------------------------------------------------------------------------------ Module: HLM2 (5.33) Date: Dec 26, 2003 Time: 11:00:22 ------------------------------------------------------------------------------ SPECIFICATIONS FOR THIS HLM2 RUN Problem Title: no title The data source for this run = EXAMPLE.MDM The command file for this run = F:\DyadBook\Chapter 4\model.hlm Output file name = F:\DyadBook\Chapter 4\hlm2.out The maximum number of level-1 units = 20 The maximum number of level-2 units = 10 The maximum number of iterations = 100 Method of estimation: restricted maximum likelihood Weighting Specification ----------------------- Weight Variable Weighting? Name Normalized? Level 1 no Level 2 no The outcome variable is FUTURE The model specified for the fixed effects was: ---------------------------------------------------- Level-1 Level-2 Coefficients Predictors ---------------------- --------------- INTRCPT1, B0 INTRCPT2, G00 CULTURE, G01 # CONTRIB slope, B1 INTRCPT2, G10 CULTURE, G11 '#' - The residual parameter variance for this level-1 coefficient has been set to zero. 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 + B1*(CONTRIB) + R Level-2 Model B0 = G00 + G01*(CULTURE) + U0 B1 = G10 + G11*(CULTURE) Level-1 OLS regressions ----------------------- Level-2 Unit INTRCPT1 ------------------------------------------------------------------------------ 1 89.90187 2 60.06542 3 51.33645 4 62.63084 5 47.46729 6 86.85661 7 77.82170 8 78.67830 9 70.53491 10 92.14339 The average OLS level-1 coefficient for INTRCPT1 = 71.74368 Least Squares Estimates ----------------------- sigma_squared = 202.61019 The outcome variable is FUTURE Least-squares estimates of fixed effects ---------------------------------------------------------------------------- Standard Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, B0 INTRCPT2, G00 71.743678 3.222764 22.262 16 0.000 CULTURE, G01 -9.463304 3.222764 -2.936 16 0.010 For CONTRIB slope, B1 INTRCPT2, G10 0.557797 0.337112 1.655 16 0.117 CULTURE, G11 0.429119 0.337112 1.273 16 0.222 ---------------------------------------------------------------------------- The outcome variable is FUTURE 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 71.743678 3.449355 20.799 16 0.000 CULTURE, G01 -9.463304 3.449355 -2.743 16 0.015 For CONTRIB slope, B1 INTRCPT2, G10 0.557797 0.260682 2.140 16 0.048 CULTURE, G11 0.429119 0.260682 1.646 16 0.119 ---------------------------------------------------------------------------- The robust standard errors are appropriate for datasets having a moderate to large number of level 2 units. These data do not meet this criterion. The least-squares likelihood value = -75.681159 Deviance = 151.36232 Number of estimated parameters = 1 STARTING VALUES --------------- sigma(0)_squared = 46.08760 Tau(0) INTRCPT1,B0 150.76165 The outcome variable is FUTURE 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 71.813131 4.186549 17.153 8 0.000 CULTURE, G01 -9.061133 4.186549 -2.164 8 0.062 For CONTRIB slope, B1 INTRCPT2, G10 0.825912 0.255297 3.235 16 0.006 CULTURE, G11 0.475421 0.255297 1.862 16 0.081 ---------------------------------------------------------------------------- The value of the likelihood function at iteration 1 = -7.150256E+001 The value of the likelihood function at iteration 2 = -7.147207E+001 The value of the likelihood function at iteration 3 = -7.146538E+001 The value of the likelihood function at iteration 4 = -7.146366E+001 The value of the likelihood function at iteration 5 = -7.146291E+001 . . . The value of the likelihood function at iteration 5 = -7.146291E+001 The value of the likelihood function at iteration 6 = -7.146289E+001 The value of the likelihood function at iteration 7 = -7.146289E+001 Iterations stopped due to small change in likelihood function ******* ITERATION 8 ******* Sigma_squared = 43.76266 Tau INTRCPT1,B0 176.42668 Tau (as correlations) INTRCPT1,B0 1.000 ---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, B0 0.890 ---------------------------------------------------- The value of the likelihood function at iteration 8 = -7.146289E+001 The outcome variable is FUTURE Final estimation of fixed effects: ---------------------------------------------------------------------------- Standard Approx. Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, B0 INTRCPT2, G00 71.830862 4.469434 16.072 8 0.000 CULTURE, G01 -9.032863 4.469434 -2.021 8 0.077 For CONTRIB slope, B1 INTRCPT2, G10 0.844758 0.255669 3.304 16 0.005 CULTURE, G11 0.487241 0.255669 1.906 16 0.074 ---------------------------------------------------------------------------- The outcome variable is FUTURE 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 71.830862 3.847896 18.668 8 0.000 CULTURE, G01 -9.032863 3.847896 -2.347 8 0.047 For CONTRIB slope, B1 INTRCPT2, G10 0.844758 0.175792 4.805 16 0.000 CULTURE, G11 0.487241 0.175792 2.772 16 0.014 ---------------------------------------------------------------------------- The robust standard errors are appropriate for datasets having a moderate to large number of level 2 units. These data do not meet this criterion. Final estimation of variance components: ----------------------------------------------------------------------------- Random Effect Standard Variance df Chi-square P-value Deviation Component ----------------------------------------------------------------------------- INTRCPT1, U0 13.28257 176.42668 8 69.08382 0.000 level-1, R 6.61534 43.76266 ----------------------------------------------------------------------------- Statistics for current covariance components model -------------------------------------------------- Deviance = 142.925780 Number of estimated parameters = 2