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Table 6.2, page 203
Table 6.2. uses wages.SSM. Alternative
discontinuous change trajectories: HS dropout data
Model A: EXPER, HGC-9, BLACK*EXPER, UE-7
Sigma_squared = 0.09479
Standard Error of Sigma_squared = 0.00191
Tau
INTRCPT1,B0 0.05065 -0.00292
EXPER,B1 -0.00292 0.00163
Standard Errors of Tau
INTRCPT1,B0 0.00467 0.00081
EXPER,B1 0.00081 0.00019
Tau (as correlations)
INTRCPT1,B0 1.000 -0.321
EXPER,B1 -0.321 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.462
EXPER, B1 0.344
----------------------------------------------------
Note: The reliability estimates reported above are based on only 850 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 17 = -2.415260E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.748988 0.011400 153.421 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.044054 0.002604 16.918 886 0.000
BLACK, G11 -0.018183 0.004485 -4.055 886 0.000
For HGC_9 slope, B2
INTRCPT2, G20 0.040010 0.006363 6.288 6397 0.000
For UE_7 slope, B3
INTRCPT2, G30 -0.011950 0.001792 -6.670 6397 0.000
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.748988 0.011429 153.033 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.044054 0.002532 17.396 886 0.000
BLACK, G11 -0.018183 0.004307 -4.222 886 0.000
For HGC_9 slope, B2
INTRCPT2, G20 0.040010 0.006435 6.218 6397 0.000
For UE_7 slope, B3
INTRCPT2, G30 -0.011950 0.002002 -5.969 6397 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.22505 0.05065 849 1740.10875 0.000
EXPER slope, U1 0.04041 0.00163 848 1630.45143 0.000
level-1, R 0.30788 0.09479
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 850 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4830.519124 Number of estimated parameters = 9
Model B: A + GED as fixed and random effect
Sigma_squared = 0.09416
Standard Error of Sigma_squared = 0.00191
Tau
INTRCPT1,B0 0.04361 -0.00262 0.00231
EXPER,B1 -0.00262 0.00166 -0.00218
GED,B2 0.00231 -0.00218 0.02830
Standard Errors of Tau
INTRCPT1,B0 0.00473 0.00082 0.00706
EXPER,B1 0.00082 0.00020 0.00130
GED,B2 0.00706 0.00130 0.01446
Tau (as correlations)
INTRCPT1,B0 1.000 -0.308 0.066
EXPER,B1 -0.308 1.000 -0.318
GED,B2 0.066 -0.318 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.378
EXPER, B1 0.233
GED, B2 0.147
----------------------------------------------------
Note: The reliability estimates reported above are based on only 104 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 22 = -2.402759E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.734212 0.011800 146.971 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.043224 0.002621 16.490 886 0.000
BLACK, G11 -0.018200 0.004471 -4.071 886 0.000
For GED slope, B2
INTRCPT2, G20 0.061321 0.018449 3.324 887 0.001
For HGC_9 slope, B3
INTRCPT2, G30 0.038334 0.006265 6.119 6396 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011609 0.001788 -6.494 6396 0.000
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.734212 0.011662 148.704 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.043224 0.002562 16.872 886 0.000
BLACK, G11 -0.018200 0.004264 -4.268 886 0.000
For GED slope, B2
INTRCPT2, G20 0.061321 0.018327 3.346 887 0.001
For HGC_9 slope, B3
INTRCPT2, G30 0.038334 0.006357 6.030 6396 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011609 0.002017 -5.757 6396 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.20882 0.04361 103 146.13199 0.004
EXPER slope, U1 0.04075 0.00166 102 177.35923 0.000
GED slope, U2 0.16823 0.02830 103 109.96355 0.301
level-1, R 0.30686 0.09416
