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4.2.4. Regressão com Coeficientes-Aleatórios |
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HLM – Output |
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Program: HLM 5 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 ------------------------------------------------------------------------------- Module:
HLM2.EXE (5.05.2330.2) Date:
Time:
-------------------------------------------------------------------------------
SPECIFICATIONS FOR THIS HLM2 RUN Sun Jul 10 -------------------------------------------------------------------------------
Problem Title: RANDOM-COEFFICIENT MODEL (TABLE
4.4, P. 77)
The data source for this run =
C:\Documents and Settings\user\Desktop\HSB_Modelos\Random_Coeff\HDB12.ssm
The command file for this run = C:\Documents and
Settings\user\Desktop\HSB_Modelos\Random_Coeff\random_coeff.hlm
Output file name =
C:\Documents and Settings\user\Desktop\HSB_Modelos\Random_Coeff\hlm2.out
The maximum number of level-2 units = 160
The maximum number of iterations = 100
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
MATHACH
The model specified for the fixed effects was: ----------------------------------------------------
Level-1 Level-2
Coefficients
Predictors ---------------------- --------------- INTRCPT1, B0 INTRCPT2, G00 *
SES slope, B1 INTRCPT2,
G10 '*' - 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 SES slope Summary of the model specified (in equation
format) --------------------------------------------------- Level-1 Model Y
= B0 + B1*(SES) + R Level-2 Model B0
= G00 + U0 B1
= G10 + U1 Level-1 OLS regressions ----------------------- Level-2 Unit INTRCPT1 SES slope ------------------------------------------------------------------------------
1224 9.71545 2.50858
1288 13.51080 3.25545
1296 7.63596 1.07596
1308 16.25550 0.12602
1317 13.17769 1.27391
1358 11.20623 5.06801
1374 9.72846 3.85432
1433 19.71914 1.85429
1436 18.11161 1.60056
1461 16.84264 6.26650 The average OLS level-1 coefficient
for INTRCPT1 = 12.62075 The average OLS level-1 coefficient
for SES = 2.20164 Least Squares Estimates ----------------------- sigma_squared = 45.22141 The outcome variable is MATHACH Least-squares estimates of fixed effects ---------------------------------------------------------------------------- Standard
Fixed Effect
Coefficient Error T-ratio d.f.
P-value ---------------------------------------------------------------------------- For
INTRCPT1, B0
INTRCPT2, G00
12.747853 0.079334 160.686 7183
0.000 For
SES slope, B1
INTRCPT2, G10
2.191172 0.120104 18.244 7183
0.000 ---------------------------------------------------------------------------- The outcome variable is MATHACH 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
12.747853 0.239305 53.270 7183
0.000 For
SES slope, B1
INTRCPT2, G10
2.191172 0.129367 16.938 7183
0.000 ---------------------------------------------------------------------------- The least-squares likelihood value =
-23889.956689 Deviance =
47779.91338 Number of estimated parameters = 1 STARTING VALUES --------------- sigma(0)_squared = 36.72025 Tau(0) INTRCPT1,B0 8.84167 0.06714
SES,B1 0.06714 0.48299 The outcome variable is MATHACH 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
12.636059 0.246557 51.250 159
0.000 For
SES slope, B1
INTRCPT2, G10
2.192865 0.122632 17.882 159
0.000 ---------------------------------------------------------------------------- The value of the likelihood function
at iteration 1 = -2.335653E+004 The value of the likelihood function
at iteration 2 = -2.335649E+004 The value of the likelihood function
at iteration 3 = -2.335646E+004 The value of the likelihood function
at iteration 4 = -2.335644E+004 The value of the likelihood function
at iteration 5 = -2.335635E+004
. .
. The value of the likelihood function
at iteration 14 = -2.335621E+004 The value of the likelihood function
at iteration 15 = -2.335620E+004 The value of the likelihood function
at iteration 16 = -2.335620E+004 The value of the likelihood function
at iteration 17 = -2.335620E+004 Iterations stopped due to small change
in likelihood function ******* ITERATION 18 ******* Sigma_squared = 36.70356 Tau INTRCPT1,B0 8.68087 0.04701
SES,B1 0.04701 0.68038 Tau (as correlations) INTRCPT1,B0
1.000 0.019
SES,B1 0.019 1.000 ----------------------------------------------------
Random level-1 coefficient
Reliability estimate ----------------------------------------------------
INTRCPT1, B0
0.908
SES, B1
0.260 ---------------------------------------------------- The value of the likelihood function
at iteration 18 = -2.335620E+004 The outcome variable is MATHACH Final estimation of fixed effects: ----------------------------------------------------------------------------
Standard Approx.
Fixed Effect
Coefficient Error T-ratio
d.f. P-value ---------------------------------------------------------------------------- For
INTRCPT1, B0
INTRCPT2, G00
12.636197 0.244503 51.681 159
0.000 For
SES slope, B1
INTRCPT2, G10 2.193157
0.127879 17.150 159
0.000 ---------------------------------------------------------------------------- The outcome variable is MATHACH 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
12.636197 0.243738 51.843 159
0.000 For
SES slope, B1
INTRCPT2, G10
2.193157 0.127846 17.155 159
0.000 ---------------------------------------------------------------------------- Final estimation of variance components: ----------------------------------------------------------------------------- Random Effect Standard Variance df
Chi-square P-value Deviation Component ----------------------------------------------------------------------------- INTRCPT1, U0 2.94633 8.68087 159
1770.85120 0.000
SES slope, U1
0.82485 0.68038 159
213.43769 0.003
level-1, R 6.05835 36.70356 ----------------------------------------------------------------------------- Statistics for current covariance components
model -------------------------------------------------- Deviance = 46712.398925 Number of estimated parameters = 4 |