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: HLM3.EXE (6.06.2857.2) Date: 25 November 2008, Tuesday Time: 0:10:41 ------------------------------------------------------------------------------- SPECIFICATIONS FOR THIS HLM3 RUN Problem Title: no title The data source for this run = acvsall_pmle_upper_R_Rmob.mdm The command file for this run = C:\Documents and Settings\FSC\My Documents\akademik\WtP\HML\analyses\ACvsALL\Upper\upper_acvrsall_acpropnew2.hlm Output file name = c:\\hlm3.txt The maximum number of level-1 units = 14525 The maximum number of level-2 units = 4045 The maximum number of level-3 units = 115 The maximum number of iterations = 100 Method of estimation: full maximum likelihood The outcome variable is RSS The model specified for the fixed effects was: ---------------------------------------------------- Level-1 Level-2 Level-3 Coefficients Predictors Predictors --------------------- --------------- ---------------- INTRCPT1, P0 INTRCPT2, B00 INTRCPT3, G000 AC, G001 % NEWST1, G002 % NEWST2, G003 % NEWST3, G004 % NEWST5, G005 % NEWST6, G006 % LOGITPR, G007 #% NUMACHT, B01 INTRCPT3, G010 TIME3 slope, P1 INTRCPT2, B10 INTRCPT3, G100 AC, G101 % NEWST1, G102 % NEWST2, G103 % NEWST3, G104 % NEWST5, G105 % NEWST6, G106 % LOGITPR, G107 #% NUMACHT, B11 INTRCPT3, G110 TIME3SQ slope, P2 INTRCPT2, B20 INTRCPT3, G200 AC, G201 % NEWST1, G202 % NEWST2, G203 % NEWST3, G204 % NEWST5, G205 % NEWST6, G206 % LOGITPR, G207 #% NUMACHT, B21 INTRCPT3, G210 # RRETAKE slope, P3 # INTRCPT2, B30 INTRCPT3, G300 AC, G301 % NEWST1, G302 % NEWST2, G303 % NEWST3, G304 % NEWST5, G305 % NEWST6, G306 % LOGITPR, G307 #% NUMACHT, B31 INTRCPT3, G310 # ENTRY slope, P4 # INTRCPT2, B40 INTRCPT3, G400 AC, G401 % NEWST1, G402 % NEWST2, G403 % NEWST3, G404 % NEWST5, G405 % NEWST6, G406 % LOGITPR, G407 #% NUMACHT, B41 INTRCPT3, G410 '#' - The residual parameter variance for the parameter has been set to zero '%' - This variable has been centered around its grand mean Summary of the model specified (in equation format) --------------------------------------------------- Level-1 Model Y = P0 + P1*(TIME3) + P2*(TIME3SQ) + P3*(RRETAKE) + P4*(ENTRY) + E Level-2 Model P0 = B00 + B01*(NUMACHT) + R0 P1 = B10 + B11*(NUMACHT) + R1 P2 = B20 + B21*(NUMACHT) + R2 P3 = B30 + B31*(NUMACHT) P4 = B40 + B41*(NUMACHT) Level-3 Model B00 = G000 + G001(AC) + G002(NEWST1) + G003(NEWST2) + G004(NEWST3) + G005(NEWST5) + G006(NEWST6) + G007(LOGITPR) + U00 B01 = G010 B10 = G100 + G101(AC) + G102(NEWST1) + G103(NEWST2) + G104(NEWST3) + G105(NEWST5) + G106(NEWST6) + G107(LOGITPR) + U10 B11 = G110 B20 = G200 + G201(AC) + G202(NEWST1) + G203(NEWST2) + G204(NEWST3) + G205(NEWST5) + G206(NEWST6) + G207(LOGITPR) + U20 B21 = G210 B30 = G300 + G301(AC) + G302(NEWST1) + G303(NEWST2) + G304(NEWST3) + G305(NEWST5) + G306(NEWST6) + G307(LOGITPR) B31 = G310 B40 = G400 + G401(AC) + G402(NEWST1) + G403(NEWST2) + G404(NEWST3) + G405(NEWST5) + G406(NEWST6) + G407(LOGITPR) B41 = G410 Run-time deletion has reduced the number of level-1 records to 14488 For starting values, data from 11751 level-1 and 2332 level-2 records were used Iterations stopped due to small change in likelihood function ******* ITERATION 13 ******* Sigma_squared = 572.41560 Standard Error of Sigma_squared = 10.17820 Tau(pi) INTRCPT1,P0 941.73857 107.23884 -108.25648 TIME3,P1 