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 104 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4805.517557 Number of estimated parameters = 13
Model C: Model B without random effect of GED
Sigma_squared = 0.09473
Standard Error of Sigma_squared = 0.00191
Tau
INTRCPT1,B0 0.05059 -0.00304
EXPER,B1 -0.00304 0.00164
Standard Errors of Tau
INTRCPT1,B0 0.00467 0.00081
EXPER,B1 0.00081 0.00019
Tau (as correlations)
INTRCPT1,B0 1.000 -0.334
EXPER,B1 -0.334 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.462
EXPER, B1 0.344
----------------------------------------------------
Note: The reliability estimates reported above are based on only 850 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 17 = -2.409162E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.734305 0.012135 142.923 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.043327 0.002609 16.607 886 0.000
BLACK, G11 -0.018523 0.004461 -4.152 886 0.000
For GED slope, B2
INTRCPT2, G20 0.059123 0.016868 3.505 6396 0.001
For HGC_9 slope, B3
INTRCPT2, G30 0.039042 0.006334 6.164 6396 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011593 0.001793 -6.467 6396 0.000
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.734305 0.011714 148.052 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.043327 0.002559 16.930 886 0.000
BLACK, G11 -0.018523 0.004258 -4.350 886 0.000
For GED slope, B2
INTRCPT2, G20 0.059123 0.018261 3.238 6396 0.002
For HGC_9 slope, B3
INTRCPT2, G30 0.039042 0.006387 6.113 6396 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011593 0.002003 -5.787 6396 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.22491 0.05059 849 1737.20223 0.000
EXPER slope, U1 0.04045 0.00164 848 1632.64720 0.000
level-1, R 0.30779 0.09473
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 850 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4818.324301 Number of estimated parameters = 10
Model D: A + POSTEXP as fixed and random effect
Sigma_squared = 0.09464
Standard Error of Sigma_squared = 0.00191
Tau
INTRCPT1,B0 0.05057 -0.00246 -0.00201
EXPER,B1 -0.00246 0.00145 -0.00003
POSTEXP,B2 -0.00201 -0.00003 0.00084
Standard Errors of Tau
INTRCPT1,B0 0.00468 0.00087 0.00142
EXPER,B1 0.00087 0.00021 0.00086
POSTEXP,B2 0.00142 0.00086 0.00171
Tau (as correlations)
INTRCPT1,B0 1.000 -0.287 -0.310
EXPER,B1 -0.287 1.000 -0.024
POSTEXP,B2 -0.310 -0.024 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.254
EXPER, B1 0.073
POSTEXP, B2 0.013
----------------------------------------------------
Note: The reliability estimates reported above are based on only 96 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 24 = -2.408689E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.749372 0.011399 153.461 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.040653 0.002777 14.637 886 0.000
BLACK, G11 -0.019495 0.004475 -4.357 886 0.000
For POSTEXP slope, B2
INTRCPT2, G20 0.014591 0.004565 3.196 887 0.002
For HGC_9 slope, B3
INTRCPT2, G30 0.039868 0.006354 6.275 6396 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011839 0.001791 -6.612 6396 0.000
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.749372 0.011467 152.563 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.040653 0.002750 14.784 886 0.000
BLACK, G11 -0.019495 0.004265 -4.571 886 0.000
For POSTEXP slope, B2
INTRCPT2, G20 0.014591 0.004539 3.215 887 0.002
For HGC_9 slope, B3
INTRCPT2, G30 0.039868 0.006400 6.229 6396 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011839 0.001998 -5.927 6396 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.22488 0.05057 95 97.32352 0.415
