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Please note that the "early_int" data file (which is used in Chapter 3) is not included among the data files. This was done at the request of the researcher who contributed this data file to ensure the privacy of the participants in the study. Although the web page shows how to obtain the results with this data file, we regret that visitors do not have access to this file to be able to replicate the results for themselves.
Table 3.3, page 69
Most of the material in this chapter can not be reproduced in HLM since they are descriptive rather than random effect models. The last model using early.SSM is run in HLM and notice that it takes HLM many iterations to converge and the starting variance-covariance matrix matches with SAS's result.
STARTING VALUES --------------- sigma(0)_squared = 76.61976
Tau(0)
INTRCPT1,B0 121.70149 -31.89337
TIME,B1 -31.89337 2.72259
New Tau(0)
INTRCPT1,B0 37.11026 0.00000
TIME,B1 0.00000 31.19242
Estimation of fixed effects
(Based on starting values of covariance components)
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 107.840741 1.497851 71.997 101 0.000
PROGRAM, G01 6.854662 1.996058 3.434 101 0.001
For TIME slope, B1
INTRCPT2, G10 -21.133333 2.024472 -10.439 101 0.000
PROGRAM, G11 5.271264 2.697841 1.954 101 0.050
----------------------------------------------------------------------------
The value of the likelihood function at iteration 1 = -1.200375E+003
The value of the likelihood function at iteration 1492 = -1.184073E+003
Iterations stopped due to small change in likelihood function ******* ITERATION 1493 *******
Sigma_squared = 74.24046
Standard Error of Sigma_squared = 10.34516
Tau
INTRCPT1,B0 124.63517 -36.41152
TIME,B1 -36.41152 12.29264
Standard Errors of Tau
INTRCPT1,B0 27.38103 22.73780
TIME,B1 22.73780 30.49581
Tau (as correlations)
INTRCPT1,B0 1.000 -0.930
TIME,B1 -0.930 1.000
----------------------------------------------------
Random level-1 coefficient Reliability estimate
----------------------------------------------------
INTRCPT1, B0 0.668
TIME, B1 0.076
----------------------------------------------------
The value of the likelihood function at iteration 1493 = -1.184073E+003
Final estimation of fixed effects:
----------------------------------------------------------------------------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 107.840741 2.035807 52.972 101 0.000
PROGRAM, G01 6.854662 2.712946 2.527 101 0.012
For TIME slope, B1
INTRCPT2, G10 -21.133333 1.890177 -11.181 101 0.000
PROGRAM, G11 5.271264 2.518878 2.093 101 0.036
----------------------------------------------------------------------------
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 107.840741 1.793931 60.114 101 0.000
PROGRAM, G01 6.854662 2.638604 2.598 101 0.010
For TIME slope, B1
INTRCPT2, G10 -21.133333 1.583433 -13.347 101 0.000
PROGRAM, G11 5.271264 2.402765 2.194 101 0.028
----------------------------------------------------------------------------
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 11.16401 124.63517 101 308.91699 0.000
TIME slope, U1 3.50609 12.29264 101 108.18963 0.294
level-1, R 8.61629 74.24046
-----------------------------------------------------------------------------
Statistics for current covariance components model -------------------------------------------------- Deviance = 2368.146438 Number of estimated parameters = 8
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