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HLM Textbook Examples
Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence
by Judith D. Singer and John B. Willett
Chapter 3: Introducing the Multilevel Model for Change

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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