EXPER slope, U1 0.03805 0.00145 94 128.15709 0.011
POSTEXP slope, U2 0.02891 0.00084 95 124.13282 0.024
level-1, R 0.30764 0.09464
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 96 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4817.378460 Number of estimated parameters = 13
Model E: Model D without random effect of POSTEXP
Sigma_squared = 0.09483
Standard Error of Sigma_squared = 0.00191
Tau
INTRCPT1,B0 0.05086 -0.00305
EXPER,B1 -0.00305 0.00161
Standard Errors of Tau
INTRCPT1,B0 0.00468 0.00081
EXPER,B1 0.00081 0.00019
Tau (as correlations)
INTRCPT1,B0 1.000 -0.336
EXPER,B1 -0.336 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.463
EXPER, B1 0.342
----------------------------------------------------
Note: The reliability estimates reported above are based on only 850 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 17 = -2.410353E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.749888 0.011412 153.341 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.040505 0.002829 14.316 886 0.000
BLACK, G11 -0.019178 0.004454 -4.306 886 0.000
For POSTEXP slope, B2
INTRCPT2, G20 0.013962 0.004424 3.156 6396 0.002
For HGC_9 slope, B3
INTRCPT2, G30 0.039534 0.006334 6.242 6396 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011847 0.001791 -6.616 6396 0.000
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.749888 0.011442 152.931 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.040505 0.002756 14.698 886 0.000
BLACK, G11 -0.019178 0.004247 -4.515 886 0.000
For POSTEXP slope, B2
INTRCPT2, G20 0.013962 0.004521 3.089 6396 0.002
For HGC_9 slope, B3
INTRCPT2, G30 0.039534 0.006396 6.181 6396 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011847 0.002005 -5.908 6396 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.22553 0.05086 849 1742.87922 0.000
EXPER slope, U1 0.04017 0.00161 848 1626.78723 0.000
level-1, R 0.30795 0.09483
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 850 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4820.706583 Number of estimated parameters = 10
Model F: Model A with fixed and random effects of GED and POSTEXP
Sigma_squared = 0.09386
Standard Error of Sigma_squared = 0.00190
Tau
INTRCPT1,B0 0.04135 -0.00170 0.01134 -0.00595
EXPER,B1 -0.00170 0.00136 0.00295 -0.00092
GED,B2 0.01134 0.00295 0.01735 -0.00399
POSTEXP,B3 -0.00595 -0.00092 -0.00399 0.00336
Standard Errors of Tau
INTRCPT1,B0 0.00471 0.00084 0.00804 0.00265
EXPER,B1 0.00084 0.00021 0.00358 0.00114
GED,B2 0.00804 0.00358 0.01543 0.00445
POSTEXP,B3 0.00265 0.00114 0.00445 0.00229
Tau (as correlations)
INTRCPT1,B0 1.000 -0.227 0.423 -0.504
EXPER,B1 -0.227 1.000 0.607 -0.431
GED,B2 0.423 0.607 1.000 -0.522
POSTEXP,B3 -0.504 -0.431 -0.522 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.227
EXPER, B1 0.054
GED, B2 0.063
POSTEXP, B3 0.049
----------------------------------------------------
Note: The reliability estimates reported above are based on only 61 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 19 = -2.394679E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.738550 0.011949 145.498 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041475 0.002798 14.824 886 0.000
BLACK, G11 -0.019620 0.004470 -4.389 886 0.000
For GED slope, B2
INTRCPT2, G20 0.040940 0.022022 1.859 887 0.063
For POSTEXP slope, B3
INTRCPT2, G30 0.009412 0.005546 1.697 887 0.089
For HGC_9 slope, B4
INTRCPT2, G40 0.039032 0.006243 6.252 6395 0.000
For UE_7 slope, B5
INTRCPT2, G50 -0.011723 0.001783 -6.575 6395 0.000
