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Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence
by Judith D. Singer and John B. Willett
Chapter 8: Modeling change using covariance structure analysis

This chapter uses data set alcohol2.txt.


Table 8.1, page 282

Basic statistics and covariance matrix

TITLE:
      alcohol2.inp
DATA:
      File is d:\alda\atsdata\ascii\alcohol2.txt;      
  VARIABLE:
      Names are ID FEMALE ALC1 ALC2 ALC3 PEER1 PEER2 PEER3;
      Missing are all(999);
      Usevariables are alc1 alc2 alc3 female peer1 peer2 peer3;
  ANALYSIS:
      Type = basic; 
RESULTS FOR BASIC ANALYSIS
     SAMPLE STATISTICS
           Means
              ALC1          ALC2          ALC3          FEMALE        PEER1
              ________      ________      ________      ________      ________
      1         0.225         0.254         0.288         0.612         0.177
           Means
              PEER2         PEER3
              ________      ________
      1         0.290         0.347
           Covariances
              ALC1          ALC2          ALC3          FEMALE        PEER1
              ________      ________      ________      ________      ________
 ALC1           0.136
 ALC2           0.078         0.155
 ALC3           0.065         0.082         0.181
 FEMALE        -0.008        -0.013        -0.005         0.238
 PEER1          0.066         0.045         0.040        -0.009         0.174
 PEER2          0.064         0.096         0.066        -0.022         0.072
 PEER3          0.060         0.074         0.132        -0.024         0.071
           Covariances
              PEER2         PEER3
              ________      ________
 PEER2          0.262
 PEER3          0.112         0.289

Table 8.2, page 289

Model A

TITLE: 
      alcohol2.inp
      Linear growth model
DATA:
      File is d:\alda\atsdata\ascii\alcohol2.txt;

VARIABLE:
      Names are ID FEMALE ALC1 ALC2 ALC3 PEER1 PEER2 PEER3;
      Missing are all(999);
      Usevariables are alc1 alc2 alc3 ;

ANALYSIS:
      Type = meanstructure;
 
MODEL:
      level by alc1 - alc3@1;
      trend by alc1@0 alc2@.75 alc3@1.75;
      [alc1-alc3@0];  
      [level  trend];
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
          Value                              0.048
          Degrees of Freedom                     1
          P-Value                           0.8262
Chi-Square Test of Model Fit for the Baseline Model
          Value                            736.696
          Degrees of Freedom                     3
          P-Value                           0.0000
CFI/TLI
          CFI                                1.000
          TLI                                1.004
Loglikelihood
          H0 Value                       -1280.854
          H1 Value                       -1280.830
Information Criteria
          Number of Free Parameters              8
          Akaike (AIC)                    2577.707
          Bayesian (BIC)                  2617.890
          Sample-Size Adjusted BIC        2592.480
            (n* = (n + 2) / 24)
RMSEA (Root Mean Square Error Of Approximation)
          Estimate                           0.000
          90 Percent C.I.                    0.000  0.048
          Probability RMSEA <= .05           0.956
SRMR (Standardized Root Mean Square Residual)
          Value                              0.001
MODEL RESULTS
                   Estimates     S.E.  Est./S.E.
 LEVEL    BY
    ALC1               1.000    0.000      0.000
    ALC2               1.000    0.000      0.000
    ALC3               1.000    0.000      0.000
 TREND    BY
    ALC1               0.000    0.000      0.000
    ALC2               0.750    0.000      0.000
    ALC3               1.750    0.000      0.000
 TREND    WITH
    LEVEL             -0.012    0.005     -2.727
 Means
    LEVEL              0.226    0.011     21.107
    TREND              0.036    0.007      4.898
 Intercepts
    ALC1               0.000    0.000      0.000
    ALC2               0.000    0.000      0.000
    ALC3               0.000    0.000      0.000
 Variances
    LEVEL              0.087    0.007     12.253
    TREND              0.020    0.005      3.795
 Residual Variances
    ALC1               0.048    0.006      7.551
    ALC2               0.076    0.004     17.052
    ALC3               0.077    0.010      7.756

