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Table 6.2 on page 203 using wages_pp.dat.
Model A: EXPER, HGC-9, BLACK*EXPER, UE-7.
Title:
Model A;
Data:
File is d:\alda\wages_pp.dat ;
Variable:
Names are
id lnw exper ged postexp black hispanic hgc hgc_9 uerate ue_7 ue_centert1
ue_mean ue_person_centered ue1;
usev = id lnw exper black hgc_9 ue_7;
Missing are all (-9999) ;
within = exper hgc_9 ue_7;
between = black;
cluster = id;
Analysis:
Type = twolevel random ;
estimator = MLF;
Model:
%within%
s1 | lnw on exper;
lnw on hgc_9;
lnw on ue_7;
%between%
s1 with lnw;
s1 on black;
Notice that the deviance is -2*Loglikelihood. That is
-2*(-2415.260) = 4830.52.
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2415.260
Information Criteria
Number of Free Parameters 9
Akaike (AIC) 4848.519
Bayesian (BIC) 4909.398
Sample-Size Adjusted BIC 4880.799
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
LNW ON
HGC_9 0.040 0.006 6.318
UE_7 -0.012 0.002 -7.299
Residual Variances
LNW 0.095 0.001 100.260
Between Level
S1 ON
BLACK -0.018 0.005 -3.871
S1 WITH
LNW -0.003 0.001 -3.825
Means
LNW 1.749 0.013 138.977
Intercepts
S1 0.044 0.003 15.884
Variances
LNW 0.051 0.004 13.279
Residual Variances
S1 0.002 0.000 7.821
Model B: Model A + GED as fixed and random effect
The calculation of deviance is the same as shown in the previous example: -2*(-2402.759)
= 4805.518.
Title:
Model B;
Data:
File is d:\alda\wages_pp.dat ;
Variable:
Names are
id lnw exper ged postexp black hispanic hgc hgc_9 uerate ue_7 ue_centert1
ue_mean ue_person_centered ue1;
usev = id lnw exper ged black hgc_9 ue_7;
Missing are all (-9999) ;
within = exper ged hgc_9 ue_7;
between = black;
cluster = id;
Analysis:
Type = twolevel random ;
estimator = MLF;
Model:
%within%
s1 | lnw on exper;
s2 | lnw on ged;
lnw on hgc_9;
lnw on ue_7;
%between%
s1 on black;
s1 with lnw;
s1 with s2;
s2 with lnw;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2402.759
Information Criteria
Number of Free Parameters 13
Akaike (AIC) 4831.518
Bayesian (BIC) 4919.454
Sample-Size Adjusted BIC 4878.144
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
LNW ON
HGC_9 0.038 0.006 6.032
UE_7 -0.012 0.002 -7.053
Residual Variances
LNW 0.094 0.001 100.223
Between Level
S1 ON
BLACK -0.018 0.005 -3.845
S1 WITH
S2 -0.002 0.001 -1.832
LNW -0.003 0.001 -3.377
S2 WITH
LNW 0.002 0.009 0.265
Means
LNW 1.734 0.013 135.239
S2 0.061 0.021 2.867
Intercepts
S1 0.043 0.003 15.513
Variances
LNW 0.044 0.004 10.421
S2 0.028 0.017 1.636
Residual Variances
S1 0.002 0.000 7.770
Model C: Model B without random effect of GED
Title:
Model C;
Data:
File is d:\alda\wages_pp.dat ;
Variable:
Names are
id lnw exper ged postexp black hispanic hgc hgc_9 uerate ue_7 ue_centert1
ue_mean ue_person_centered ue1;
usev = id lnw exper ged black hgc_9 ue_7;
Missing are all (-9999) ;
within = exper ged hgc_9 ue_7;
between = black;
cluster = id;
Analysis:
Type = twolevel random ;
estimator = MLF;
Model:
%within%
s1 | lnw on exper;
lnw on ged;
lnw on hgc_9;
lnw on ue_7;
%between%
s1 on black;
s1 with lnw;
The deviance is -2*(-2409.162) = 4818.324.