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.738550 0.011902 146.069 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041475 0.002755 15.056 886 0.000
BLACK, G11 -0.019620 0.004255 -4.611 886 0.000
For GED slope, B2
INTRCPT2, G20 0.040940 0.021962 1.864 887 0.062
For POSTEXP slope, B3
INTRCPT2, G30 0.009412 0.005547 1.697 887 0.089
For HGC_9 slope, B4
INTRCPT2, G40 0.039032 0.006339 6.158 6395 0.000
For UE_7 slope, B5
INTRCPT2, G50 -0.011723 0.002001 -5.859 6395 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.20336 0.04135 60 79.33686 0.048
EXPER slope, U1 0.03690 0.00136 59 70.25123 0.150
GED slope, U2 0.13172 0.01735 60 45.99434 >.500
POSTEXP slope, U3 0.05801 0.00336 60 66.49441 0.263
level-1, R 0.30637 0.09386
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 61 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4789.358670 Number of estimated parameters = 18
Model G: Model F without random effect of POSTEXP
Sigma_squared = 0.09417
Standard Error of Sigma_squared = 0.00191
Tau
INTRCPT1,B0 0.04349 -0.00258 0.00250
EXPER,B1 -0.00258 0.00165 -0.00235
GED,B2 0.00250 -0.00235 0.02856
Standard Errors of Tau
INTRCPT1,B0 0.00472 0.00082 0.00702
EXPER,B1 0.00082 0.00020 0.00130
GED,B2 0.00702 0.00130 0.01441
Tau (as correlations)
INTRCPT1,B0 1.000 -0.304 0.071
EXPER,B1 -0.304 1.000 -0.342
GED,B2 0.071 -0.342 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.377
EXPER, B1 0.232
GED, B2 0.148
----------------------------------------------------
Note: The reliability estimates reported above are based on only 104 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 22 = -2.401344E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.738929 0.012113 143.560 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041169 0.002884 14.274 886 0.000
BLACK, G11 -0.018706 0.004470 -4.185 886 0.000
For GED slope, B2
INTRCPT2, G20 0.043071 0.021362 2.016 887 0.043
For POSTEXP slope, B3
INTRCPT2, G30 0.008663 0.005120 1.692 6395 0.090
For HGC_9 slope, B4
INTRCPT2, G40 0.038309 0.006263 6.116 6395 0.000
For UE_7 slope, B5
INTRCPT2, G50 -0.011635 0.001787 -6.509 6395 0.000
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.738929 0.011873 146.455 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041169 0.002773 14.849 886 0.000
BLACK, G11 -0.018706 0.004256 -4.395 886 0.000
For GED slope, B2
INTRCPT2, G20 0.043071 0.022058 1.953 887 0.050
For POSTEXP slope, B3
INTRCPT2, G30 0.008663 0.005464 1.585 6395 0.113
For HGC_9 slope, B4
INTRCPT2, G40 0.038309 0.006352 6.031 6395 0.000
For UE_7 slope, B5
INTRCPT2, G50 -0.011635 0.002019 -5.762 6395 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.20855 0.04349 103 146.91169 0.003
EXPER slope, U1 0.04063 0.00165 102 181.91198 0.000
GED slope, U2 0.16900 0.02856 103 110.20574 0.295
level-1, R 0.30688 0.09417
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 104 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4802.688491 Number of estimated parameters = 14
Model H: Model F without random effect of GED
Sigma_squared = 0.09458
Standard Error of Sigma_squared = 0.00191
Tau
INTRCPT1,B0 0.05038 -0.00247 -0.00192
EXPER,B1 -0.00247 0.00145 0.00002
POSTEXP,B3 -0.00192 0.00002 0.00073
Standard Errors of Tau
INTRCPT1,B0 0.00467 0.00087 0.00142
EXPER,B1 0.00087 0.00021 0.00086
POSTEXP,B3 0.00142 0.00086 0.00172
Tau (as correlations)
INTRCPT1,B0 1.000 -0.289 -0.317
EXPER,B1 -0.289 1.000 0.019
POSTEXP,B3 -0.317 0.019 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.253
EXPER, B1 0.073
POSTEXP, B3 0.012
