Program: HLM 6 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: HLM3S.EXE (6.00.24282.2) Date: 12 December 2004, Sunday Time: 20:30:19 ------------------------------------------------------------------------------- SPECIFICATIONS FOR THIS HLM3 RUN Problem Title: UNCONDITIONAL LINEAR GROWTH MODEL The data source for this run = eg.mdm The command file for this run = whlmtemp.hlm Output file name = EG1.OUT The maximum number of level-1 units = 7230 The maximum number of level-2 units = 1721 The maximum number of level-3 units = 60 The maximum number of iterations = 100 Method of estimation: full maximum likelihood The outcome variable is MATH The model specified for the fixed effects was: ---------------------------------------------------- Level-1 Level-2 Level-3 Coefficients Predictors Predictors --------------------- --------------- ---------------- INTRCPT1, P0 INTRCPT2, B00 INTRCPT3, G000 %MOBILITY, G001 #* FEMALE, B01 INTRCPT3, G010 LOWINC, G011 YEAR slope, P1 INTRCPT2, B10 INTRCPT3, G100 %MOBILITY, G101 # BLACK, B11 INTRCPT3, G110 %MOBILITY, G111 #* GRADE slope, P2 # INTRCPT2, B20 INTRCPT3, G200 #*HISPANIC, B21 INTRCPT3, G210 '#' - The residual parameter variance for the parameter has been set to zero '*' - This variable has been centered around its group mean '%' - This variable has been centered around its grand mean Summary of the model specified (in equation format) --------------------------------------------------- Level-1 Model Y = P0 + P1*(YEAR) + P2*(GRADE) + E Level-2 Model P0 = B00 + B01*(FEMALE) + R0 P1 = B10 + B11*(BLACK) + R1 P2 = B20 + B21*(HISPANIC) Level-3 Model B00 = G000 + G001(MOBILITY) + U00 B01 = G010 + G011(LOWINC) B10 = G100 + G101(MOBILITY) + U10 B11 = G110 + G111(MOBILITY) B20 = G200 B21 = G210 Least Squares Estimates ----------------------- sigma_squared = 1.13612 The outcome variable is MATH Least-squares estimates of fixed effects ---------------------------------------------------------------------------- Standard Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, P0 For INTRCPT2, B00 INTRCPT3, G000 -0.868737 0.014799 -58.703 7220 0.000 MOBILITY, G001 -0.015963 0.000936 -17.063 7220 0.000 For FEMALE, B01 INTRCPT3, G010 -0.282050 0.078810 -3.579 7220 0.001 LOWINC, G011 0.003389 0.000957 3.541 7220 0.001 For YEAR slope, P1 For INTRCPT2, B10 INTRCPT3, G100 0.950623 0.025403 37.421 7220 0.000 MOBILITY, G101 -0.006109 0.001166 -5.238 7220 0.000 For BLACK, B11 INTRCPT3, G110 -0.160492 0.019372 -8.285 7220 0.000 MOBILITY, G111 0.005473 0.001379 3.968 7220 0.000 For GRADE slope, P2 For INTRCPT2, B20 INTRCPT3, G200 -0.106044 0.023661 -4.482 7220 0.000 For HISPANIC, B21 INTRCPT3, G210 -0.017956 0.042449 -0.423 7220 0.672 ---------------------------------------------------------------------------- The outcome variable is MATH Least-squares estimates of fixed effects (with robust standard errors) ---------------------------------------------------------------------------- Standard Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, P0 For INTRCPT2, B00 INTRCPT3, G000 -0.868737 0.067429 -12.884 7220 0.000 MOBILITY, G001 -0.015963 0.004674 -3.415 7220 0.001 For FEMALE, B01 INTRCPT3, G010 -0.282050 0.129743 -2.174 7220 0.030 LOWINC, G011 0.003389 0.001498 2.262 7220 0.024 For YEAR slope, P1 For INTRCPT2, B10 INTRCPT3, G100 0.950623 0.046336 20.516 7220 0.000 MOBILITY, G101 -0.006109 0.001659 -3.683 7220 0.000 For BLACK, B11 INTRCPT3, G110 -0.160492 0.035232 -4.555 7220 0.000 MOBILITY, G111 0.005473 0.002534 2.160 7220 0.031 For GRADE slope, P2 For INTRCPT2, B20 INTRCPT3, G200 -0.106044 0.042803 -2.477 7220 0.013 For HISPANIC, B21 INTRCPT3, G210 -0.017956 0.027820 -0.645 7220 0.518 ---------------------------------------------------------------------------- The least-squares likelihood value = -10720.269914 Deviance = 21440.53983 Number of estimated parameters = 11 For starting values, data from 7230 level-1 and 1721 level-2 records were used STARTING VALUES --------------- Sigma_squared(0) = 0.29489 Tau(pi)(0) INTRCPT1,P0 0.72274 0.05301 YEAR,P1 0.05301 0.01756 Tau(beta)(0) INTRCPT1 YEAR INTRCPT2,B00 INTRCPT2,B10 0.08781 0.00072 0.00072 0.00847 The value of the likelihood function at iteration 1 = -8.172607E+003 The value of the likelihood function at iteration 2 = -8.137648E+003 The value of the likelihood function at iteration 3 = -8.135602E+003 The value of the likelihood function at iteration 4 = -8.134971E+003 The value of the likelihood function at iteration 5 = -8.134630E+003 . . . The value of the likelihood function at iteration 9 = -8.132144E+003 The value of the likelihood function at iteration 10 = -8.132143E+003 The value of the likelihood function at iteration 11 = -8.132142E+003 The value of the likelihood function at iteration 12 = -8.132141E+003 Iterations stopped due to small change in likelihood function ******* ITERATION 13 ******* Sigma_squared = 0.29854 Standard Error of Sigma_squared = 0.00654 Tau(pi) INTRCPT1,P0 0.63676 0.05290 YEAR,P1 0.05290 0.01290 Tau(pi) (as correlations) INTRCPT1,P0 1.000 0.584 YEAR,P1 0.584 1.000 Standard Errors of Tau(pi) INTRCPT1,P0 0.02500 0.00506 YEAR,P1 0.00506 0.00201 ---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, P0 0.839 YEAR, P1 0.212 ---------------------------------------------------- Tau(beta) INTRCPT1 YEAR INTRCPT2,B00 INTRCPT2,B10 0.10309 0.00993 0.00993 0.00848 Tau(beta) (as correlations) INTRCPT1/INTRCPT2,B00 1.000 0.336 YEAR/INTRCPT2,B10 0.336 1.000 Standard Errors of Tau(beta) INTRCPT1 YEAR INTRCPT2,B00 INTRCPT2,B10 0.02475 0.00526 0.00526 0.00205 ---------------------------------------------------- Random level-2 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1/INTRCPT2, B00 0.749 YEAR/INTRCPT2, B10 0.741 ---------------------------------------------------- The value of the likelihood function at iteration 13 = -8.132141E+003 The outcome variable is MATH Final estimation of fixed effects: ---------------------------------------------------------------------------- Standard Approx. Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, P0 For INTRCPT2, B00 INTRCPT3, G000 -0.831777 0.048485 -17.156 58 0.000 MOBILITY, G001 -0.018109 0.003607 -5.021 58 0.000 For FEMALE, B01 INTRCPT3, G010 -0.244955 0.127642 -1.919 1719 0.055 LOWINC, G011 0.002636 0.001545 1.705 1719 0.088 For YEAR slope, P1 For INTRCPT2, B10 INTRCPT3, G100 0.908400 0.030349 29.931 58 0.000 MOBILITY, G101 -0.002793 0.001362 -2.050 58 0.045 For BLACK, B11 INTRCPT3, G110 -0.027838 0.020049 -1.389 1719 0.165 MOBILITY, G111 0.000908 0.001359 0.668 1719 0.504 For GRADE slope, P2 For INTRCPT2, B20 INTRCPT3, G200 -0.142357 0.025236 -5.641 7220 0.000 For HISPANIC, B21 INTRCPT3, G210 0.041914 0.025446 1.647 7220 0.099 ---------------------------------------------------------------------------- The