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2409.162
Information Criteria
Number of Free Parameters 10
Akaike (AIC) 4838.324
Bayesian (BIC) 4905.968
Sample-Size Adjusted BIC 4874.190
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
LNW ON
GED 0.059 0.016 3.700
HGC_9 0.039 0.006 6.133
UE_7 -0.012 0.002 -7.044
Residual Variances
LNW 0.095 0.001 100.185
Between Level
S1 ON
BLACK -0.019 0.005 -3.933
S1 WITH
LNW -0.003 0.001 -3.958
Means
LNW 1.734 0.013 129.538
Intercepts
S1 0.043 0.003 15.715
Variances
LNW 0.051 0.004 13.084
Residual Variances
S1 0.002 0.000 7.830
Model D: A + POSTEXP as fixed and random effect
Title:
Model D;
Data:
File is d:\alda\wages_pp.dat ;
Variable:
Names are
id lnw exper ged postexp black hispanic hgc hgc_9 uerate ue_7 ue_centert1
ue_mean ue_person_centered ue1;
usev = id lnw exper postexp black hgc_9 ue_7;
Missing are all (-9999) ;
within = exper postexp hgc_9 ue_7;
between = black;
cluster = id;
Analysis:
Type = twolevel random ;
estimator = MLF;
Model:
%within%
s1 | lnw on exper;
s2 | lnw on postexp;
lnw on hgc_9;
lnw on ue_7;
%between%
s1 on black;
s1 with lnw;
s1 with s2;
s2 with lnw;
The deviance is -2*(-2408.689) = 4817.378.
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2408.689
Information Criteria
Number of Free Parameters 13
Akaike (AIC) 4843.377
Bayesian (BIC) 4931.314
Sample-Size Adjusted BIC 4890.004
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
LNW ON
HGC_9 0.040 0.007 6.129
UE_7 -0.012 0.002 -7.170
Residual Variances
LNW 0.095 0.001 100.126
Between Level
S1 ON
BLACK -0.019 0.005 -4.116
S1 WITH
LNW -0.002 0.001 -3.193
S2 0.000 0.001 -0.066
S2 WITH
LNW -0.002 0.002 -1.308
Means
LNW 1.749 0.013 138.889
S2 0.015 0.005 3.025
Intercepts
S1 0.041 0.003 13.912
Variances
LNW 0.051 0.004 13.219
S2 0.001 0.001 0.590
Residual Variances
S1 0.001 0.000 6.622
Model E: Model D without random effect of POSTEXP
Title:
Model E;
Data:
File is d:\alda\wages_pp.dat ;
Variable:
Names are
id lnw exper ged postexp black hispanic hgc hgc_9 uerate ue_7 ue_centert1
ue_mean ue_person_centered ue1;
usev = id lnw exper postexp black hgc_9 ue_7;
Missing are all (-9999) ;
within = exper postexp hgc_9 ue_7;
between = black;
cluster = id;
Analysis:
Type = twolevel random ;
estimator = MLF;
Model:
%within%
s1 | lnw on exper;
lnw on postexp;
lnw on hgc_9;
lnw on ue_7;
%between%
s1 on black;
s1 with lnw;
The deviance is -2*(-2410.353) = 4820.706.
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2410.353
Information Criteria
Number of Free Parameters 10
Akaike (AIC) 4840.707
Bayesian (BIC) 4908.350
Sample-Size Adjusted BIC 4876.573
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
LNW ON
POSTEXP 0.014 0.004 3.188
HGC_9 0.040 0.006 6.228
UE_7 -0.012 0.002 -7.243
Residual Variances
LNW 0.095 0.001 100.231
Between Level
S1 ON
BLACK -0.019 0.005 -4.076
S1 WITH
LNW -0.003 0.001 -4.009
Means
LNW 1.750 0.013 138.737
Intercepts
S1 0.041 0.003 13.515
Variances
LNW 0.051 0.004 13.269
Residual Variances
S1 0.002 0.000 7.844
Model F: Model A with fixed and random effects of GED and POSTEXP
Title:
Model F;
Data:
File is d:\alda\wages_pp.dat ;
Variable:
Names are
id lnw exper ged postexp black hispanic hgc hgc_9 uerate ue_7 ue_centert1
ue_mean ue_person_centered ue1;
usev = id lnw exper ged postexp black hgc_9 ue_7;
Missing are all (-9999) ;
within = exper ged postexp hgc_9 ue_7;
between = black;
cluster = id;
Analysis:
Type = twolevel random ;
estimator = MLF;
Model:
%within%
s1 | lnw on exper;
s2 | lnw on ged;
s3 | lnw on postexp;
lnw on hgc_9;
lnw on ue_7;
%between%
s1 on black;
s1 with lnw;
s1 with s2;
s1 with s3;
s2 with lnw;
s2 with s3;
s3 with lnw;
The deviance is -2*(-2394.677) =4789.354.
