Mplus VERSION 6
MUTHEN & MUTHEN
04/22/2010 6:34 PM
INPUT INSTRUCTIONS
TITLE: this is an example of a two-level CFA with
categorical factor indicators, a random intercept
factor, and covariates
DATA: FILE IS ex9.7.dat;
VARIABLE: NAMES ARE u1-u4 x1 x2 w clus;
CATEGORICAL = u1-u4;
WITHIN = x1 x2;
BETWEEN = w;
CLUSTER = clus;
MISSING = ALL (999);
ANALYSIS: TYPE = TWOLEVEL;
MODEL:
%WITHIN%
fw BY u1-u4;
fw ON x1 x2;
%BETWEEN%
fb BY u1-u4;
fb ON w;
OUTPUT: TECH1 TECH8;
INPUT READING TERMINATED NORMALLY
this is an example of a two-level CFA with
categorical factor indicators, a random intercept
factor, and covariates
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 1000
Number of dependent variables 4
Number of independent variables 3
Number of continuous latent variables 2
Observed dependent variables
Binary and ordered categorical (ordinal)
U1 U2 U3 U4
Observed independent variables
X1 X2 W
Continuous latent variables
FW FB
Variables with special functions
Cluster variable CLUS
Within variables
X1 X2
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
Maximum number of iterations for H1 2000
Convergence criterion for H1 0.100D-03
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 2
Adaptive quadrature ON
Link LOGIT
Cholesky ON
Input data file(s)
ex9.7.dat
Input data format FREE
SUMMARY OF DATA
Number of missing data patterns 1
Number of clusters 110
COVARIANCE COVERAGE OF DATA
Minimum covariance coverage value 0.100
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U1
Category 1 0.508 508.000
Category 2 0.492 492.000
U2
Category 1 0.532 532.000
Category 2 0.468 468.000
U3
Category 1 0.518 518.000
Category 2 0.482 482.000
U4
Category 1 0.507 507.000
Category 2 0.493 493.000
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2352.334
H0 Scaling Correction Factor 1.052
for MLR
Information Criteria
Number of Free Parameters 15
Akaike (AIC) 4734.669
Bayesian (BIC) 4808.285
Sample-Size Adjusted BIC 4760.644
(n* = (n + 2) / 24)
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Within Level
FW BY
U1 1.000 0.000 999.000 999.000
U2 1.234 0.177 6.980 0.000
U3 1.308 0.170 7.676 0.000
U4 1.296 0.167 7.741 0.000
FW ON
X1 0.834 0.089 9.379 0.000
X2 0.387 0.047 8.220 0.000
Residual Variances
FW 0.660 0.135 4.886 0.000
Between Level
FB BY
U1 1.000 0.000 999.000 999.000
U2 1.563 0.596 2.621 0.009
U3 1.368 0.422 3.242 0.001
U4 1.714 0.592 2.894 0.004
FB ON
W 0.242 0.082 2.944 0.003
Thresholds
U1$1 0.011 0.087 0.132 0.895
U2$1 0.136 0.096 1.418 0.156
U3$1 0.065 0.094 0.689 0.491
U4$1 -0.015 0.111 -0.137 0.891
Residual Variances
FB 0.110 0.061 1.796 0.073
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.160E-02
(ratio of smallest to largest eigenvalue)
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
1 0 0 0 0
NU
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
1 0 0 0 0 0
NU
X2 W
________ ________
1 0 0
LAMBDA
FW FB X1 X2 W
________ ________ ________ ________ ________
U1 0 0 0 0 0
U2 1 0 0 0 0
U3 2 0 0 0 0
U4 3 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
THETA
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
THETA
X2 W
________ ________
X2 0
W 0 0
ALPHA
FW FB X1 X2 W
________ ________ ________ ________ ________
1 0 0 0 0 0
BETA
FW FB X1 X2 W
________ ________ ________ ________ ________
FW 0 0 4 5 0
FB 0 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
PSI
FW FB X1 X2 W
________ ________ ________ ________ ________
FW 6
FB 0 0
X1 0 0 0
X2 0 0 0 0
W 0 0 0 0 0
PARAMETER SPECIFICATION FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
1 12 13 14 15
NU
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
1 0 0 0 0 0
NU
X2 W
________ ________
1 0 0
LAMBDA
FW FB X1 X2 W
________ ________ ________ ________ ________
U1 0 0 0 0 0
U2 0 7 0 0 0
U3 0 8 0 0 0
U4 0 9 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
THETA