Model B      

TITLE:
      alcohol2.inp
      Linear growth model

DATA:
      File is d:\alda\atsdata\ascii\alcohol2.txt;      
VARIABLE:
      Names are ID FEMALE ALC1 ALC2 ALC3 PEER1 PEER2 PEER3;
      Missing are all(999);
      Usevariables are alc1 alc2 alc3 female;
ANALYSIS:
      Type = meanstructure;

MODEL:
      level by alc1 - alc3@1;
      trend by alc1@0 alc2@.75 alc3@1.75;
      [alc1-alc3@0];
      level trend on female;
      [level  trend];
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
          Value                              1.545
          Degrees of Freedom                     2
          P-Value                           0.4585
Chi-Square Test of Model Fit for the Baseline Model
          Value                            742.014
          Degrees of Freedom                     6
          P-Value                           0.0000
CFI/TLI
          CFI                                1.000
          TLI                                1.002
Loglikelihood
          H0 Value                       -2064.242
          H1 Value                       -2063.470
Information Criteria
          Number of Free Parameters             10
          Akaike (AIC)                    4148.485
          Bayesian (BIC)                  4198.714
          Sample-Size Adjusted BIC        4166.951
            (n* = (n + 2) / 24)
RMSEA (Root Mean Square Error Of Approximation)
          Estimate                           0.000
          90 Percent C.I.                    0.000  0.055
          Probability RMSEA <= .05           0.924
SRMR (Standardized Root Mean Square Residual)
          Value                              0.007
MODEL RESULTS
                   Estimates     S.E.  Est./S.E.    Std     StdYX
 LEVEL    BY
    ALC1               1.000    0.000      0.000    0.295    0.800
    ALC2               1.000    0.000      0.000    0.295    0.748
    ALC3               1.000    0.000      0.000    0.295    0.693
 TREND    BY
    ALC1               0.000    0.000      0.000    0.000    0.000
    ALC2               0.750    0.000      0.000    0.105    0.266
    ALC3               1.750    0.000      0.000    0.244    0.575
 LEVEL    ON
    FEMALE            -0.042    0.022     -1.914   -0.142   -0.069
 TREND    ON
    FEMALE             0.008    0.015      0.522    0.056    0.027
 TREND    WITH
    LEVEL             -0.012    0.005     -2.662   -0.296   -0.296
 Intercepts
    ALC1               0.000    0.000      0.000    0.000    0.000
    ALC2               0.000    0.000      0.000    0.000    0.000
    ALC3               0.000    0.000      0.000    0.000    0.000
    LEVEL              0.251    0.017     14.661    0.853    0.853
    TREND              0.031    0.012      2.641    0.223    0.223
 Residual Variances
    ALC1               0.049    0.006      7.621    0.049    0.360
    ALC2               0.075    0.004     17.042    0.075    0.488
    ALC3               0.077    0.010      7.794    0.077    0.427
    LEVEL              0.086    0.007     12.194    0.995    0.995
    TREND              0.019    0.005      3.742    0.999    0.999
R-SQUARE
    Observed
    Variable  R-Square
    ALC1         0.640
    ALC2         0.512
    ALC3         0.573
     Latent
    Variable  R-Square
    LEVEL        0.005
    TREND        0.001

Baseline model to be compared with for model B

TITLE:
      alcohol2.inp
      Linear growth model
DATA:
      File is d:\alda\atsdata\ascii\alcohol2.txt;
      
VARIABLE:
      Names are ID FEMALE ALC1 ALC2 ALC3 PEER1 PEER2 PEER3;
      Missing are all(999);
      Usevariables are alc1 alc2 alc3 female;
ANALYSIS:
      Type = meanstructure;
 
MODEL:
      level by alc1 - alc3@1;
      trend by alc1@0 alc2@.75 alc3@1.75;
      [alc1-alc3@0];
      level trend on female@0;
      [level  trend];
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
          Value                              5.367
          Degrees of Freedom                     4
          P-Value                           0.2512

