```Mplus VERSION 8
MUTHEN & MUTHEN
04/10/2017   5:03 AM

INPUT INSTRUCTIONS

TITLE:	this is an example of a two-level
regression analysis for a continuous
dependent variable with a random slope
and an observed covariate
part b
DATA:	FILE = ex9.2a.dat;
VARIABLE:	NAMES = y x w xm clus;
WITHIN = x;
BETWEEN = w xm;
CLUSTER = clus;
DEFINE:	CENTER x (GROUPMEAN);
ANALYSIS:	TYPE = TWOLEVEL RANDOM;
MODEL:	%WITHIN%
s | y ON x;
%BETWEEN%
y ON w xm;
[s] (gam0);
s ON w (gam1)
xm;
y WITH s;
MODEL CONSTRAINT:
PLOT(ylow yhigh);
LOOP(level1,-3,3,0.01);
ylow = (gam0+gam1*(-1))*level1;
yhigh = (gam0+gam1*1)*level1;
PLOT:	TYPE = PLOT2;

this is an example of a two-level
regression analysis for a continuous
dependent variable with a random slope
and an observed covariate
part b

SUMMARY OF ANALYSIS

Number of groups                                                 1
Number of observations                                        1000

Number of dependent variables                                    1
Number of independent variables                                  3
Number of continuous latent variables                            1

Observed dependent variables

Continuous
Y

Observed independent variables
X           W           XM

Continuous latent variables
S

Variables with special functions

Cluster variable      CLUS

Within variables
X

Between variables
W           XM

Centering (GROUPMEAN)
X

Estimator                                                      MLR
Information matrix                                        OBSERVED
Maximum number of iterations                                   100
Convergence criterion                                    0.100D-05
Maximum number of EM iterations                                500
Convergence criteria for the EM algorithm
Loglikelihood change                                   0.100D-02
Relative loglikelihood change                          0.100D-05
Derivative                                             0.100D-03
Minimum variance                                         0.100D-03
Maximum number of steepest descent iterations                   20
Maximum number of iterations for H1                           2000
Convergence criterion for H1                             0.100D-03
Optimization algorithm                                         EMA

Input data file(s)
ex9.2a.dat
Input data format  FREE

SUMMARY OF DATA

Number of clusters                        110

Average cluster size        9.091

Estimated Intraclass Correlations for the Y Variables

Intraclass              Intraclass
Variable  Correlation   Variable  Correlation

Y            0.587

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

Y                     1.493       0.265      -5.451    0.10%      -0.438      0.866      1.359
1000.000       5.547       0.223       9.654    0.10%       1.895      3.342
X                     0.000       0.003      -2.949    0.10%      -0.802     -0.227      0.001
1000.000       0.953       0.066       3.161    0.10%       0.213      0.811
W                    -0.328      -0.091      -3.044    0.91%      -1.079     -0.629     -0.313
110.000       0.885       0.005       2.076    0.91%      -0.087      0.518
XM                   -0.277       0.224      -2.034    0.91%      -0.946     -0.479     -0.258
110.000       0.458       0.069       1.919    0.91%      -0.133      0.304

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL FIT INFORMATION

Number of Free Parameters                       10

Loglikelihood

H0 Value                       -1596.165
H0 Scaling Correction Factor      0.9216
for MLR

Information Criteria

Akaike (AIC)                    3212.331
Bayesian (BIC)                  3261.408
(n* = (n + 2) / 24)

MODEL RESULTS

Two-Tailed
Estimate       S.E.  Est./S.E.    P-Value

Within Level

Residual Variances
Y                  1.035      0.047     21.915      0.000

Between Level

S          ON
W                  0.412      0.097      4.236      0.000
XM                 0.526      0.133      3.969      0.000

Y          ON
W                  0.968      0.127      7.603      0.000
XM                 1.231      0.179      6.872      0.000

Y        WITH
S                  0.308      0.063      4.856      0.000

Intercepts
Y                  2.134      0.099     21.599      0.000
S                  1.039      0.076     13.620      0.000

Residual Variances
Y                  0.728      0.111      6.568      0.000
S                  0.336      0.061      5.535      0.000

QUALITY OF NUMERICAL RESULTS

Condition Number for the Information Matrix              0.279E-05
(ratio of smallest to largest eigenvalue)

PLOT INFORMATION

The following plots are available:

Loop plots

Beginning Time:  05:03:49
Ending Time:  05:03:49
Elapsed Time:  00:00:00

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Copyright (c) 1998-2017 Muthen & Muthen
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