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
U1 0
U2 0 0
U3 0 0 0
U4 0 0 0 0
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
THETA
X2 W
________ ________
X2 0
W 0 0
ALPHA
FW FB X1 X2 W
________ ________ ________ ________ ________
1 0 0 0 0 0
BETA
FW FB X1 X2 W
________ ________ ________ ________ ________
FW 0 0 0 0 0
FB 0 0 0 0 10
X1 0 0 0 0 0
X2 0 0 0 0 0
W 0 0 0 0 0
PSI
FW FB X1 X2 W
________ ________ ________ ________ ________
FW 0
FB 0 11
X1 0 0 0
X2 0 0 0 0
W 0 0 0 0 0
STARTING VALUES FOR WITHIN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
1 0.000 0.000 0.000 0.000
NU
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
1 0.000 0.000 0.000 0.000 0.000
NU
X2 W
________ ________
1 0.000 0.000
LAMBDA
FW FB X1 X2 W
________ ________ ________ ________ ________
U1 1.000 0.000 0.000 0.000 0.000
U2 1.000 0.000 0.000 0.000 0.000
U3 1.000 0.000 0.000 0.000 0.000
U4 1.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 1.000 0.000 0.000
X2 0.000 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 0.000 1.000
THETA
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
U1 1.000
U2 0.000 1.000
U3 0.000 0.000 1.000
U4 0.000 0.000 0.000 1.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
THETA
X2 W
________ ________
X2 0.000
W 0.000 0.000
ALPHA
FW FB X1 X2 W
________ ________ ________ ________ ________
1 0.000 0.000 0.000 0.000 0.000
BETA
FW FB X1 X2 W
________ ________ ________ ________ ________
FW 0.000 0.000 0.000 0.000 0.000
FB 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
FW FB X1 X2 W
________ ________ ________ ________ ________
FW 0.050
FB 0.000 0.000
X1 0.000 0.000 0.476
X2 0.000 0.000 0.000 0.544
W 0.000 0.000 0.000 0.000 0.000
STARTING VALUES FOR BETWEEN
TAU
U1$1 U2$1 U3$1 U4$1
________ ________ ________ ________
1 0.032 0.128 0.072 0.028
NU
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
1 0.000 0.000 0.000 0.000 0.000
NU
X2 W
________ ________
1 0.000 0.000
LAMBDA
FW FB X1 X2 W
________ ________ ________ ________ ________
U1 0.000 1.000 0.000 0.000 0.000
U2 0.000 1.000 0.000 0.000 0.000
U3 0.000 1.000 0.000 0.000 0.000
U4 0.000 1.000 0.000 0.000 0.000
X1 0.000 0.000 1.000 0.000 0.000
X2 0.000 0.000 0.000 1.000 0.000
W 0.000 0.000 0.000 0.000 1.000
THETA
U1 U2 U3 U4 X1
________ ________ ________ ________ ________
U1 0.000
U2 0.000 0.000
U3 0.000 0.000 0.000
U4 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
THETA
X2 W
________ ________
X2 0.000
W 0.000 0.000
ALPHA
FW FB X1 X2 W
________ ________ ________ ________ ________
1 0.000 0.000 0.000 0.000 0.000
BETA
FW FB X1 X2 W
________ ________ ________ ________ ________
FW 0.000 0.000 0.000 0.000 0.000
FB 0.000 0.000 0.000 0.000 0.000
X1 0.000 0.000 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.000
PSI
FW FB X1 X2 W
________ ________ ________ ________ ________
FW 0.000
FB 0.000 0.050
X1 0.000 0.000 0.000
X2 0.000 0.000 0.000 0.000
W 0.000 0.000 0.000 0.000 0.308
TECHNICAL 8 OUTPUT
E STEP ITER LOGLIKELIHOOD ABS CHANGE REL CHANGE ALGORITHM
1 -0.27181127D+04 0.0000000 0.0000000 EM
2 -0.26423047D+04 75.8080890 0.0278900 EM
3 -0.23792705D+04 263.0341738 0.0995473 EM
4 -0.23598525D+04 19.4179879 0.0081613 EM
5 -0.23556237D+04 4.2287706 0.0017920 EM
6 -0.23538034D+04 1.8203093 0.0007728 EM
7 -0.23529855D+04 0.8179035 0.0003475 EM
8 -0.23526243D+04 0.3612025 0.0001535 EM
9 -0.23524659D+04 0.1583870 0.0000673 EM
10 -0.23523957D+04 0.0702196 0.0000298 EM
11 -0.23523638D+04 0.0319116 0.0000136 EM
12 -0.23523488D+04 0.0149795 0.0000064 EM
13 -0.23523415D+04 0.0072796 0.0000031 EM
14 -0.23523379D+04 0.0036567 0.0000016 EM
15 -0.23523360D+04 0.0018911 0.0000008 EM
16 -0.23523350D+04 0.0010017 0.0000004 EM
17 -0.23523344D+04 0.0005407 0.0000002 EM
Beginning Time: 18:34:28
Ending Time: 18:34:39
Elapsed Time: 00:00:11
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