
 Program:                       HLM 7 Hierarchical Linear and Nonlinear Modeling
 Authors:                       Stephen Raudenbush, Tony Bryk, & Richard Congdon
 Publisher:                     Scientific Software International, Inc. (c) 2000
                                                      techsupport@ssicentral.com
                                                              www.ssicentral.com
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 Module:      HLM3.EXE (7.00.21103.1002)
 Date:        12 November 2017, Sunday
 Time:        23:52: 8
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 Specifications for this HLM3 run


  Problem Title: no title

  The data source for this run  = ch13hlm3level
  The command file for this run = C:\Users\Hawjeng\AppData\Local\Temp\whlmtemp.hlm
  Output file name              = N:\MyBooks\Data3\2017\Data\Ch13\hlm3.txt
  The maximum number of level-1 units = 3364
  The maximum number of level-2 units = 841
  The maximum number of level-3 units = 76
  The maximum number of iterations = 100

  Method of estimation: full maximum likelihood

  The outcome variable is    SCORE    

  The model specified for the fixed effects was:
 ----------------------------------------------------

   Level-1                Level-2           Level-3
   Coefficients           Predictors        Predictors
 ---------------------  ---------------   ----------------
        INTRCPT1, P0      INTRCPT2, B00    INTRCPT3, G000
#       D1 slope, P1    # INTRCPT2, B10    INTRCPT3, G100
#       D2 slope, P2    # INTRCPT2, B20    INTRCPT3, G200
#       D3 slope, P3    # INTRCPT2, B30    INTRCPT3, G300

 '#' - The residual parameter variance for the parameter has been set to zero


 Summary of the model specified (in equation format)
 ---------------------------------------------------

Level-1 Model

	SCORE = P0 + P1*(D1) + P2*(D2) + P3*(D3) + e

Level-2 Model

	P0 = B00 + r0
	P1 = B10 
	P2 = B20 
	P3 = B30 


Level-3 Model

	B00 = G000 + u00
	B10 = G100 
	B20 = G200 
	B30 = G300 


Mixed Model
    SCORE = G000 + G100*D1 + G200*D2 + G300*D3+ r0 + u00 + e
 For starting values, data from 3364 level-1 and 841 level-2 records were used
******* ITERATION 7 *******


Iterations stopped due to small change in likelihood function
 sigma^2 =      0.22990
 Standard error of sigma^2 =      0.00647

tau(pi)
 INTRCPT1,P0      0.21948 

Standard error of tau(pi)
 INTRCPT1,P0      0.01425 


 ----------------------------------------------------
  Random level-1 coefficient   Reliability estimate
 ----------------------------------------------------
  INTRCPT1, P0                        0.792
 ----------------------------------------------------

tau(beta)
 INTRCPT1    
 INTRCPT2,B00
    0.14022  
Standard error of tau(beta)
 INTRCPT1    
 INTRCPT2,B00
    0.02772  

 ----------------------------------------------------
  Random level-2 coefficient   Reliability estimate
 ----------------------------------------------------
  INTRCPT1/INTRCPT2, B00               0.817
 ----------------------------------------------------
The value of the log-likelihood function at iteration 7 = -3.030189E+003
 The outcome variable is    SCORE

 Final estimation of fixed effects:
 ----------------------------------------------------------------------------
                                       Standard             Approx.
    Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
 ----------------------------------------------------------------------------
 For       INTRCPT1, P0
    For INTRCPT2, B00
      INTRCPT3, G000      3.631224    0.049625     73.173       75    0.000
 For       D1 slope, P1
    For INTRCPT2, B10
      INTRCPT3, G100     -0.079667    0.023382     -3.407     2444    0.001
 For       D2 slope, P2
    For INTRCPT2, B20
      INTRCPT3, G200     -0.181926    0.023382     -7.780     2444    0.000
 For       D3 slope, P3
    For INTRCPT2, B30
      INTRCPT3, G300     -0.105826    0.023382     -4.526     2444    0.000
 ----------------------------------------------------------------------------

 The outcome variable is    SCORE

 Final estimation of fixed effects
 (with robust standard errors)
 ----------------------------------------------------------------------------
                                       Standard             Approx.
    Fixed Effect         Coefficient   Error      T-ratio   d.f.     P-value
 ----------------------------------------------------------------------------
 For       INTRCPT1, P0
    For INTRCPT2, B00
      INTRCPT3, G000      3.631224    0.052869     68.684       75    0.000
 For       D1 slope, P1
    For INTRCPT2, B10
      INTRCPT3, G100     -0.079667    0.028336     -2.812     2444    0.005
 For       D2 slope, P2
    For INTRCPT2, B20
      INTRCPT3, G200     -0.181926    0.037517     -4.849     2444    0.000
 For       D3 slope, P3
    For INTRCPT2, B30
      INTRCPT3, G300     -0.105826    0.035754     -2.960     2444    0.003
 ----------------------------------------------------------------------------



 Final estimation of level-1 and level-2 variance components:
 ------------------------------------------------------------------------------
 Random Effect           Standard      Variance     df    Chi-square   P-value
                         Deviation     Component
 ------------------------------------------------------------------------------
 INTRCPT1,        r0      0.46849       0.21948     765    3690.24363    0.000
  level-1,        e       0.47948       0.22990
 ------------------------------------------------------------------------------


 Final estimation of level-3 variance components:
 ------------------------------------------------------------------------------
 Random Effect           Standard      Variance     df    Chi-square   P-value
                         Deviation     Component
 ------------------------------------------------------------------------------
INTRCPT1/INTRCPT2,  u00     0.37446       0.14022    75     532.99602    0.000
 ------------------------------------------------------------------------------


 Statistics for the current model
 --------------------------------------------------
 Deviance                       = 6060.377088
 Number of estimated parameters = 7