----------------------------------------------------
Note: The reliability estimates reported above are based on only 96 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 23 = -2.406320E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.738568 0.012421 139.968 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041471 0.002804 14.791 886 0.000
BLACK, G11 -0.019353 0.004477 -4.322 886 0.000
For GED slope, B2
INTRCPT2, G20 0.042538 0.019488 2.183 6395 0.029
For POSTEXP slope, B3
INTRCPT2, G30 0.008548 0.005330 1.604 887 0.108
For HGC_9 slope, B4
INTRCPT2, G40 0.039345 0.006351 6.195 6395 0.000
For UE_7 slope, B5
INTRCPT2, G50 -0.011623 0.001792 -6.485 6395 0.000
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.738568 0.011942 145.587 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041471 0.002764 15.001 886 0.000
BLACK, G11 -0.019353 0.004262 -4.540 886 0.000
For GED slope, B2
INTRCPT2, G20 0.042538 0.021941 1.939 6395 0.052
For POSTEXP slope, B3
INTRCPT2, G30 0.008548 0.005518 1.549 887 0.121
For HGC_9 slope, B4
INTRCPT2, G40 0.039345 0.006383 6.164 6395 0.000
For UE_7 slope, B5
INTRCPT2, G50 -0.011623 0.001999 -5.813 6395 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.22445 0.05038 95 98.74449 0.376
EXPER slope, U1 0.03810 0.00145 94 126.58021 0.014
POSTEXP slope, U3 0.02703 0.00073 95 121.89981 0.033
level-1, R 0.30754 0.09458
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 96 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4812.639706 Number of estimated parameters = 14
Model I: Model A with GED and GED*EXPER as fixed and random effects. Notice that it took HLM more than 4,000 iterations to converge.
Sigma_squared = 0.09370
Standard Error of Sigma_squared = 0.00190
Tau
INTRCPT1,B0 0.04128 -0.00182 -0.00476 -0.00072
EXPER,B1 -0.00182 0.00140 0.00472 -0.00052
GED,B2 -0.00476 0.00472 0.06257 -0.01142
GEDXEXP,B5 -0.00072 -0.00052 -0.01142 0.00232
Standard Errors of Tau
INTRCPT1,B0 0.00478 0.00086 0.01707 0.00314
EXPER,B1 0.00086 0.00021 0.01036 0.00146
GED,B2 0.01707 0.01036 0.03410 0.01203
GEDXEXP,B5 0.00314 0.00146 0.01203 0.00288
Tau (as correlations)
INTRCPT1,B0 1.000 -0.239 -0.094 -0.073
EXPER,B1 -0.239 1.000 0.504 -0.289
GED,B2 -0.094 0.504 1.000 -0.948
GEDXEXP,B5 -0.073 -0.289 -0.948 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.224
EXPER, B1 0.053
GED, B2 0.107
GEDXEXP, B5 0.035
----------------------------------------------------
Note: The reliability estimates reported above are based on only 60 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 4228 = -2.396857E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.737949 0.012228 142.123 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041880 0.002877 14.554 886 0.000
BLACK, G11 -0.019002 0.004470 -4.251 886 0.000
For GED slope, B2
INTRCPT2, G20 0.045858 0.026144 1.754 887 0.079
For HGC_9 slope, B3
INTRCPT2, G30 0.038095 0.006253 6.092 6395 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011729 0.001786 -6.567 6395 0.000
For GEDXEXP slope, B5
INTRCPT2, G50 0.005401 0.005452 0.991 887 0.322
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.737949 0.012150 143.043 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041880 0.002815 14.878 886 0.000
BLACK, G11 -0.019002 0.004255 -4.466 886 0.000
For GED slope, B2
INTRCPT2, G20 0.045858 0.026025 1.762 887 0.078
For HGC_9 slope, B3
INTRCPT2, G30 0.038095 0.006344 6.005 6395 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011729 0.002013 -5.826 6395 0.000
For GEDXEXP slope, B5
INTRCPT2, G50 0.005401 0.005429 0.995 887 0.320
