Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:11 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a SEM with
continuous factor indicators and an
interaction between two latent variables
DATA: FILE IS ex5.13.dat;
VARIABLE: NAMES ARE y1-y12;
ANALYSIS: TYPE = RANDOM;
ALGORITHM = INTEGRATION;
MODEL: f1 BY y1-y3;
f2 BY y4-y6;
f3 BY y7-y9;
f4 BY y10-y12;
f4 ON f3;
f3 ON f1 f2;
f1xf2 | f1 XWITH f2;
f3 ON f1xf2;
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a SEM with
continuous factor indicators and an
interaction between two latent variables
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 5
Observed dependent variables
Continuous
Y1 Y2 Y3 Y4 Y5 Y6
Y7 Y8 Y9 Y10 Y11 Y12
Continuous latent variables
F1 F2 F3 F4 F1XF2
Estimator MLR
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 algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 2
Adaptive quadrature ON
Cholesky OFF
Input data file(s)
ex5.13.dat
Input data format FREE
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 -0.011 0.040 -5.010 0.20% -1.203 -0.383 0.005
500.000 2.157 0.384 4.825 0.20% 0.292 1.158
Y2 -0.010 -0.070 -4.190 0.20% -1.214 -0.383 0.044
500.000 2.189 -0.201 3.806 0.20% 0.384 1.212
Y3 -0.022 0.115 -4.236 0.20% -1.352 -0.483 -0.050
500.000 2.170 -0.335 4.860 0.20% 0.282 1.336
Y4 -0.118 -0.025 -4.546 0.20% -1.225 -0.463 -0.180
500.000 1.983 0.031 4.120 0.20% 0.153 1.135
Y5 -0.083 0.011 -3.493 0.20% -1.168 -0.341 -0.104
500.000 1.592 -0.096 3.698 0.20% 0.213 1.051
Y6 -0.104 -0.024 -3.433 0.20% -1.107 -0.381 -0.107
500.000 1.617 0.010 4.107 0.20% 0.184 1.035
Y7 -0.060 0.209 -4.997 0.20% -1.466 -0.477 -0.158
500.000 2.658 0.161 5.606 0.20% 0.274 1.244
Y8 -0.077 0.187 -4.842 0.20% -1.263 -0.473 -0.079
500.000 2.226 0.454 5.193 0.20% 0.278 1.086
Y9 -0.100 0.362 -4.792 0.20% -1.373 -0.559 -0.208
500.000 2.294 0.807 5.010 0.20% 0.171 1.039
Y10 0.042 -0.081 -4.178 0.20% -1.386 -0.303 0.124
500.000 2.200 -0.210 4.034 0.20% 0.399 1.291
Y11 -0.014 -0.058 -3.947 0.20% -1.085 -0.316 0.064
500.000 1.596 -0.170 3.921 0.20% 0.310 1.124
Y12 -0.006 -0.131 -3.745 0.20% -0.980 -0.266 0.034
500.000 1.429 0.060 3.302 0.20% 0.334 1.008
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 41
Loglikelihood
H0 Value -9672.065
H0 Scaling Correction Factor 1.0047
for MLR
Information Criteria
Akaike (AIC) 19426.131
Bayesian (BIC) 19598.930
Sample-Size Adjusted BIC 19468.793
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
F1 BY
Y1 1.000 0.000 999.000 999.000
Y2 1.031 0.076 13.659 0.000
Y3 1.071 0.081 13.212 0.000
F2 BY
Y4 1.000 0.000 999.000 999.000
Y5 0.856 0.072 11.807 0.000
Y6 0.762 0.080 9.500 0.000
F3 BY
Y7 1.000 0.000 999.000 999.000
Y8 0.910 0.049 18.423 0.000
