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: 7:50 ------------------------------------------------------------------------------- SPECIFICATIONS FOR THIS HLM2 RUN Sun Jul 10 16:07:50 2005 ------------------------------------------------------------------------------- Problem Title: ONE-WAY ANOVA (TABLE 4.2, P. 70) The data source for this run = C:\Documents and Settings\user\Desktop\HSB_Modelos\ANOVA\HDB12.ssm The command file for this run = C:\Documents and Settings\user\Desktop\HSB_Modelos\ANOVA\anova.hlm Output file name = C:\Documents and Settings\user\Desktop\HSB_Modelos\ANOVA\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 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
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 = 47.31026 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 0.081145 157.099 7184 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 7184 0.000 ---------------------------------------------------------------------------- The least-squares likelihood value = -24051.458626 Deviance = 48102.91725 Number of estimated parameters = 1 STARTING VALUES --------------- sigma(0)_squared = 39.14163 Tau(0) INTRCPT1,B0 8.78270
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 12.636711 0.246541 51.256 159 0.000 ---------------------------------------------------------------------------- The value of the likelihood function at iteration 1 = -2.355841E+004 The value of the likelihood function at iteration 2 = -2.355840E+004 The value of the likelihood function at iteration 3 = -2.355840E+004 Iterations stopped due to small change in likelihood function
******* ITERATION 4 ******* Sigma_squared = 39.14831 Tau INTRCPT1,B0 8.61431 Tau (as correlations) INTRCPT1,B0 1.000 ---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, B0 0.901 ---------------------------------------------------- The value of the likelihood function at iteration 4 = -2.355840E+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 12.636972 0.244412 51.704 159 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 12.636972 0.243628 51.870 159 0.000 ---------------------------------------------------------------------------- Final estimation of variance components: ----------------------------------------------------------------------------- Random Effect Standard Variance df Chi-square P-value Deviation Component ----------------------------------------------------------------------------- INTRCPT1, U0 2.93501 8.61431 159 1660.23264 0.000 level-1, R 6.25686 39.14831 ----------------------------------------------------------------------------- Statistics for current covariance components model -------------------------------------------------- Deviance = 47116.793475 Number of estimated parameters = 2 Test of homogeneity of level-1 variance ---------------------------------------- Chi-square statistic = 297.95284 Number of degrees of freedom = 159 P-value = 0.000 A residual file, called anova_resi.sps, has been created. Note, some statistics could not be computed and a value of -99 has been entered. These should be recoded to 'missing values' before any analyses are performed. |