Program: HLM 5 Hierarchical Linear and Nonlinear Modeling
Authors: Stephen Raudenbush, Tony Bryk, & Richard Congdon
Publisher: Scientific Software International, Inc. (c) 2000
------
Module: HLM2S.EXE (5.00.2045.1)
Date: 8 April 2000, Saturday
Time: 14:55:22
------
SPECIFICATIONS FOR THIS HLM2 RUN
------
Problem Title: NULL MODEL / ONE-WAY ANALYSIS OF VARIANCE
The data source for this run = SIOPET.SSM
The command file for this run = C:\HLM5S\siopet\null.hlm
Output file name = C:\HLM5S\SIOPET\null.OUT
The maximum number of level-2 units = 50
The maximum number of iterations = 1000
Method of estimation: restricted maximum likelihood
Weighting Specification
------
Weight
Variable
Weighting? Name Normalized?
Level 1 no no
Level 2 no no
The outcome variable is HELPING
The model specified for the fixed effects was:
------
Level-1 Level-2
Coefficients Predictors
------
INTRCPT1, B0 INTRCPT2, G00
The model specified for the covariance components was:
------
Sigma squared (constant across level-2 units)
Tau dimensions
INTRCPT1
Summary of the model specified (in equation format)
------
Level-1 Model
Y = B0 + R
Level-2 Model
B0 = G00 + U0
Least Squares Estimates
------
sigma_squared = 129.67348
Least-squares estimates of fixed effects
------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 31.394346 0.360102 87.182 999 0.000
------
Least-squares estimates of fixed effects
(with robust standard errors)
------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 31.394346 1.409786 22.269 999 0.000
------
The least-squares likelihood value = -3851.050779
Deviance = 7702.10156
Number of estimated parameters = 1
STARTING VALUES
------
sigma(0)_squared = 31.75676
Tau(0)
INTRCPT1,B0 99.81511
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 31.394354 1.424099 22.045 49 0.000
------
The value of the likelihood function at iteration 1 = -3.249218E+003
Iterations stopped due to small change in likelihood function
******* ITERATION 2 *******
Sigma_squared = 31.75676
Tau
INTRCPT1,B0 99.81511
Tau (as correlations)
INTRCPT1,B0 1.000
------
Random level-1 coefficient Reliability estimate
------
INTRCPT1, B0 0.984
------
Final estimation of fixed effects:
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 31.394354 1.424099 22.045 49 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 31.394354 1.409786 22.269 49 0.000
------
Final estimation of variance components:
------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
------
INTRCPT1, U0 9.99075 99.81511 49 3129.25201 0.000
level-1, R 5.63531 31.75676
------
Statistics for current covariance components model
------
Deviance = 6498.43618
Number of estimated parameters = 2
Program: HLM 5 Hierarchical Linear and Nonlinear Modeling
Authors: Stephen Raudenbush, Tony Bryk, & Richard Congdon
Publisher: Scientific Software International, Inc. (c) 2000
------
Module: HLM2S.EXE (5.00.2045.1)
Date: 8 April 2000, Saturday
Time: 14:46: 8
------
SPECIFICATIONS FOR THIS HLM2 RUN
------
Problem Title: RANDOM COEFFICIENT REGRESSION MODEL
The data source for this run = siopet.ssm
The command file for this run = C:\HLM5S\siopet\r_reg.hlm
Output file name = C:\HLM5S\siopet\r_reg.out
The maximum number of level-2 units = 50
The maximum number of iterations = 1000
Method of estimation: restricted maximum likelihood
Weighting Specification
------
Weight
Variable
Weighting? Name Normalized?
Level 1 no no
Level 2 no no
The outcome variable is HELPING
The model specified for the fixed effects was:
------
Level-1 Level-2
Coefficients Predictors
------
INTRCPT1, B0 INTRCPT2, G00
% MOOD slope, B1 INTRCPT2, G10
'%' - This level-1 predictor has been centered around its grand mean.
