Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:18 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level
growth model for a categorical outcome
(three-level analysis)
DATA: FILE IS ex9.13.dat;
VARIABLE: NAMES ARE u1-u4 x w clus;
CATEGORICAL = u1-u4;
WITHIN = x;
BETWEEN = w;
CLUSTER = clus;
ANALYSIS: TYPE = TWOLEVEL;
INTEGRATION = 7;
MODEL:
%WITHIN%
iw sw | u1@0 u2@1 u3@2 u4@3;
iw sw ON x;
%BETWEEN%
ib sb | u1@0 u2@1 u3@2 u4@3;
ib sb ON w;
OUTPUT: TECH1 TECH8;
*** WARNING
One or more individual-level variables have no variation within a
cluster for the following clusters.
Variable Cluster IDs with no within-cluster variation
U1 12 14 18 21 22 23 26 29 31 32 35 37 38 42 43 44 46 47 49 51 79
U2 1 2 7 11 13 18 19 22 23 25 26 27 33 34 36 37 38 44 47 49 51 53
U3 3 5 14 15 19 20 23 26 27 28 34 36 37 38 39 41 47 48 49 51 52 53 55 85
U4 3 5 7 9 13 15 19 20 22 26 27 28 31 34 37 38 39 43 48 49 51 52 53 55 79 85 89
90
1 WARNING(S) FOUND IN THE INPUT INSTRUCTIONS
this is an example of a two-level
growth model for a categorical outcome
(three-level analysis)
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 4
Number of independent variables 2
Number of continuous latent variables 4
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Observed independent variables
X W
Continuous latent variables
IW SW IB SB
Variables with special functions
Cluster variable CLUS
Within variables
X
Between variables
W
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 7
Dimensions of numerical integration 4
Adaptive quadrature ON
Link LOGIT
Cholesky ON
Input data file(s)
ex9.13.dat
Input data format FREE
SUMMARY OF DATA
Number of clusters 90
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.452 226.000
Category 2 0.548 274.000
U2
Category 1 0.432 216.000
Category 2 0.568 284.000
U3
Category 1 0.382 191.000
Category 2 0.618 309.000
U4
Category 1 0.364 182.000
Category 2 0.636 318.000
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
X 0.030 0.093 -2.648 0.20% -0.813 -0.253 0.033
500.000 1.048 -0.163 2.947 0.20% 0.267 0.892
W 0.068 -0.386 -3.512 1.11% -0.802 -0.188 0.124
90.000 1.146 0.868 2.622 1.11% 0.352 0.849
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 12
Loglikelihood
H0 Value -1053.709
H0 Scaling Correction Factor 0.9258
for MLR
Information Criteria
Akaike (AIC) 2131.419
Bayesian (BIC) 2181.994
Sample-Size Adjusted BIC 2143.905
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
IW |
U1 1.000 0.000 999.000 999.000
U2 1.000 0.000 999.000 999.000
U3 1.000 0.000 999.000 999.000
U4 1.000 0.000 999.000 999.000
SW |
U1 0.000 0.000 999.000 999.000
U2 1.000 0.000 999.000 999.000
U3 2.000 0.000 999.000 999.000
U4 3.000 0.000 999.000 999.000
IW ON
X 1.119 0.133 8.402 0.000
SW ON
X 0.103 0.082 1.258 0.208
SW WITH
IW 0.177 0.099 1.794 0.073
Residual Variances
IW 0.539 0.287 1.878 0.060
SW 0.232 0.122 1.907 0.057
Between Level
IB |
U1 1.000 0.000 999.000 999.000
U2 1.000 0.000 999.000 999.000
U3 1.000 0.000 999.000 999.000
U4 1.000 0.000 999.000 999.000
SB |
U1 0.000 0.000 999.000 999.000
U2 1.000 0.000 999.000 999.000
U3 2.000 0.000 999.000 999.000
U4 3.000 0.000 999.000 999.000
IB ON
W 0.350 0.114 3.078 0.002
SB ON
W 0.319 0.093 3.432 0.001
SB WITH
IB -0.181 0.124 -1.456 0.145
Intercepts
IB 0.000 0.000 999.000 999.000
SB 0.352 0.093 3.762 0.000
Thresholds
U1$1 -0.137 0.131 -1.047 0.295
U2$1 -0.137 0.131 -1.047 0.295
U3$1 -0.137 0.131 -1.047 0.295
U4$1 -0.137 0.131 -1.047 0.295
Residual Variances
IB 0.514 0.235 2.186 0.029
SB 0.308 0.118 2.607 0.009
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.347E-02
(ratio of smallest to largest eigenvalue)
RESULTS IN PROBABILITY SCALE
Estimate
Within Level
Between Level
U1
Category 1 0.467
Category 2 0.533
U2
Category 1 0.466
Category 2 0.534
U3
Category 1 0.467
Category 2 0.533
U4
Category 1 0.470
Category 2 0.530
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0 0 0 0
NU
U1 U2 U3 U4 X
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IW SW X
________ ________ ________
U1 0 0 0
U2 0 0 0
U3 0 0 0
U4 0 0 0
X 0 0 0
THETA
U1 U2 U3 U4 X
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
X 0 0 0 0 0
ALPHA
IW SW X
________ ________ ________
0 0 0
BETA
IW SW X
________ ________ ________
IW 0 0 1
SW 0 0 2
X 0 0 0
PSI
IW SW X