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2394.677
Information Criteria
Number of Free Parameters 18
Akaike (AIC) 4825.354
Bayesian (BIC) 4947.113
Sample-Size Adjusted BIC 4889.913
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
LNW ON
HGC_9 0.039 0.006 6.142
UE_7 -0.012 0.002 -7.029
Residual Variances
LNW 0.094 0.001 99.722
Between Level
S1 ON
BLACK -0.020 0.005 -4.132
S1 WITH
LNW -0.002 0.001 -2.354
S2 0.003 0.003 0.899
S3 -0.001 0.001 -0.895
S2 WITH
LNW 0.012 0.010 1.255
S3 -0.004 0.004 -0.908
S3 WITH
LNW -0.006 0.003 -2.066
Means
LNW 1.739 0.013 134.314
S2 0.041 0.027 1.531
S3 0.009 0.006 1.584
Intercepts
S1 0.041 0.003 14.058
Variances
LNW 0.041 0.004 10.347
S2 0.016 0.018 0.880
S3 0.003 0.002 1.635
Residual Variances
S1 0.001 0.000 6.515
Model G: Model F without random effect of POSTEXP
Title:
Model G;
Data:
File is d:\alda\wages_pp.dat ;
Variable:
Names are
id lnw exper ged postexp black hispanic hgc hgc_9 uerate ue_7 ue_centert1
ue_mean ue_person_centered ue1;
usev = id lnw exper ged postexp black hgc_9 ue_7;
Missing are all (-9999) ;
within = exper ged postexp hgc_9 ue_7;
between = black;
cluster = id;
Analysis:
Type = twolevel random ;
estimator = MLF;
Model:
%within%
s1 | lnw on exper;
s2 | lnw on ged;
lnw on postexp;
lnw on hgc_9;
lnw on ue_7;
%between%
s1 on black;
s1 with lnw;
s1 with s2;
s2 with lnw;
The deviance is -2*(-2401.344) =4802.688.
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2401.344
Information Criteria
Number of Free Parameters 14
Akaike (AIC) 4830.688
Bayesian (BIC) 4925.390
Sample-Size Adjusted BIC 4880.901
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
LNW ON
POSTEXP 0.009 0.005 1.703
HGC_9 0.038 0.006 6.029
UE_7 -0.012 0.002 -7.068
Residual Variances
LNW 0.094 0.001 100.184
Between Level
S1 ON
BLACK -0.019 0.005 -3.945
S1 WITH
LNW -0.003 0.001 -3.325
S2 -0.002 0.001 -1.926
S2 WITH
LNW 0.003 0.009 0.290
Means
LNW 1.739 0.013 131.905
S2 0.043 0.024 1.758
Intercepts
S1 0.041 0.003 13.347
Variances
LNW 0.043 0.004 10.345
S2 0.028 0.017 1.642
Residual Variances
S1 0.002 0.000 7.798
Model H: Model F without random effect of GED
Title:
Model H;
Data:
File is d:\alda\wages_pp.dat ;
Variable:
Names are
id lnw exper ged postexp black hispanic hgc hgc_9 uerate ue_7 ue_centert1
ue_mean ue_person_centered ue1;
usev = id lnw exper ged postexp black hgc_9 ue_7;
Missing are all (-9999) ;
within = exper ged postexp hgc_9 ue_7;
between = black;
cluster = id;
Analysis:
Type = twolevel random ;
estimator = MLF;
Model:
%within%
s1 | lnw on exper;
s2 | lnw on postexp;
lnw on ged;
lnw on hgc_9;
lnw on ue_7;
%between%
s1 on black;
s1 with lnw;
s1 with s2;
s2 with lnw;
The deviance is -2*(-2406.320) =4812.64.