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.20317 0.04128 59 79.05320 0.042
EXPER slope, U1 0.03748 0.00140 58 66.52456 0.207
GED slope, U2 0.25014 0.06257 59 68.13995 0.194
GEDXEXP slope, U5 0.04814 0.00232 59 66.62055 0.231
level-1, R 0.30611 0.09370
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 60 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4793.713277 Number of estimated parameters = 18
Model J: Model I without random effect of GED*EXPER
Sigma_squared = 0.09416
Standard Error of Sigma_squared = 0.00191
Tau
INTRCPT1,B0 0.04363 -0.00261 0.00164
EXPER,B1 -0.00261 0.00166 -0.00222
GED,B2 0.00164 -0.00222 0.02962
Standard Errors of Tau
INTRCPT1,B0 0.00473 0.00082 0.00711
EXPER,B1 0.00082 0.00020 0.00130
GED,B2 0.00711 0.00130 0.01458
Tau (as correlations)
INTRCPT1,B0 1.000 -0.307 0.046
EXPER,B1 -0.307 1.000 -0.317
GED,B2 0.046 -0.317 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.378
EXPER, B1 0.232
GED, B2 0.152
----------------------------------------------------
Note: The reliability estimates reported above are based on only 104 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 22 = -2.402301E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.737770 0.012387 140.288 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041881 0.002972 14.093 886 0.000
BLACK, G11 -0.018329 0.004467 -4.103 886 0.000
For GED slope, B2
INTRCPT2, G20 0.045708 0.024698 1.851 887 0.064
For HGC_9 slope, B3
INTRCPT2, G30 0.038275 0.006264 6.110 6395 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011626 0.001788 -6.504 6395 0.000
For GEDXEXP slope, B5
INTRCPT2, G50 0.004874 0.005064 0.962 6395 0.336
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.737770 0.012132 143.237 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041881 0.002827 14.813 886 0.000
BLACK, G11 -0.018329 0.004254 -4.309 886 0.000
For GED slope, B2
INTRCPT2, G20 0.045708 0.025935 1.762 887 0.078
For HGC_9 slope, B3
INTRCPT2, G30 0.038275 0.006351 6.026 6395 0.000
For UE_7 slope, B4
INTRCPT2, G40 -0.011626 0.002019 -5.759 6395 0.000
For GEDXEXP slope, B5
INTRCPT2, G50 0.004874 0.005337 0.913 6395 0.361
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.20887 0.04363 103 146.42608 0.003
EXPER slope, U1 0.04068 0.00166 102 179.59296 0.000
GED slope, U2 0.17209 0.02962 103 110.33494 0.292
level-1, R 0.30685 0.09416
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 104 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4804.601475 Number of estimated parameters = 14
Table 6.3, page 205
Table 6.3
Model F (with discontinuities in elevation and slope)
Sigma_squared = 0.09386
Standard Error of Sigma_squared = 0.00190
Tau
INTRCPT1,B0 0.04135 -0.00170 0.01134 -0.00595
EXPER,B1 -0.00170 0.00136 0.00295 -0.00092
GED,B2 0.01134 0.00295 0.01735 -0.00399
POSTEXP,B3 -0.00595 -0.00092 -0.00399 0.00336
Standard Errors of Tau
INTRCPT1,B0 0.00471 0.00084 0.00804 0.00265
EXPER,B1 0.00084 0.00021 0.00358 0.00114
GED,B2 0.00804 0.00358 0.01543 0.00445
POSTEXP,B3 0.00265 0.00114 0.00445 0.00229
Tau (as correlations)
INTRCPT1,B0 1.000 -0.227 0.423 -0.504
EXPER,B1 -0.227 1.000 0.607 -0.431
GED,B2 0.423 0.607 1.000 -0.522
POSTEXP,B3 -0.504 -0.431 -0.522 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.227
EXPER, B1 0.054
GED, B2 0.063
POSTEXP, B3 0.049
----------------------------------------------------
Note: The reliability estimates reported above are based on only 61 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
