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: 10 July 2005, Sunday Time: 16:13:37 ------------------------------------------------------------------------------- SPECIFICATIONS FOR THIS HLM2 RUN Sun Jul 10 16:13:37 2005 ------------------------------------------------------------------------------- Problem Title: MEANS_AS_OUTCOMES (TABLE 4.3, P. 73) The data source for this run = C:\Documents and Settings\user\Desktop\HSB_Modelos\Means_as_Outcomes\HDB12.ssm The command file for this run = C:\Documents and Settings\user\Desktop\HSB_Modelos\Means_as_Outcomes\means_as_out.hlm Output file name = C:\Documents and Settings\user\Desktop\HSB_Modelos\Means_as_Outcomes\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 $ MEANSES, G01 '$' - This level-2 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 Summary of the model specified (in equation format) --------------------------------------------------- Level-1 Model Y = B0 + R Level-2 Model B0 = G00 + G01*(MEANSES) + U0
Level-1 OLS regressions ----------------------- Level-2 Unit INTRCPT1 ------------------------------------------------------------------------------ 1224 9.71545 1288 13.51080 1296 7.63596 1308 16.25550 1317 13.17769 1358 11.20623 1374 9.72846 1433 19.71914 1436 18.11161 1461 16.84264 The average OLS level-1 coefficient for INTRCPT1 = 12.62075 Least Squares Estimates ----------------------- sigma_squared = 41.72661 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 12.711688 0.076216 166.786 7183 0.000 MEANSES, G01 5.716800 0.184286 31.021 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 12.711688 0.149509 85.023 7183 0.000 MEANSES, G01 5.716800 0.326862 17.490 7183 0.000 ---------------------------------------------------------------------------- The least-squares likelihood value = -23600.617858 Deviance = 47201.23572 Number of estimated parameters = 1 STARTING VALUES --------------- sigma(0)_squared = 39.14163 Tau(0) INTRCPT1,B0 2.82047
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 12.647176 0.153054 82.632 158 0.000 MEANSES, G01 5.865861 0.370606 15.828 158 0.000 ---------------------------------------------------------------------------- The value of the likelihood function at iteration 1 = -2.347982E+004 The value of the likelihood function at iteration 2 = -2.347974E+004 The value of the likelihood function at iteration 3 = -2.347973E+004 The value of the likelihood function at iteration 4 = -2.347972E+004 The value of the likelihood function at iteration 5 = -2.347972E+004 . . . The value of the likelihood function at iteration 5 = -2.347972E+004 Iterations stopped due to small change in likelihood function
******* ITERATION 6 ******* Sigma_squared = 39.15708 Tau INTRCPT1,B0 2.63870 Tau (as correlations) INTRCPT1,B0 1.000 ---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, B0 0.740 ---------------------------------------------------- The value of the likelihood function at iteration 6 = -2.347972E+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 12.648336 0.149280 84.729 158 0.000 MEANSES, G01 5.863538 0.361457 16.222 158 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 12.648336 0.148382 85.242 158 0.000 MEANSES, G01 5.863538 0.320211 18.311 158 0.000 ---------------------------------------------------------------------------- Final estimation of variance components: ----------------------------------------------------------------------------- Random Effect Standard Variance df Chi-square P-value Deviation Component ----------------------------------------------------------------------------- INTRCPT1, U0 1.62441 2.63870 158 633.51745 0.000 level-1, R 6.25756 39.15708 ----------------------------------------------------------------------------- Statistics for current covariance components model -------------------------------------------------- Deviance = 46959.446954 Number of estimated parameters = 2 |