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2406.320
Information Criteria
Number of Free Parameters 14
Akaike (AIC) 4840.639
Bayesian (BIC) 4935.340
Sample-Size Adjusted BIC 4890.852
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
LNW ON
GED 0.042 0.018 2.377
HGC_9 0.039 0.007 6.036
UE_7 -0.012 0.002 -7.020
Residual Variances
LNW 0.095 0.001 100.089
Between Level
S1 ON
BLACK -0.019 0.005 -4.074
S1 WITH
LNW -0.002 0.001 -3.201
S2 0.000 0.001 0.006
S2 WITH
LNW -0.002 0.002 -1.247
Means
LNW 1.739 0.014 126.940
S2 0.009 0.005 1.602
Intercepts
S1 0.041 0.003 14.058
Variances
LNW 0.050 0.004 13.043
S2 0.001 0.002 0.489
Residual Variances
S1 0.001 0.000 6.627
Model I: Model A with GED and GED*EXPER as fixed and random effects
With Mplus version 2.13, we are unable to make the calculation converge for the model.
Model J: Model I without random effect of GED*EXPER
Title:
Model J;
Data:
File is d:\alda\wages_pp.dat ;
Variable:
Names are
id lnw exper ged postexp black hispanic hgc hgc_9 uerate ue_7 ue_centert1
ue_mean ue_person_centered ue1;
usev = id lnw exper ged black hgc_9 ue_7 gedxexp;
Missing are all (-9999) ;
within = exper ged hgc_9 ue_7 gedxexp;
between = black;
cluster = id;
Define: gedxexp = ged*exper;
Analysis:
Type = twolevel random ;
estimator = MLF;
Model:
%within%
s1 | lnw on exper;
s2 | lnw on ged;
lnw on gedxexp;
lnw on hgc_9;
lnw on ue_7;
%between%
s1 on black;
s1 with lnw;
s1 with s2;
s2 with lnw;
The deviance is -2*(-2402.301) =4804.602.
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2402.301
Information Criteria
Number of Free Parameters 14
Akaike (AIC) 4832.602
Bayesian (BIC) 4927.303
Sample-Size Adjusted BIC 4882.814
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
LNW ON
GEDXEXP 0.005 0.005 0.935
HGC_9 0.038 0.006 6.022
UE_7 -0.012 0.002 -7.070
Residual Variances
LNW 0.094 0.001 100.163
Between Level
S1 ON
BLACK -0.018 0.005 -3.870
S1 WITH
LNW -0.003 0.001 -3.357
S2 -0.002 0.001 -1.768
S2 WITH
LNW 0.002 0.009 0.187
Means
LNW 1.738 0.013 128.932
S2 0.046 0.028 1.634
Intercepts
S1 0.042 0.003 13.057
Variances
LNW 0.044 0.004 10.361
S2 0.030 0.018 1.670
Residual Variances
S1 0.002 0.000 7.760
Table 6.3 on page 205, detailed output of model F.
Title:
Model F;
Data:
File is d:\alda\wages_pp.dat ;
Variable:
Names are
id lnw exper ged postexp black hispanic hgc hgc_9 uerate ue_7 ue_centert1
ue_mean ue_person_centered ue1;
usev = id lnw exper ged postexp black hgc_9 ue_7;
Missing are all (-9999) ;
within = exper ged postexp hgc_9 ue_7;
between = black;
cluster = id;
Analysis:
Type = twolevel random ;
estimator = MLF;
Model:
%within%
s1 | lnw on exper;
s2 | lnw on ged;
s3 | lnw on postexp;
lnw on hgc_9;
lnw on ue_7;
%between%
s1 on black;
s1 with lnw;
s1 with s2;
s1 with s3;
s2 with lnw;
s2 with s3;
s3 with lnw;
The deviance is -2*(-2394.677) =4789.354.