107.23884 36.19167 -9.02778 TIME3SQ,P2 -108.25648 -9.02778 51.08164 Tau(pi) (as correlations) INTRCPT1,P0 1.000 0.581 -0.494 TIME3,P1 0.581 1.000 -0.210 TIME3SQ,P2 -0.494 -0.210 1.000 Standard Errors of Tau(pi) INTRCPT1,P0 31.52091 12.16284 14.91444 TIME3,P1 12.16284 8.99242 7.55156 TIME3SQ,P2 14.91444 7.55156 11.55560 ---------------------------------------------------- Random level-1 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1, P0 0.743 TIME3, P1 0.101 TIME3SQ, P2 0.107 ---------------------------------------------------- Note: The reliability estimates reported above are based on only 2332 of 4045 units that had sufficient data for computation. Fixed effects and variance components are based on all the data. Tau(beta) INTRCPT1 TIME3 TIME3SQ INTRCPT2,B00 INTRCPT2,B10 INTRCPT2,B20 116.42342 3.15246 -13.23148 3.15246 15.05640 -5.91235 -13.23148 -5.91235 11.08916 Tau(beta) (as correlations) INTRCPT1/INTRCPT2,B00 1.000 0.075 -0.368 TIME3/INTRCPT2,B10 0.075 1.000 -0.458 TIME3SQ/INTRCPT2,B20 -0.368 -0.458 1.000 Standard Errors of Tau(beta) INTRCPT1 TIME3 TIME3SQ INTRCPT2,B00 INTRCPT2,B10 INTRCPT2,B20 21.15902 6.41221 6.68303 6.41221 3.77607 2.83877 6.68303 2.83877 3.58013 ---------------------------------------------------- Random level-2 coefficient Reliability estimate ---------------------------------------------------- INTRCPT1/INTRCPT2, B00 0.722 TIME3/INTRCPT2, B10 0.507 TIME3SQ/INTRCPT2, B20 0.391 ---------------------------------------------------- Note: The reliability estimates reported above are based on only 112 of 115 units that had sufficient data for computation. Fixed effects and variance components are based on all the data. The value of the likelihood function at iteration 13 = -7.055337E+004 The outcome variable is RSS 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 613.142491 1.588645 385.953 107 0.000 AC, G001 1.181142 3.522163 0.335 107 0.738 NEWST1, G002 -23.977027 7.171071 -3.344 107 0.001 NEWST2, G003 -9.367051 5.579149 -1.679 107 0.096 NEWST3, G004 0.521875 4.511228 0.116 107 0.909 NEWST5, G005 2.908349 4.363034 0.667 107 0.506 NEWST6, G006 15.730135 5.053681 3.113 107 0.003 LOGITPR, G007 2.190570 2.610678 0.839 107 0.403 For NUMACHT, B01 INTRCPT3, G010 2.158532 0.421292 5.124 4043 0.000 For TIME3 slope, P1 For INTRCPT2, B10 INTRCPT3, G100 12.402795 0.854656 14.512 107 0.000 AC, G101 4.598338 1.804983 2.548 107 0.013 NEWST1, G102 0.585907 3.790286 0.155 107 0.878 NEWST2, G103 -0.109909 2.905187 -0.038 107 0.970 NEWST3, G104 -1.279699 2.309419 -0.554 107 0.580 NEWST5, G105 -6.603577 2.228642 -2.963 107 0.004 NEWST6, G106 -3.982482 2.654480 -1.500 107 0.136 LOGITPR, G107 -2.358023 1.430285 -1.649 107 0.102 For NUMACHT, B11 INTRCPT3, G110 0.306771 0.293609 1.045 4043 0.297 For TIME3SQ slope, P2 For INTRCPT2, B20 INTRCPT3, G200 -1.752003 0.755484 -2.319 107 0.022 AC, G201 -2.485836 1.576112 -1.577 107 0.117 NEWST1, G202 4.583979 3.320343 1.381 107 0.170 NEWST2, G203 2.618674 2.550169 1.027 107 0.307 NEWST3, G204 3.050141 2.038772 1.496 107 0.137 NEWST5, G205 3.906616 1.978299 1.975 107 0.050 NEWST6, G206 1.532180 2.342032 0.654 107 0.514 LOGITPR, G207 -0.142751 1.236159 -0.115 107 0.909 For NUMACHT, B21 INTRCPT3, G210 -0.657120 0.287990 -2.282 4043 0.023 For RRETAKE slope, P3 For INTRCPT2, B30 INTRCPT3, G300 6.914961 0.954733 7.243 14443 0.000 AC, G301 