Model C

TITLE:
      alcohol2.inp
      Linear growth model
DATA:
      File is d:\alda\atsdata\ascii\alcohol2.txt;
      
VARIABLE:
      Names are ID FEMALE ALC1 ALC2 ALC3 PEER1 PEER2 PEER3;
      Missing are all(999);
      Usevariables are alc1 alc2 alc3 female;
ANALYSIS:
      Type = meanstructure;
MODEL:
      level by alc1 - alc3@1;
      trend by alc1@0 alc2@.75 alc3@1.75;
      [alc1-alc3@0];
      level on female;
      trend on female@0;
      [level  trend];
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
          Value                              1.817
          Degrees of Freedom                     3
          P-Value                           0.6103
Chi-Square Test of Model Fit for the Baseline Model
          Value                            742.014
          Degrees of Freedom                     6
          P-Value                           0.0000
CFI/TLI
          CFI                                1.000
          TLI                                1.003
Loglikelihood
          H0 Value                       -2064.379
          H1 Value                       -2063.470
Information Criteria
          Number of Free Parameters              9
          Akaike (AIC)                    4146.758
          Bayesian (BIC)                  4191.963
          Sample-Size Adjusted BIC        4163.377
            (n* = (n + 2) / 24)
RMSEA (Root Mean Square Error Of Approximation)
          Estimate                           0.000
          90 Percent C.I.                    0.000  0.042
          Probability RMSEA <= .05           0.981
SRMR (Standardized Root Mean Square Residual)
          Value                              0.008
MODEL RESULTS
                   Estimates     S.E.  Est./S.E.
 LEVEL    BY
    ALC1               1.000    0.000      0.000
    ALC2               1.000    0.000      0.000
    ALC3               1.000    0.000      0.000
 TREND    BY
    ALC1               0.000    0.000      0.000
    ALC2               0.750    0.000      0.000
    ALC3               1.750    0.000      0.000
 LEVEL    ON
    FEMALE            -0.037    0.019     -1.887
 TREND    ON
    FEMALE             0.000    0.000      0.000
 TREND    WITH
    LEVEL             -0.012    0.005     -2.668
 Intercepts
    ALC1               0.000    0.000      0.000
    ALC2               0.000    0.000      0.000
    ALC3               0.000    0.000      0.000
    LEVEL              0.248    0.016     15.533
    TREND              0.036    0.007      4.898
 Residual Variances
    ALC1               0.049    0.006      7.613
    ALC2               0.075    0.004     17.041
    ALC3               0.077    0.010      7.804
    LEVEL              0.086    0.007     12.198
    TREND              0.019    0.005      3.741

Model D

TITLE:
      alcohol2.inp
      Linear growth model
DATA:
      File is d:\alda\atsdata\ascii\alcohol2.txt;
      
VARIABLE:
      Names are ID FEMALE ALC1 ALC2 ALC3 PEER1 PEER2 PEER3;
      Missing are all(999);
      Usevariables are alc1 alc2 alc3 peer1 peer2 peer3;
ANALYSIS:
      Type = meanstructure;
MODEL:
      level by alc1 - alc3@1;
      trend by alc1@0 alc2@.75 alc3@1.75;
      levelp by peer1 - peer3@1;
      trendp by peer1@0 peer2@.75 peer3@1.75;
      level on levelp*.8 trendp*.08;
      trend on levelp*-.1 trendp*.6;
      