TESTS OF MODEL FIT
Loglikelihood
H0 Value -2394.677
Information Criteria
Number of Free Parameters 18
Akaike (AIC) 4825.354
Bayesian (BIC) 4947.113
Sample-Size Adjusted BIC 4889.913
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
LNW ON
HGC_9 0.039 0.006 6.142
UE_7 -0.012 0.002 -7.029
Residual Variances
LNW 0.094 0.001 99.722
Between Level
S1 ON
BLACK -0.020 0.005 -4.132
S1 WITH
LNW -0.002 0.001 -2.354
S2 0.003 0.003 0.899
S3 -0.001 0.001 -0.895
S2 WITH
LNW 0.012 0.010 1.255
S3 -0.004 0.004 -0.908
S3 WITH
LNW -0.006 0.003 -2.066
Means
LNW 1.739 0.013 134.314
S2 0.041 0.027 1.531
S3 0.009 0.006 1.584
Intercepts
S1 0.041 0.003 14.058
Variances
LNW 0.041 0.004 10.347
S2 0.016 0.018 0.880
S3 0.003 0.002 1.635
Residual Variances
S1 0.001 0.000 6.515
Table 6.5, page 221
Model A: no change
Title:
table 6_5 Model A;
Data:
File is d:\alda\external_pp.dat ;
Variable:
Names are
id external female time grade;
usev external ;
!female time;
Missing are all (-9999) ;
! within = female time;
cluster = id;
Analysis:
Type = twolevel random;
estimator = MLF;
model:
%between%
external;
Loglikelihood
H0 Value -1005.127
H1 Value -1005.127
Information Criteria
Number of Free Parameters 3
Akaike (AIC) 2016.253
Bayesian (BIC) 2027.048
Sample-Size Adjusted BIC 2017.536
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
Variances
EXTERNAL 70.237 6.944 10.115
Between Level
Means
EXTERNAL 12.960 3.052 4.246
Variances
EXTERNAL 87.282 26.660 3.274
Table 6.5, page 221 using external_pp.dat.
Model B: linear change
Title:
table 6_5 Model B;
Data:
File is d:\alda\external_pp.dat ;
Variable:
Names are
id external female time grade;
usev external time;
Missing are all (-9999) ;
within = time;
cluster = id;
Analysis:
Type = twolevel random;
estimator = MLF;
model:
%within%
s1 | external on time;
%between%
s1 with external;
Loglikelihood
H0 Value -995.873
Information Criteria
Number of Free Parameters 6
Akaike (AIC) 2003.746
Bayesian (BIC) 2025.336
Sample-Size Adjusted BIC 2006.312
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
Residual Variances
EXTERNAL 53.787 6.022 8.932
Between Level
S1 WITH
EXTERNAL -12.405 7.227 -1.717
Means
EXTERNAL 13.290 3.866 3.437
S1 -0.131 0.577 -0.227
Variances
EXTERNAL 123.174 35.791 3.441
S1 4.640 1.994 2.326
Table 6.5, page 221
Model C: quadratic change
Title:
table 6_5 Model C;
Data:
File is d:\alda\external_pp.dat ;
Variable:
Names are
id external female time grade;
usev external time time2;
Missing are all (-9999) ;
within = time time2;
cluster = id;
Define: time2 = time*time;
Analysis:
Type = twolevel random;
estimator = MLF;
model:
%within%
s1 | external on time;
s2 | external on time2;
%between%
s1 with external;
s2 with external;
s1 with s2;
TESTS OF MODEL FIT
Loglikelihood
H0 Value -987.919
Information Criteria
Number of Free Parameters 10
Akaike (AIC) 1995.838
Bayesian (BIC) 2031.823
Sample-Size Adjusted BIC 2000.116
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
Within Level
Residual Variances
EXTERNAL 42.052 6.021 6.985
Between Level
S1 WITH
EXTERNAL -3.340 15.753 -0.212
S2 -4.876 3.143 -1.551
S2 WITH
EXTERNAL -1.438 2.862 -0.502
Means
EXTERNAL 13.962 3.809 3.666
S1 -1.142 1.499 -0.762
S2 0.202 0.348 0.581
Variances
EXTERNAL 106.756 39.788 2.683
S1 24.209 16.894 1.433
S2 1.197 0.627 1.910
Table 6.5, page 221
Model D: cubic change
Title:
table 6_5 Model D;
Data:
File is d:\alda\external_pp.dat ;
Variable:
Names are
id external female time grade;
usev external time time2 time3;
Missing are all (-9999) ;
within = time time2 time3;
cluster = id;
Define:
time2 = time*time;
time3 = time2*time;
Analysis:
Type = twolevel random;
estimator = MLF;
iteration = 5000;
miterations = 5000;
convergence = .001;
model:
%within%
s1 | external on time;
s2 | external on time2;
s3 | external on time3;
%between%
s1 with external;
s2 with external;
s3 with external;
s1 with s2;
s1 with s3;
s2 with s3;
THE ESTIMATED BETWEEN COVARIANCE MATRIX IS NOT POSITIVE DEFINITE AS IT SHOULD BE. COMPUTATION COULD NOT BE COMPLETED. PROBLEM INVOLVING VARIABLE S3.
THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES.
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