Y9 0.918 0.058 15.832 0.000
F4 BY
Y10 1.000 0.000 999.000 999.000
Y11 0.671 0.070 9.608 0.000
Y12 0.542 0.059 9.246 0.000
F4 ON
F3 0.585 0.050 11.679 0.000
F3 ON
F1 0.439 0.066 6.676 0.000
F2 0.812 0.085 9.587 0.000
F1XF2 0.397 0.062 6.385 0.000
F2 WITH
F1 0.054 0.069 0.780 0.435
Intercepts
Y1 -0.011 0.066 -0.162 0.871
Y2 -0.011 0.066 -0.162 0.871
Y3 -0.021 0.066 -0.325 0.746
Y4 -0.118 0.063 -1.876 0.061
Y5 -0.083 0.056 -1.475 0.140
Y6 -0.104 0.057 -1.838 0.066
Y7 -0.082 0.073 -1.123 0.261
Y8 -0.096 0.066 -1.458 0.145
Y9 -0.119 0.066 -1.798 0.072
Y10 0.030 0.066 0.450 0.653
Y11 -0.023 0.056 -0.401 0.688
Y12 -0.013 0.054 -0.235 0.814
Variances
F1 1.112 0.138 8.041 0.000
F2 0.971 0.133 7.309 0.000
Residual Variances
Y1 1.044 0.093 11.221 0.000
Y2 1.007 0.093 10.880 0.000
Y3 0.895 0.091 9.800 0.000
Y4 1.011 0.095 10.599 0.000
Y5 0.882 0.078 11.296 0.000
Y6 1.053 0.080 13.163 0.000
Y7 1.101 0.098 11.261 0.000
Y8 0.936 0.080 11.635 0.000
Y9 0.982 0.079 12.360 0.000
Y10 0.911 0.121 7.545 0.000
Y11 1.015 0.082 12.439 0.000
Y12 1.049 0.072 14.640 0.000
F3 0.471 0.089 5.298 0.000
F4 0.756 0.119 6.357 0.000
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.302E-01
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
1 2 3 4 5
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
6 7 8 9 10
NU
Y11 Y12
________ ________
11 12
LAMBDA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
Y1 0 0 0 0 0
Y2 13 0 0 0 0
Y3 14 0 0 0 0
Y4 0 0 0 0 0
Y5 0 15 0 0 0
Y6 0 16 0 0 0
Y7 0 0 0 0 0
Y8 0 0 17 0 0
Y9 0 0 18 0 0
Y10 0 0 0 0 0
Y11 0 0 0 19 0
Y12 0 0 0 20 0
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 21
Y2 0 22
Y3 0 0 23
Y4 0 0 0 24
Y5 0 0 0 0 25
Y6 0 0 0 0 0
Y7 0 0 0 0 0
Y8 0 0 0 0 0
Y9 0 0 0 0 0
Y10 0 0 0 0 0
Y11 0 0 0 0 0
Y12 0 0 0 0 0
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 26
Y7 0 27
Y8 0 0 28
Y9 0 0 0 29
Y10 0 0 0 0 30
Y11 0 0 0 0 0
Y12 0 0 0 0 0
THETA
Y11 Y12
________ ________
Y11 31
Y12 0 32
ALPHA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
0 0 0 0 0
BETA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
F1 0 0 0 0 0
F2 0 0 0 0 0
F3 33 34 0 0 35
F4 0 0 36 0 0
F1XF2 0 0 0 0 0
PSI
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
F1 37
F2 38 39
F3 0 0 40
F4 0 0 0 41
F1XF2 0 0 0 0 0
STARTING VALUES
NU
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
-0.011 -0.010 -0.022 -0.118 -0.083
NU
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
-0.104 -0.060 -0.077 -0.100 0.042
NU
Y11 Y12
________ ________
-0.014 -0.006
LAMBDA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
Y1 1.000 0.000 0.000 0.000 0.000
Y2 1.000 0.000 0.000 0.000 0.000
Y3 1.000 0.000 0.000 0.000 0.000
Y4 0.000 1.000 0.000 0.000 0.000
Y5 0.000 1.000 0.000 0.000 0.000