The model specified for the covariance components was:
------
Sigma squared (constant across level-2 units)
Tau dimensions
INTRCPT1
MOOD slope
Summary of the model specified (in equation format)
------
Level-1 Model
Y = B0 + B1*(MOOD) + R
Level-2 Model
B0 = G00 + U0
B1 = G10 + U1
Least Squares Estimates
------
sigma_squared = 46.34416
Least-squares estimates of fixed effects
------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 31.394348 0.215277 145.832 998 0.000
For MOOD slope, B1
INTRCPT2, G10 3.889450 0.091745 42.394 998 0.000
------
Least-squares estimates of fixed effects
(with robust standard errors)
------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 31.394348 0.876668 35.811 998 0.000
For MOOD slope, B1
INTRCPT2, G10 3.889450 0.245918 15.816 998 0.000
------
The least-squares likelihood value = -3338.072922
Deviance = 6676.14584
Number of estimated parameters = 1
STARTING VALUES
------
sigma(0)_squared = 5.60718
Tau(0)
INTRCPT1,B0 46.31097 0.56111
MOOD,B1 0.56111 0.95020
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 31.486284 0.968396 32.514 49 0.000
For MOOD slope, B1
INTRCPT2, G10 3.008250 0.145820 20.630 49 0.000
------
The value of the likelihood function at iteration 1 = -2.445746E+003
The value of the likelihood function at iteration 10 = -2.427653E+003
Iterations stopped due to small change in likelihood function
******* ITERATION 11 *******
Sigma_squared = 5.61081
Tau
INTRCPT1,B0 45.63410 0.63550
MOOD,B1 0.63550 0.12917
Tau (as correlations)
INTRCPT1,B0 1.000 0.262
MOOD,B1 0.262 1.000
------
Random level-1 coefficient Reliability estimate
------
INTRCPT1, B0 0.987
MOOD, B1 0.541
------
The value of the likelihood function at iteration 11 = -2.427653E+003
The outcome variable is HELPING
Final estimation of fixed effects:
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 31.429052 0.960006 32.738 49 0.000
For MOOD slope, B1
INTRCPT2, G10 3.012354 0.068961 43.682 49 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 31.429052 0.950326 33.072 49 0.000
For MOOD slope, B1
INTRCPT2, G10 3.012354 0.068257 44.133 49 0.000
------
Final estimation of variance components:
------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
------
INTRCPT1, U0 6.75530 45.63410 49 4605.68268 0.000
MOOD slope, U1 0.35941 0.12917 49 110.16628 0.000
level-1, R 2.36871 5.61081
------
Statistics for current covariance components model
------
Deviance = 4855.30564
Number of estimated parameters = 4
Program: HLM 5 Hierarchical Linear and Nonlinear Modeling
Authors: Stephen Raudenbush, Tony Bryk, & Richard Congdon
Publisher: Scientific Software International, Inc. (c) 2000
------
Module: HLM2S.EXE (5.00.2045.1)
Date: 8 April 2000, Saturday
Time: 14:49: 2
------
SPECIFICATIONS FOR THIS HLM2 RUN
------
Problem Title: INTERCEPTS-AS-OUTCOMES
The data source for this run = siopet.ssm
The command file for this run = C:\HLM5S\siopet\inter.hlm
Output file name = C:\HLM5S\siopet\inter.out
The maximum number of level-2 units = 50
The maximum number of iterations = 1000
Method of estimation: restricted maximum likelihood
Weighting Specification
------
Weight
Variable
Weighting? Name Normalized?
Level 1 no no
Level 2 no no
The outcome variable is HELPING
The model specified for the fixed effects was:
------
Level-1 Level-2
Coefficients Predictors
------
INTRCPT1, B0 INTRCPT2, G00
PROX, G01
% MOOD slope, B1 INTRCPT2, G10
'%' - This level-1 predictor has been centered around its grand mean.
