCTION VALUE 0.37724
GEOMIN ROTATED LOADINGS (* significant at 5% level)
1 2 3 4
________ ________ ________ ________
U4 0.996* -0.043 -0.043 -0.028
U5 0.998* -0.011 -0.034 -0.049
U6 0.993* 0.045 0.094 0.095
Y4 -0.007 0.651* 0.066 -0.015
Y5 -0.018 0.620* -0.116* -0.078
Y6 0.020 0.801* 0.002 0.073
U1 0.092 -0.061 -0.125 0.227
U2 -0.033 -0.014 -0.021 0.504
U3 0.054 0.064 0.016 0.307
Y1 -0.060 0.013 0.646* 0.019
Y2 0.034 0.014 0.726* -0.178
Y3 -0.008 -0.055 0.704* 0.025
GEOMIN FACTOR CORRELATIONS (* significant at 5% level)
1 2 3 4
________ ________ ________ ________
1 1.000
2 -0.004 1.000
3 -0.074 0.066 1.000
4 0.045 -0.033 -0.049 1.000
ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.565 0.603
ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
0.357 0.912 0.744 0.899 0.573
ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
0.430 0.506
S.E. GEOMIN ROTATED LOADINGS
1 2 3 4
________ ________ ________ ________
U4 0.008 0.075 0.024 0.032
U5 0.008 0.053 0.024 0.058
U6 0.046 0.077 0.110 0.309
Y4 0.043 0.055 0.055 0.068
Y5 0.041 0.052 0.054 0.085
Y6 0.038 0.058 0.022 0.112
U1 0.067 0.065 0.069 0.117
U2 0.046 0.062 0.071 0.306
U3 0.069 0.075 0.069 0.221
Y1 0.046 0.037 0.048 0.105
Y2 0.029 0.025 0.048 0.141
Y3 0.035 0.044 0.049 0.097
S.E. GEOMIN FACTOR CORRELATIONS
1 2 3 4
________ ________ ________ ________
1 0.000
2 0.070 0.000
3 0.083 0.063 0.000
4 0.131 0.136 0.174 0.000
S.E. ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.000 0.000 0.000 0.071 0.065
S.E. ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
0.096 0.057 0.306 0.137 0.059
S.E. ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
0.076 0.069
Est./S.E. GEOMIN ROTATED LOADINGS
1 2 3 4
________ ________ ________ ________
U4 120.612 -0.580 -1.745 -0.889
U5 127.623 -0.212 -1.391 -0.837
U6 21.723 0.582 0.861 0.307
Y4 -0.167 11.863 1.214 -0.224
Y5 -0.430 11.890 -2.162 -0.918
Y6 0.536 13.836 0.102 0.653
U1 1.367 -0.937 -1.807 1.939
U2 -0.709 -0.228 -0.300 1.647
U3 0.789 0.856 0.233 1.391
Y1 -1.291 0.348 13.550 0.176
Y2 1.167 0.551 15.191 -1.260
Y3 -0.237 -1.241 14.273 0.252
Est./S.E. GEOMIN FACTOR CORRELATIONS
1 2 3 4
________ ________ ________ ________
1 0.000
2 -0.054 0.000
3 -0.884 1.054 0.000
4 0.344 -0.242 -0.284 0.000
Est./S.E. ESTIMATED RESIDUAL VARIANCES
U4 U5 U6 Y4 Y5
________ ________ ________ ________ ________
0.200 0.188 0.228 7.981 9.233
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y6 U1 U2 U3 Y1
________ ________ ________ ________ ________
3.697 16.075 2.435 6.538 9.725
Est./S.E. ESTIMATED RESIDUAL VARIANCES
Y2 Y3
________ ________
5.640 7.290
FACTOR STRUCTURE
1 2 3 4
________ ________ ________ ________
U4 0.998 -0.049 -0.117 0.020
U5 0.998 -0.015 -0.105 -0.002
U6 0.990 0.044 0.020 0.133
Y4 -0.015 0.656 0.111 -0.040
Y5 -0.015 0.615 -0.070 -0.094
Y6 0.020 0.798 0.050 0.047
U1 0.111 -0.077 -0.147 0.239
U2 -0.008 -0.032 -0.045 0.504
U3 0.066 0.055 0.001 0.307
Y1 -0.107 0.055 0.650 -0.017
Y2 -0.027 0.068 0.733 -0.213
Y3 -0.059 -0.009 0.700 -0.009
Beginning Time: 23:09:28
Ending Time: 23:10:56
Elapsed Time: 00:01:28
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