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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. The examples are created using HLM 6.06. The method we choose for estimating these models is ML. Estimation method is selected from Other Settings -> Estimation Settings menu.
Figure 3.1 on page 50, not quite, since we don't have a way of making the regression lines, but it gives us a way of looking at the data. Choose File -> Graph Data -> line plots, scatter plots from the pull-down menu to get the window below.
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 6.06 and notice that it takes HLM many iterations to converge.
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
The outcome variable is COG
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 0.013
For TIME slope, B1
INTRCPT2, G10 -21.133333 1.890177 -11.181 101 0.000
PROGRAM, G11 5.271264 2.518878 2.093 101 0.039
----------------------------------------------------------------------------
The outcome variable is COG
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 0.011
For TIME slope, B1
INTRCPT2, G10 -21.133333 1.583433 -13.347 101 0.000
PROGRAM, G11 5.271264 2.402765 2.194 101 0.030
----------------------------------------------------------------------------
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
Figure 3.5 on page 71. We used the predictor variable time as x-axis since this is based on the model.
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