The model specified for the covariance components was:
------
Sigma squared (constant across level-2 units)
Tau dimensions
INTRCPT1
MOOD slope
Summary of the model specified (in equation format)
------
Level-1 Model
Y = B0 + B1*(MOOD) + R
Level-2 Model
B0 = G00 + G01*(PROX) + U0
B1 = G10 + U1
Least Squares Estimates
------
sigma_squared = 41.08266
Least-squares estimates of fixed effects
------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 24.714388 0.622483 39.703 997 0.000
PROX, G01 1.261370 0.111137 11.350 997 0.000
For MOOD slope, B1
INTRCPT2, G10 3.975459 0.086712 45.847 997 0.000
------
Least-squares estimates of fixed effects
(with robust standard errors)
------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 24.714388 2.523145 9.795 997 0.000
PROX, G01 1.261370 0.422335 2.987 997 0.003
For MOOD slope, B1
INTRCPT2, G10 3.975459 0.222004 17.907 997 0.000
------
The least-squares likelihood value = -3278.716808
Deviance = 6557.43362
Number of estimated parameters = 1
STARTING VALUES
------
sigma(0)_squared = 5.60718
Tau(0)
INTRCPT1,B0 42.29461 -0.21053
MOOD,B1 -0.21053 1.11501
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 25.028366 2.833095 8.834 48 0.000
PROX, G01 1.221252 0.505558 2.416 48 0.020
For MOOD slope, B1
INTRCPT2, G10 3.009646 0.156721 19.204 49 0.000
------
The value of the likelihood function at iteration 1 = -2.444995E+003
The value of the likelihood function at iteration 10 = -2.424730E+003
Iterations stopped due to small change in likelihood function
******* ITERATION 11 *******
Sigma_squared = 5.61079
Tau
INTRCPT1,B0 41.67890 -0.08356
MOOD,B1 -0.08356 0.12924
Tau (as correlations)
INTRCPT1,B0 1.000 -0.036
MOOD,B1 -0.036 1.000
------
Random level-1 coefficient Reliability estimate
------
INTRCPT1, B0 0.985
MOOD, B1 0.541
------
Final estimation of fixed effects:
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 24.922580 2.808705 8.873 48 0.000
PROX, G01 1.235956 0.501261 2.466 48 0.018
For MOOD slope, B1
INTRCPT2, G10 3.013404 0.068981 43.684 49 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 24.922580 2.920104 8.535 48 0.000
PROX, G01 1.235956 0.476908 2.592 48 0.013
For MOOD slope, B1
INTRCPT2, G10 3.013404 0.068234 44.163 49 0.000
------
Final estimation of variance components:
------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
------
INTRCPT1, U0 6.45592 41.67890 48 4127.70255 0.000
MOOD slope, U1 0.35950 0.12924 49 110.18076 0.000
level-1, R 2.36871 5.61079
------
Statistics for current covariance components model
------
Deviance = 4849.46082
Number of estimated parameters = 4
Program: HLM 5 Hierarchical Linear and Nonlinear Modeling
Authors: Stephen Raudenbush, Tony Bryk, & Richard Congdon
Publisher: Scientific Software International, Inc. (c) 2000
------
Module: HLM2S.EXE (5.00.2045.1)
Date: 8 April 2000, Saturday
Time: 14:50:59
------
SPECIFICATIONS FOR THIS HLM2 RUN
------
Problem Title: SLOPES-AS-OUTCOMES
The data source for this run = siopet.ssm
The command file for this run = C:\HLM5S\siopet\slopes.hlm
Output file name = C:\HLM5S\siopet\slopes.out
The maximum number of level-2 units = 50
The maximum number of iterations = 1000
Method of estimation: restricted maximum likelihood
Weighting Specification
------
Weight
Variable
Weighting? Name Normalized?
Level 1 no no
Level 2 no no
The outcome variable is HELPING
The model specified for the fixed effects was:
------
Level-1 Level-2
Coefficients Predictors
------
INTRCPT1, B0 INTRCPT2, G00
PROX, G01
% MOOD slope, B1 INTRCPT2, G10
PROX, G11
'%' - This level-1 predictor has been centered around its grand mean.