________ ________ ________
IW 3
SW 4 5
X 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
12 12 12 12
NU
U1 U2 U3 U4 W
________ ________ ________ ________ ________
0 0 0 0 0
LAMBDA
IB SB W
________ ________ ________
U1 0 0 0
U2 0 0 0
U3 0 0 0
U4 0 0 0
W 0 0 0
THETA
U1 U2 U3 U4 W
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
W 0 0 0 0 0
ALPHA
IB SB W
________ ________ ________
0 6 0
BETA
IB SB W
________ ________ ________
IB 0 0 7
SB 0 0 8
W 0 0 0
PSI
IB SB W
________ ________ ________
IB 9
SB 10 11
W 0 0 0
STARTING VALUES FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4 X
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IW SW X
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 1.000 0.000
U3 1.000 2.000 0.000
U4 1.000 3.000 0.000
X 0.000 0.000 1.000
THETA
U1 U2 U3 U4 X
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
X 0.000 0.000 0.000 0.000 0.000
ALPHA
IW SW X
________ ________ ________
0.000 0.000 0.000
BETA
IW SW X
________ ________ ________
IW 0.000 0.000 0.000
SW 0.000 0.000 0.000
X 0.000 0.000 0.000
PSI
IW SW X
________ ________ ________
IW 0.050
SW 0.000 0.050
X 0.000 0.000 0.524
STARTING VALUES FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
-0.376 -0.376 -0.376 -0.376
NU
U1 U2 U3 U4 W
________ ________ ________ ________ ________
0.000 0.000 0.000 0.000 0.000
LAMBDA
IB SB W
________ ________ ________
U1 1.000 0.000 0.000
U2 1.000 1.000 0.000
U3 1.000 2.000 0.000
U4 1.000 3.000 0.000
W 0.000 0.000 1.000
THETA
U1 U2 U3 U4 W
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
ALPHA
IB SB W
________ ________ ________
0.000 0.000 0.000
BETA
IB SB W
________ ________ ________
IB 0.000 0.000 0.000
SB 0.000 0.000 0.000
W 0.000 0.000 0.000
PSI
IB SB W
________ ________ ________
IB 0.050
SB 0.000 0.050
W 0.000 0.000 0.610
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.12658086D+04 0.0000000 0.0000000 EM
2 -0.12086660D+04 57.1426365 0.0451432 FS
3 -0.11639679D+04 44.6980350 0.0369813 FS
4 -0.11254112D+04 38.5567602 0.0331253 FS
5 -0.10920824D+04 33.3287306 0.0296147 FS
6 -0.10686368D+04 23.4456551 0.0214688 FS
7 -0.10570201D+04 11.6166712 0.0108706 FS
8 -0.10541172D+04 2.9029111 0.0027463 FS
9 -0.10538863D+04 0.2308671 0.0002190 EM
10 -0.10538302D+04 0.0561775 0.0000533 EM
11 -0.10538072D+04 0.0229585 0.0000218 EM
12 -0.10537954D+04 0.0117841 0.0000112 EM
13 -0.10537881D+04 0.0073030 0.0000069 EM
14 -0.10537829D+04 0.0052467 0.0000050 EM
15 -0.10537787D+04 0.0041791 0.0000040 EM
16 -0.10537751D+04 0.0035637 0.0000034 EM
17 -0.10537719D+04 0.0031770 0.0000030 EM
18 -0.10537690D+04 0.0029151 0.0000028 EM
19 -0.10537663D+04 0.0027256 0.0000026 EM
20 -0.10537637D+04 0.0025800 0.0000024 EM
21 -0.10537613D+04 0.0024619 0.0000023 EM
22 -0.10537589D+04 0.0023620 0.0000022 EM
23 -0.10537566D+04 0.0022744 0.0000022 EM
24 -0.10537544D+04 0.0021957 0.0000021 EM
25 -0.10537523D+04 0.0021235 0.0000020 EM
26 -0.10537502D+04 0.0020565 0.0000020 EM
27 -0.10537483D+04 0.0019937 0.0000019 EM
28 -0.10537463D+04 0.0019345 0.0000018 EM
29 -0.10537444D+04 0.0018783 0.0000018 EM
30 -0.10537426D+04 0.0018249 0.0000017 EM
31 -0.10537408D+04 0.0017740 0.0000017 EM
32 -0.10537391D+04 0.0017252 0.0000016 EM
33 -0.10537374D+04 0.0016786 0.0000016 EM
34 -0.10537358D+04 0.0016339 0.0000016 EM
35 -0.10537342D+04 0.0015910 0.0000015 EM
36 -0.10537327D+04 0.0015497 0.0000015 EM
37 -0.10537312D+04 0.0015101 0.0000014 EM
38 -0.10537297D+04 0.0014719 0.0000014 EM
39 -0.10537282D+04 0.0014351 0.0000014 EM
40 -0.10537268D+04 0.0013997 0.0000013 EM
41 -0.10537255D+04 0.0013655 0.0000013 EM
42 -0.10537241D+04 0.0013325 0.0000013 EM
43 -0.10537228D+04 0.0013006 0.0000012 EM
44 -0.10537216D+04 0.0012698 0.0000012 EM
45 -0.10537203D+04 0.0012401 0.0000012 EM
46 -0.10537191D+04 0.0012113 0.0000011 EM
47 -0.10537179D+04 0.0011835 0.0000011 EM
48 -0.10537168D+04 0.0011565 0.0000011 EM
49 -0.10537157D+04 0.0011305 0.0000011 EM
50 -0.10537145D+04 0.0011052 0.0000010 EM
51 -0.10537135D+04 0.0010807 0.0000010 EM
52 -0.10537124D+04 0.0010570 0.0000010 EM
53 -0.10537114D+04 0.0010347 0.0000010 EM
54 -0.10537104D+04 0.0010117 0.0000010 EM
55 -0.10537094D+04 0.0009900 0.0000009 EM
Beginning Time: 23:18:46
Ending Time: 23:19:24
Elapsed Time: 00:00:38
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