outcome variable is MATH Final estimation of fixed effects (with robust standard errors) ---------------------------------------------------------------------------- Standard Approx. Fixed Effect Coefficient Error T-ratio d.f. P-value ---------------------------------------------------------------------------- For INTRCPT1, P0 For INTRCPT2, B00 INTRCPT3, G000 -0.831777 0.048485 -17.155 58 0.000 MOBILITY, G001 -0.018109 0.003475 -5.211 58 0.000 For FEMALE, B01 INTRCPT3, G010 -0.244955 0.138431 -1.770 1719 0.077 LOWINC, G011 0.002636 0.001593 1.654 1719 0.098 For YEAR slope, P1 For INTRCPT2, B10 INTRCPT3, G100 0.908400 0.040001 22.710 58 0.000 MOBILITY, G101 -0.002793 0.001173 -2.382 58 0.021 For BLACK, B11 INTRCPT3, G110 -0.027838 0.020705 -1.345 1719 0.179 MOBILITY, G111 0.000908 0.001218 0.745 1719 0.456 For GRADE slope, P2 For INTRCPT2, B20 INTRCPT3, G200 -0.142357 0.037105 -3.837 7220 0.000 For HISPANIC, B21 INTRCPT3, G210 0.041914 0.026228 1.598 7220 0.110 ---------------------------------------------------------------------------- Final estimation of level-1 and level-2 variance components: ------------------------------------------------------------------------------ Random Effect Standard Variance df Chi-square P-value Deviation Component ------------------------------------------------------------------------------ INTRCPT1, R0 0.79797 0.63676 1660 7503.18775 0.000 YEAR slope, R1 0.11358 0.01290 1660 2156.04618 0.000 level-1, E 0.54639 0.29854 ------------------------------------------------------------------------------ Final estimation of level-3 variance components: ------------------------------------------------------------------------------ Random Effect Standard Variance df Chi-square P-value Deviation Component ------------------------------------------------------------------------------ INTRCPT1/INTRCPT2, U00 0.32107 0.10309 58 366.19367 0.000 YEAR/INTRCPT2, U10 0.09209 0.00848 58 299.78527 0.000 ------------------------------------------------------------------------------ Statistics for current covariance components model -------------------------------------------------- Deviance = 16264.282868 Number of estimated parameters = 17 Exploratory Analysis: estimated level-2 coefficients and their standard errors obtained by regressing EB residuals on level-2 predictors selected for possible inclusion in subsequent runs ----------------------------------------------------------------------------- Level-1 Coefficient Potential Level-2 Predictors ----------------------------------------------------------------------------- BLACK HISPANIC INTRCPT1, P0 Coefficient -0.356 -0.045 Standard Error 0.067 0.070 t value -5.355 -0.648 FEMALE HISPANIC YEAR, P1 Coefficient 0.004 -0.003 Standard Error 0.004 0.007 t value 1.150 -0.442 Exploratory Analysis: estimated level-3 coefficients and their standard errors obtained by regressing EB residuals on level-3 predictors selected for possible inclusion in subsequent runs ----------------------------------------------------------------------------- Level-2 Predictor Potential Level-3 Predictors ----------------------------------------------------------------------------- SIZE INTRCPT1/INTRCPT2, B00 Coefficient -0.000 Standard Error 0.000 t value -1.020 SIZE LOWINC YEAR/INTRCPT2, B10 Coefficient -0.000 -0.001 Standard Error 0.000 0.000 t value -1.012 -1.878