Y6 0.000 1.000 0.000 0.000 0.000
Y7 0.000 0.000 1.000 0.000 0.000
Y8 0.000 0.000 1.000 0.000 0.000
Y9 0.000 0.000 1.000 0.000 0.000
Y10 0.000 0.000 0.000 1.000 0.000
Y11 0.000 0.000 0.000 1.000 0.000
Y12 0.000 0.000 0.000 1.000 0.000
THETA
Y1 Y2 Y3 Y4 Y5
________ ________ ________ ________ ________
Y1 1.078
Y2 0.000 1.095
Y3 0.000 0.000 1.085
Y4 0.000 0.000 0.000 0.992
Y5 0.000 0.000 0.000 0.000 0.796
Y6 0.000 0.000 0.000 0.000 0.000
Y7 0.000 0.000 0.000 0.000 0.000
Y8 0.000 0.000 0.000 0.000 0.000
Y9 0.000 0.000 0.000 0.000 0.000
Y10 0.000 0.000 0.000 0.000 0.000
Y11 0.000 0.000 0.000 0.000 0.000
Y12 0.000 0.000 0.000 0.000 0.000
THETA
Y6 Y7 Y8 Y9 Y10
________ ________ ________ ________ ________
Y6 0.808
Y7 0.000 1.329
Y8 0.000 0.000 1.113
Y9 0.000 0.000 0.000 1.147
Y10 0.000 0.000 0.000 0.000 1.100
Y11 0.000 0.000 0.000 0.000 0.000
Y12 0.000 0.000 0.000 0.000 0.000
THETA
Y11 Y12
________ ________
Y11 0.798
Y12 0.000 0.714
ALPHA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
BETA
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
F1 0.000 0.000 0.000 0.000 0.000
F2 0.000 0.000 0.000 0.000 0.000
F3 0.000 0.000 0.000 0.000 0.000
F4 0.000 0.000 0.000 0.000 0.000
F1XF2 0.000 0.000 0.000 0.000 0.000
PSI
F1 F2 F3 F4 F1XF2
________ ________ ________ ________ ________
F1 0.050
F2 0.000 0.050
F3 0.000 0.000 0.050
F4 0.000 0.000 0.000 0.050
F1XF2 0.000 0.000 0.000 0.000 0.000
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.11104434D+05 0.0000000 0.0000000 EM
2 -0.99231297D+04 1181.3046817 0.1063813 EM
3 -0.98374318D+04 85.6979277 0.0086362 EM
4 -0.98029025D+04 34.5292702 0.0035100 EM
5 -0.97913562D+04 11.5463196 0.0011778 EM
6 -0.97867439D+04 4.6122998 0.0004711 EM
7 -0.97840315D+04 2.7124478 0.0002772 EM
8 -0.97818569D+04 2.1745412 0.0002223 EM
9 -0.97798439D+04 2.0129674 0.0002058 EM
10 -0.97778751D+04 1.9688380 0.0002013 EM
11 -0.97759065D+04 1.9685823 0.0002013 EM
12 -0.97739185D+04 1.9880008 0.0002034 EM
13 -0.97719009D+04 2.0176159 0.0002064 EM
14 -0.97698478D+04 2.0530719 0.0002101 EM
15 -0.97677558D+04 2.0920855 0.0002141 EM
16 -0.97656224D+04 2.1333221 0.0002184 EM
17 -0.97634465D+04 2.1759226 0.0002228 EM
18 -0.97612272D+04 2.2192734 0.0002273 EM
19 -0.97589643D+04 2.2629015 0.0002318 EM
20 -0.97566579D+04 2.3063883 0.0002363 EM
21 -0.97543086D+04 2.3493618 0.0002408 EM
22 -0.97519171D+04 2.3914588 0.0002452 EM
23 -0.97494848D+04 2.4322995 0.0002494 EM
24 -0.97470133D+04 2.4714923 0.0002535 EM
25 -0.97445047D+04 2.5086497 0.0002574 EM
26 -0.97419614D+04 2.5432984 0.0002610 EM
27 -0.97393864D+04 2.5750144 0.0002643 EM
28 -0.97367831D+04 2.6033027 0.0002673 EM
29 -0.97341554D+04 2.6276536 0.0002699 EM
30 -0.97315079D+04 2.6475245 0.0002720 EM