The value of the likelihood function at iteration 19 = -2.394679E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.738550 0.011949 145.498 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041475 0.002798 14.824 886 0.000
BLACK, G11 -0.019620 0.004470 -4.389 886 0.000
For GED slope, B2
INTRCPT2, G20 0.040940 0.022022 1.859 887 0.063
For POSTEXP slope, B3
INTRCPT2, G30 0.009412 0.005546 1.697 887 0.089
For HGC_9 slope, B4
INTRCPT2, G40 0.039032 0.006243 6.252 6395 0.000
For UE_7 slope, B5
INTRCPT2, G50 -0.011723 0.001783 -6.575 6395 0.000
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 1.738550 0.011902 146.069 887 0.000
For EXPER slope, B1
INTRCPT2, G10 0.041475 0.002755 15.056 886 0.000
BLACK, G11 -0.019620 0.004255 -4.611 886 0.000
For GED slope, B2
INTRCPT2, G20 0.040940 0.021962 1.864 887 0.062
For POSTEXP slope, B3
INTRCPT2, G30 0.009412 0.005547 1.697 887 0.089
For HGC_9 slope, B4
INTRCPT2, G40 0.039032 0.006339 6.158 6395 0.000
For UE_7 slope, B5
INTRCPT2, G50 -0.011723 0.002001 -5.859 6395 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 0.20336 0.04135 60 79.33687 0.048
EXPER slope, U1 0.03690 0.00136 59 70.25125 0.150
GED slope, U2 0.13172 0.01735 60 45.99438 >.500
POSTEXP slope, U3 0.05801 0.00336 60 66.49441 0.263
level-1, R 0.30637 0.09386
-----------------------------------------------------------------------------
Note: The chi-square statistics reported above are based on only 61 of 888 units that had sufficient data for computation. Fixed effects and variance components are based on all the data.
Statistics for current covariance components model -------------------------------------------------- Deviance = 4789.358653 Number of estimated parameters = 18
Table 6.5, page 221
Table 6.5: Alternative polynomial change trajectories for externalizing data.
Model A: no change
Sigma_squared = 70.20296
Standard Error of Sigma_squared = 6.61880
Tau INTRCPT1,B0 87.41789
Standard Errors of Tau INTRCPT1,B0 20.92509
Tau (as correlations) INTRCPT1,B0 1.000
---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, B0 0.882 ----------------------------------------------------
The value of the likelihood function at iteration 2 = -1.005127E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 12.962963 1.484126 8.734 44 0.000
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 12.962963 1.484126 8.734 44 0.000
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 9.34975 87.41789 44 381.20846 0.000
level-1, R 8.37872 70.20296
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 2010.253021 Number of estimated parameters = 3
Model B: linear change
Sigma_squared = 53.71799
Standard Error of Sigma_squared = 5.66237
Tau
INTRCPT1,B0 123.52437 -12.53790
TIME,B1 -12.53790 4.69289
Standard Errors of Tau
INTRCPT1,B0 32.11051 5.99118
TIME,B1 5.99118 1.66816
Tau (as correlations)
INTRCPT1,B0 1.000 -0.521
TIME,B1 -0.521 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.814
TIME, B1 0.605
----------------------------------------------------
The value of the likelihood function at iteration 2 = -9.958722E+002
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 13.289947 1.835831 7.239 44 0.000
For TIME slope, B1
INTRCPT2, G10 -0.130794 0.415331 -0.315 44 0.754
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 13.289947 1.835831 7.239 44 0.000
For TIME slope, B1
INTRCPT2, G10 -0.130794 0.415331 -0.315 44 0.754
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 11.11415 123.52437 44 242.54772 0.000
TIME slope, U1 2.16631 4.69289 44 113.79720 0.000
level-1, R 7.32926 53.71799
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 1991.744454 Number of estimated parameters = 6