2.794984 1.516792 1.843 14443 0.065 NEWST1, G302 -1.174147 3.183955 -0.369 14443 0.712 NEWST2, G303 1.403632 2.459898 0.571 14443 0.568 NEWST3, G304 3.723011 1.907869 1.951 14443 0.051 NEWST5, G305 5.545763 1.838348 3.017 14443 0.003 NEWST6, G306 5.150173 2.226410 2.313 14443 0.021 LOGITPR, G307 1.471714 1.188863 1.238 14443 0.216 For NUMACHT, B31 INTRCPT3, G310 -0.093503 0.425112 -0.220 14443 0.826 For ENTRY slope, P4 For INTRCPT2, B40 INTRCPT3, G400 3.516097 0.993257 3.540 14443 0.001 AC, G401 5.076831 2.129519 2.384 14443 0.017 NEWST1, G402 5.375033 4.467783 1.203 14443 0.229 NEWST2, G403 4.145331 3.467918 1.195 14443 0.232 NEWST3, G404 -2.621424 2.753433 -0.952 14443 0.341 NEWST5, G405 -4.413658 2.635835 -1.674 14443 0.094 NEWST6, G406 -7.214082 3.214602 -2.244 14443 0.025 LOGITPR, G407 -3.137335 1.758360 -1.784 14443 0.074 For NUMACHT, B41 INTRCPT3, G410 0.409474 0.454325 0.901 14443 0.368 ---------------------------------------------------------------------------- The outcome variable is RSS 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 613.142491 1.628808 376.436 107 0.000 AC, G001 1.181142 2.667345 0.443 107 0.658 NEWST1, G002 -23.977027 8.437786 -2.842 107 0.006 NEWST2, G003 -9.367051 5.489760 -1.706 107 0.090 NEWST3, G004 0.521875 4.374194 0.119 107 0.906 NEWST5, G005 2.908349 4.916137 0.592 107 0.555 NEWST6, G006 15.730135 5.354291 2.938 107 0.005 LOGITPR, G007 2.190570 3.704751 0.591 107 0.555 For NUMACHT, B01 INTRCPT3, G010 2.158532 0.446842 4.831 4043 0.000 For TIME3 slope, P1 For INTRCPT2, B10 INTRCPT3, G100 12.402795 0.866454 14.314 107 0.000 AC, G101 4.598338 1.775074 2.591 107 0.011 NEWST1, G102 0.585907 3.943739 0.149 107 0.883 NEWST2, G103 -0.109909 3.098255 -0.035 107 0.972 NEWST3, G104 -1.279699 2.163284 -0.592 107 0.555 NEWST5, G105 -6.603577 2.336307 -2.827 107 0.006 NEWST6, G106 -3.982482 2.541742 -1.567 107 0.120 LOGITPR, G107 -2.358023 1.658369 -1.422 107 0.158 For NUMACHT, B11 INTRCPT3, G110 0.306771 0.340374 0.901 4043 0.368 For TIME3SQ slope, P2 For INTRCPT2, B20 INTRCPT3, G200 -1.752003 0.772402 -2.268 107 0.025 AC, G201 -2.485836 1.638495 -1.517 107 0.132 NEWST1, G202 4.583979 3.255320 1.408 107 0.162 NEWST2, G203 2.618674 2.532831 1.034 107 0.304 NEWST3, G204 3.050141 2.054908 1.484 107 0.141 NEWST5, G205 3.906616 1.837034 2.127 107 0.036 NEWST6, G206 1.532180 2.052154 0.747 107 0.457 LOGITPR, G207 -0.142751 0.942522 -0.151 107 0.880 For NUMACHT, B21 INTRCPT3, G210 -0.657120 0.288447 -2.278 4043 0.023 For RRETAKE slope, P3 For INTRCPT2, B30 INTRCPT3, G300 6.914961 0.904034 7.649 14443 0.000 AC, G301 2.794984 1.594865 1.752 14443 0.079 NEWST1, G302 -1.174147 2.990115 -0.393 14443 0.694 NEWST2, G303 1.403632 2.614473 0.537 14443 0.591 NEWST3, G304 3.723011 1.671580 2.227 14443 0.026 NEWST5, G305 5.545763 1.859174 2.983 14443 0.003 NEWST6, G306 5.150173 2.391713 2.153 14443 0.031 LOGITPR, G307 1.471714 1.262160 1.166 14443 0.244 For NUMACHT, B31 INTRCPT3, G310 -0.093503 0.440713 -0.212 14443 0.832 For ENTRY slope, P4 For INTRCPT2, B40 INTRCPT3, G400 3.516097 1.073218 3.276 14443 0.001 AC, G401 5.076831 2.140704 2.372 14443 0.018 NEWST1, G402 5.375033 4.853888 1.107 14443 0.269 NEWST2, G403 4.145331 3.262684 1.271 14443 0.204 NEWST3, G404 -2.621424 3.198314 -0.820 14443 0.413 NEWST5, G405 -4.413658 2.616206 -1.687 14443 0.091 NEWST6, G406 -7.214082 