The model specified for the covariance components was:
------
Sigma squared (constant across level-2 units)
Tau dimensions
INTRCPT1
MOOD slope
Summary of the model specified (in equation format)
------
Level-1 Model
Y = B0 + B1*(MOOD) + R
Level-2 Model
B0 = G00 + G01*(PROX) + U0
B1 = G10 + G11*(PROX) + U1
Least Squares Estimates
------
sigma_squared = 40.98631
Least-squares estimates of fixed effects
------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 24.784955 0.622949 39.786 996 0.000
PROX, G01 1.241624 0.111531 11.133 996 0.000
For MOOD slope, B1
INTRCPT2, G10 4.453726 0.275517 16.165 996 0.000
PROX, G11 -0.090575 0.049533 -1.829 996 0.067
------
Least-squares estimates of fixed effects
(with robust standard errors)
------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 24.784955 2.493567 9.940 996 0.000
PROX, G01 1.241624 0.421545 2.945 996 0.004
For MOOD slope, B1
INTRCPT2, G10 4.453726 0.756304 5.889 996 0.000
PROX, G11 -0.090575 0.118460 -0.765 996 0.445
------
The least-squares likelihood value = -3279.132496
Deviance = 6558.26499
Number of estimated parameters = 1
STARTING VALUES
------
sigma(0)_squared = 5.60718
Tau(0)
INTRCPT1,B0 42.29566 -0.25107
MOOD,B1 -0.25107 1.27823
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 25.167937 2.834108 8.880 48 0.000
PROX, G01 1.195398 0.505750 2.364 48 0.022
For MOOD slope, B1
INTRCPT2, G10 2.096086 0.512071 4.093 48 0.000
PROX, G11 0.172432 0.091396 1.887 48 0.065
------
The value of the likelihood function at iteration 1 = -2.448101E+003
The value of the likelihood function at iteration 30 = -2.414026E+003
Iterations stopped due to small change in likelihood function
******* ITERATION 31 *******
Sigma_squared = 5.61465
Tau
INTRCPT1,B0 42.94618 0.00716
MOOD,B1 0.00716 0.02207
Tau (as correlations)
INTRCPT1,B0 1.000 0.007
MOOD,B1 0.007 1.000
------
Random level-1 coefficient Reliability estimate
------
INTRCPT1, B0 0.986
MOOD, B1 0.173
------
Final estimation of fixed effects:
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 25.140965 2.847498 8.829 48 0.000
PROX, G01 1.194664 0.508198 2.351 48 0.023
For MOOD slope, B1
INTRCPT2, G10 2.064738 0.158144 13.056 48 0.000
PROX, G11 0.179906 0.028447 6.324 48 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 25.140965 2.985770 8.420 48 0.000
PROX, G01 1.194664 0.483758 2.470 48 0.017
For MOOD slope, B1
INTRCPT2, G10 2.064738 0.167640 12.317 48 0.000
PROX, G11 0.179906 0.033319 5.400 48 0.000
------
Final estimation of variance components:
------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
------
INTRCPT1, U0 6.55333 42.94618 48 4122.21950 0.000
MOOD slope, U1 0.14856 0.02207 48 59.21764 0.129
level-1, R 2.36953 5.61465
------
Statistics for current covariance components model
------
Deviance = 4828.05107
Number of estimated parameters = 4
Program: HLM 5 Hierarchical Linear and Nonlinear Modeling
Authors: Stephen Raudenbush, Tony Bryk, & Richard Congdon
Publisher: Scientific Software International, Inc. (c) 2000
------
Module: HLM2S.EXE (5.00.2045.1)
Date: 8 April 2000, Saturday
Time: 14:53:33
------
SPECIFICATIONS FOR THIS HLM2 RUN
------
Problem Title: SLOPES-AS-OUTCOMES / GROUP MEAN CENTERED WITH AVE-MOOD ENTERED
The data source for this run = siopet.ssm
The command file for this run = C:\HLM5S\siopet\slopes2.hlm
Output file name = C:\HLM5S\siopet\slopes2.out
The maximum number of level-2 units = 50
The maximum number of iterations = 1000
Method of estimation: restricted maximum likelihood
Weighting Specification
------
Weight
Variable
Weighting? Name Normalized?
Level 1 no no
Level 2 no no
The outcome variable is HELPING
The model specified for the fixed effects was:
------
Level-1 Level-2
Coefficients Predictors
------
INTRCPT1, B0 INTRCPT2, G00
AVE_MOOD, G01
PROX, G02
* MOOD slope, B1 INTRCPT2, G10
PROX, G11
'*' - This level-1 predictor has been centered around its group mean.