Model C: Quadratic change
Sigma_squared = 41.98360
Standard Error of Sigma_squared = 5.11008
Tau
INTRCPT1,B0 107.08541 -3.69057 -1.36174
TIME,B1 -3.69057 24.60986 -4.96378
TIME2,B2 -1.36174 -4.96378 1.21565
Standard Errors of Tau
INTRCPT1,B0 30.13971 14.15802 2.77438
TIME,B1 14.15802 12.19998 2.41363
TIME2,B2 2.77438 2.41363 0.51200
Tau (as correlations)
INTRCPT1,B0 1.000 -0.072 -0.119
TIME,B1 -0.072 1.000 -0.908
TIME2,B2 -0.119 -0.908 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.756
TIME, B1 0.446
TIME2, B2 0.519
----------------------------------------------------
The value of the likelihood function at iteration 2 = -9.879182E+002
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 13.969841 1.773709 7.876 44 0.000
For TIME slope, B1
INTRCPT2, G10 -1.150635 1.106776 -1.040 44 0.305
For TIME2 slope, B2
INTRCPT2, G20 0.203968 0.228046 0.894 44 0.376
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 13.969841 1.773709 7.876 44 0.000
For TIME slope, B1
INTRCPT2, G10 -1.150635 1.106776 -1.040 44 0.305
For TIME2 slope, B2
INTRCPT2, G20 0.203968 0.228046 0.894 44 0.376
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 10.34821 107.08541 44 184.73120 0.000
TIME slope, U1 4.96083 24.60986 44 81.29406 0.001
TIME2 slope, U2 1.10257 1.21565 44 93.64513 0.000
level-1, R 6.47947 41.98360
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 1975.836435 Number of estimated parameters = 10
Model D: Cubic change. Notice that it takes this model many iterations to converge.
Sigma_squared = 37.76460
Standard Error of Sigma_squared = 5.62961
Tau
INTRCPT1,B0 128.92000 -56.31227 24.64387 -3.26316
TIME,B1 -56.31227 107.26226 -41.38144 4.11826
TIME2,B2 24.64387 -41.38144 16.80332 -1.70590
TIME3,B3 -3.26316 4.11826 -1.70590 0.18016
Standard Errors of Tau
INTRCPT1,B0 35.24141 34.30770 15.14460 1.85113
TIME,B1 34.30770 55.35433 24.88704 2.96815
TIME2,B2 15.14460 24.88704 11.79645 1.45017
TIME3,B3 1.85113 2.96815 1.45017 0.18281
Tau (as correlations)
INTRCPT1,B0 1.000 -0.479 0.529 -0.677
TIME,B1 -0.479 1.000 -0.975 0.937
TIME2,B2 0.529 -0.975 1.000 -0.980
TIME3,B3 -0.677 0.937 -0.980 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.780
TIME, B1 0.439
TIME2, B2 0.332
TIME3, B3 0.236
----------------------------------------------------
The value of the likelihood function at iteration 1357 = -9.836930E+002
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 13.794533 1.915934 7.200 44 0.000
For TIME slope, B1
INTRCPT2, G10 -0.350059 2.329009 -0.150 44 0.882
For TIME2 slope, B2
INTRCPT2, G20 -0.234303 1.060364 -0.221 44 0.826
For TIME3 slope, B3
INTRCPT2, G30 0.058436 0.130209 0.449 44 0.655
----------------------------------------------------------------------------
Final estimation of fixed effects
(with robust standard errors)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 13.794533 1.915922 7.200 44 0.000
For TIME slope, B1
INTRCPT2, G10 -0.350059 2.301917 -0.152 44 0.880
For TIME2 slope, B2
INTRCPT2, G20 -0.234303 1.034269 -0.227 44 0.822
For TIME3 slope, B3
INTRCPT2, G30 0.058436 0.125693 0.465 44 0.644
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 11.35429 128.92000 44 204.96557 0.000
TIME slope, U1 10.35675 107.26226 44 78.41929 0.001
TIME2 slope, U2 4.09919 16.80332 44 64.10048 0.025
TIME3 slope, U3 0.42445 0.18016 44 54.89527 0.126
level-1, R 6.14529 37.76460
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 1967.385967 Number of estimated parameters = 15
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