31 -0.97288455D+04 2.6623772 0.0002736 EM
32 -0.97261739D+04 2.6716438 0.0002746 EM
33 -0.97234991D+04 2.6747867 0.0002750 EM
34 -0.97208278D+04 2.6712337 0.0002747 EM
35 -0.97181673D+04 2.6605013 0.0002737 EM
36 -0.97155253D+04 2.6420901 0.0002719 EM
37 -0.97129097D+04 2.6155926 0.0002692 EM
38 -0.97103290D+04 2.5806280 0.0002657 EM
39 -0.97077920D+04 2.5370054 0.0002613 EM
40 -0.97053075D+04 2.4845573 0.0002559 EM
41 -0.97028842D+04 2.4233034 0.0002497 EM
42 -0.97005308D+04 2.3533504 0.0002425 EM
43 -0.96982557D+04 2.2751035 0.0002345 EM
44 -0.96960668D+04 2.1889507 0.0002257 EM
45 -0.96939712D+04 2.0955818 0.0002161 EM
46 -0.96919754D+04 1.9958079 0.0002059 EM
47 -0.96900848D+04 1.8905985 0.0001951 EM
48 -0.96883037D+04 1.7810406 0.0001838 EM
49 -0.96866354D+04 1.6683439 0.0001722 EM
50 -0.96850816D+04 1.5537435 0.0001604 EM
51 -0.96836431D+04 1.4385573 0.0001485 EM
52 -0.96823190D+04 1.3240428 0.0001367 EM
53 -0.96811076D+04 1.2114391 0.0001251 EM
54 -0.96800057D+04 1.1018675 0.0001138 EM
55 -0.96790094D+04 0.9963469 0.0001029 EM
56 -0.96781137D+04 0.8957344 0.0000925 EM
57 -0.96773129D+04 0.8007436 0.0000827 EM
58 -0.96766011D+04 0.7118640 0.0000736 EM
59 -0.96754743D+04 1.1267751 0.0001164 QN
60 -0.96743205D+04 1.1538161 0.0001193 EM
61 -0.96739445D+04 0.3759713 0.0000389 EM
62 -0.96736475D+04 0.2969571 0.0000307 EM
63 -0.96733990D+04 0.2485256 0.0000257 EM
64 -0.96731882D+04 0.2108081 0.0000218 EM
65 -0.96730091D+04 0.1791387 0.0000185 EM
66 -0.96728570D+04 0.1520147 0.0000157 EM
67 -0.96727283D+04 0.1287076 0.0000133 EM
68 -0.96726196D+04 0.1087171 0.0000112 EM
69 -0.96725280D+04 0.0916163 0.0000095 EM
70 -0.96724510D+04 0.0770370 0.0000080 EM
71 -0.96723863D+04 0.0646448 0.0000067 EM
72 -0.96723322D+04 0.0541429 0.0000056 EM
73 -0.96722869D+04 0.0452687 0.0000047 EM
74 -0.96722491D+04 0.0377883 0.0000039 EM
75 -0.96722176D+04 0.0314973 0.0000033 EM
76 -0.96721914D+04 0.0262191 0.0000027 EM
77 -0.96721696D+04 0.0217998 0.0000023 EM
78 -0.96721515D+04 0.0181038 0.0000019 EM
79 -0.96721365D+04 0.0150195 0.0000016 EM
80 -0.96721240D+04 0.0124495 0.0000013 EM
81 -0.96721137D+04 0.0103104 0.0000011 EM
82 -0.96721052D+04 0.0085329 0.0000009 EM
83 -0.96720981D+04 0.0070564 0.0000007 EM
84 -0.96720923D+04 0.0058320 0.0000006 EM
85 -0.96720875D+04 0.0048172 0.0000005 EM
86 -0.96720835D+04 0.0039771 0.0000004 EM
87 -0.96720782D+04 0.0052653 0.0000005 QN
88 -0.96720729D+04 0.0053483 0.0000006 EM
89 -0.96720714D+04 0.0014827 0.0000002 EM
90 -0.96720662D+04 0.0052270 0.0000005 FS
91 -0.96720654D+04 0.0008039 0.0000001 FS
Beginning Time: 23:11:08
Ending Time: 23:11:14
Elapsed Time: 00:00:06
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