The model specified for the covariance components was:
------
Sigma squared (constant across level-2 units)
Tau dimensions
INTRCPT1
MOOD slope
Summary of the model specified (in equation format)
------
Level-1 Model
Y = B0 + B1*(MOOD) + R
Level-2 Model
B0 = G00 + G01*(AVE_MOOD) + G02*(PROX) + U0
B1 = G10 + G11*(PROX) + U1
Least Squares Estimates
------
sigma_squared = 35.67115
Least-squares estimates of fixed effects
------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 -4.744154 0.934278 -5.078 995 0.000
AVE_MOOD, G01 4.946582 0.114113 43.348 995 0.000
PROX, G02 1.370148 0.103952 13.181 995 0.000
For MOOD slope, B1
INTRCPT2, G10 2.028703 0.361477 5.612 995 0.000
PROX, G11 0.184708 0.065270 2.830 995 0.005
------
Least-squares estimates of fixed effects
(with robust standard errors)
------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 -4.744154 3.413768 -1.390 995 0.165
AVE_MOOD, G01 4.946582 0.438139 11.290 995 0.000
PROX, G02 1.370148 0.403980 3.392 995 0.001
For MOOD slope, B1
INTRCPT2, G10 2.028703 0.166272 12.201 995 0.000
PROX, G11 0.184708 0.032923 5.610 995 0.000
------
The least-squares likelihood value = -3210.020772
Deviance = 6420.04154
Number of estimated parameters = 1
STARTING VALUES
------
sigma(0)_squared = 5.60718
Tau(0)
INTRCPT1,B0 31.75619 0.02801
MOOD,B1 0.02801 0.02752
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 -4.760707 3.959427 -1.202 47 0.236
AVE_MOOD, G01 4.949141 0.483588 10.234 47 0.000
PROX, G02 1.370446 0.440566 3.111 47 0.004
For MOOD slope, B1
INTRCPT2, G10 2.033388 0.161959 12.555 48 0.000
PROX, G11 0.183345 0.029116 6.297 48 0.000
------
The value of the likelihood function at iteration 1 = -2.405170E+003
The value of the likelihood function at iteration 25 = -2.405129E+003
Iterations stopped due to small change in likelihood function
******* ITERATION 26 *******
Sigma_squared = 5.61932
Tau
INTRCPT1,B0 31.75516 0.05813
MOOD,B1 0.05813 0.01987
Tau (as correlations)
INTRCPT1,B0 1.000 0.073
MOOD,B1 0.073 1.000
------
Random level-1 coefficient Reliability estimate
------
INTRCPT1, B0 0.991
MOOD, B1 0.159
------
Final estimation of fixed effects:
------
Standard Approx.
Fixed Effect Coefficient Error T-ratio d.f. P-value
------
For INTRCPT1, B0
INTRCPT2, G00 -4.780527 3.958677 -1.208 47 0.234
AVE_MOOD, G01 4.952222 0.483442 10.244 47 0.000
PROX, G02 1.370791 0.440561 3.111 47 0.004
For MOOD slope, B1
INTRCPT2, G10 2.032463 0.157216 12.928 48 0.000
PROX, G11 0.183645 0.028289 6.492 48 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 -4.780527 3.426374 -1.395 47 0.170
AVE_MOOD, G01 4.952222 0.439851 11.259 47 0.000
PROX, G02 1.370791 0.404053 3.393 47 0.002
For MOOD slope, B1
INTRCPT2, G10 2.032463 0.168370 12.071 48 0.000
PROX, G11 0.183645 0.033537 5.476 48 0.000
------
Final estimation of variance components:
------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
------
INTRCPT1, U0 5.63517 31.75516 47 5359.09498 0.000
MOOD slope, U1 0.14095 0.01987 48 59.08077 0.131
level-1, R 2.37051 5.61932
------
Statistics for current covariance components model
------
Deviance = 4810.25736
Number of estimated parameters = 4
1