      [alc1-alc3@0];
      [peer1-peer3@0];
      alc1 with peer1;
      alc2 with peer2;
      alc3 with peer3;
      [level  trend];
      [levelp trendp];
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
          Value                             11.557
          Degrees of Freedom                     4
          P-Value                           0.0209
Chi-Square Test of Model Fit for the Baseline Model
          Value                           1926.612
          Degrees of Freedom                    15
          P-Value                           0.0000
CFI/TLI
          CFI                                0.996
          TLI                                0.985
Loglikelihood
          H0 Value                       -3037.266
          H1 Value                       -3031.487
Information Criteria
          Number of Free Parameters             23
          Akaike (AIC)                    6120.532
          Bayesian (BIC)                  6236.058
          Sample-Size Adjusted BIC        6163.004
            (n* = (n + 2) / 24)
RMSEA (Root Mean Square Error Of Approximation)
          Estimate                           0.041
          90 Percent C.I.                    0.014  0.070
          Probability RMSEA <= .05           0.656
SRMR (Standardized Root Mean Square Residual)
          Value                              0.016
MODEL RESULTS
                   Estimates     S.E.  Est./S.E.
 LEVEL    BY
    ALC1               1.000    0.000      0.000
    ALC2               1.000    0.000      0.000
    ALC3               1.000    0.000      0.000
 TREND    BY
    ALC1               0.000    0.000      0.000
    ALC2               0.750    0.000      0.000
    ALC3               1.750    0.000      0.000
 LEVELP   BY
    PEER1              1.000    0.000      0.000
    PEER2              1.000    0.000      0.000
    PEER3              1.000    0.000      0.000
 TRENDP   BY
    PEER1              0.000    0.000      0.000
    PEER2              0.750    0.000      0.000
    PEER3              1.750    0.000      0.000
 LEVEL    ON
    LEVELP             0.799    0.102      7.810
    TRENDP             0.080    0.182      0.441
 TREND    ON
    LEVELP            -0.143    0.076     -1.888
    TRENDP             0.577    0.192      3.002
 TREND    WITH
    LEVEL             -0.006    0.005     -1.252
 TRENDP   WITH
    LEVELP             0.001    0.007      0.167
 ALC1     WITH
    PEER1              0.011    0.006      1.785
 ALC2     WITH
    PEER2              0.034    0.005      7.310
 ALC3     WITH
    PEER3              0.037    0.010      3.678
 Means
    LEVELP             0.188    0.012     15.795
    TRENDP             0.096    0.010      9.956
 Intercepts
    ALC1               0.000    0.000      0.000
    ALC2               0.000    0.000      0.000
    ALC3               0.000    0.000      0.000
    PEER1              0.000    0.000      0.000
    PEER2              0.000    0.000      0.000
    PEER3              0.000    0.000      0.000
    LEVEL              0.067    0.016      4.272
    TREND              0.008    0.015      0.572
 Variances
    LEVELP             0.070    0.010      6.735
    TRENDP             0.028    0.009      3.224
 Residual Variances
    ALC1               0.048    0.006      7.560
    ALC2               0.076    0.004     17.235
    ALC3               0.076    0.010      7.831
    PEER1              0.106    0.011      9.850
    PEER2              0.171    0.009     19.656
    PEER3              0.129    0.018      7.355
    LEVEL              0.042    0.007      5.671
    TREND              0.009    0.005      1.702

Baseline model for comparing with model D

TITLE:
      alcohol2.inp
      Linear growth model
DATA:
      File is d:\alda\atsdata\ascii\alcohol2.txt;
      
VARIABLE:
      Names are ID FEMALE ALC1 ALC2 ALC3 PEER1 PEER2 PEER3;
      Missing are all(999);
      Usevariables are alc1 alc2 alc3 peer1 peer2 peer3;
ANALYSIS:
      Type = meanstructure;
MODEL:
      level by alc1 - alc3@1;
      trend by alc1@0 alc2@.75 alc3@1.75;
      levelp by peer1 - peer3@1;
      trendp by peer1@0 peer2@.75 peer3@1.75;
      level on levelp@0 trendp@0;
      trend on levelp@0 trendp@0;
      
      [alc1-alc3@0];
      [peer1-peer3@0];
      alc1 with peer1;
      alc2 with peer2;
      alc3 with peer3;
      [level  trend];
      [levelp trendp];
TESTS OF MODEL FIT
Chi-Square Test of Model Fit
          Value                            342.648
          Degrees of Freedom                     8
          P-Value                           0.0000

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