3.186003 -2.264 14443 0.024 LOGITPR, G407 -3.137335 1.747522 -1.795 14443 0.072 For NUMACHT, B41 INTRCPT3, G410 0.409474 0.438912 0.933 14443 0.351 ---------------------------------------------------------------------------- Final estimation of level-1 and level-2 variance components: ------------------------------------------------------------------------------ Random Effect Standard Variance df Chi-square P-value Deviation Component ------------------------------------------------------------------------------ INTRCPT1, R0 30.68776 941.73857 2219 9896.16476 0.000 TIME3 slope, R1 6.01595 36.19167 2219 2575.97426 0.000 TIME3SQ slope, R2 7.14714 51.08164 2219 2525.32931 0.000 level-1, E 23.92521 572.41560 ------------------------------------------------------------------------------ Note: The chi-square statistics reported above are based on only 2332 of 4045 units that had sufficient data for computation. Fixed effects and variance components are based on all the data. Final estimation of level-3 variance components: ------------------------------------------------------------------------------ Random Effect Standard Variance df Chi-square P-value Deviation Component ------------------------------------------------------------------------------ INTRCPT1/INTRCPT2, U00 10.78997 116.42342 104 401.14637 0.000 TIME3/INTRCPT2, U10 3.88026 15.05640 104 245.89434 0.000 TIME3SQ/INTRCPT2, U20 3.33004 11.08916 104 193.84716 0.000 ------------------------------------------------------------------------------ Note: The chi-square statistics reported above are based on only 112 of 115 units that had sufficient data for computation. Fixed effects and variance components are based on all the data. Statistics for current covariance components model -------------------------------------------------- Deviance = 141106.747997 Number of estimated parameters = 58 Model comparison test ----------------------------------- Chi-square statistic = 40.15200 Number of degrees of freedom = 5 P-value = 0.000 Latent Variable Regression Results B10 = G100* + G101*(AC) + G102*(NEWST1) + G103*(NEWST2) + G104*(NEWST3) + G105*(NEWST5) + G106*(NEWST6) + G107*(LOGITPR) + G108*(B00) + U10* B20 = G200* + G201*(AC) + G202*(NEWST1) + G203*(NEWST2) + G204*(NEWST3) + G205*(NEWST5) + G206*(NEWST6) + G207*(LOGITPR) + G208*(B00) + U20* ------------------------------------------------------------------------------ Outcome Predictor Estimated Standard T-ratio P-value Coefficient Error ------------------------------------------------------------------------------ TIME3/INTRCPT2,B10 INTRCPT3,G100* -4.199572 33.28265 -0.126 0.900 AC,G101* 4.566356 1.80132 2.535 0.013 NEWST1,G102* 1.235145 3.99427 0.309 0.758 NEWST2,G103* 0.143728 2.94050 0.049 0.961 NEWST3,G104* -1.293830 2.30262 -0.562 0.575 NEWST5,G105* -6.682328 2.22695 -3.001 0.004 NEWST6,G106* -4.408415 2.77994 -1.586 0.115 LOGITPR,G107* -2.417338 1.42935 -1.691 0.093 B00,G108* 0.027078 0.05426 0.499 0.618 TIME3SQ/INTRCPT2,B20 INTRCPT3,G200* 67.931441 30.38143 2.236 0.027 AC,G201* -2.351600 1.48792 -1.580 0.117 NEWST1,G202* 1.858997 3.34699 0.555 0.579 NEWST2,G203* 1.554111 2.44835 0.635 0.527 NEWST3,G204* 3.109452 1.92429 1.616 0.109 NEWST5,G205* 4.237149 1.87284 2.262 0.026 NEWST6,G206* 3.319905 2.34411 1.416 0.160 LOGITPR,G207* 0.106207 1.16801 0.091 0.928 B00,G208* -0.113650 0.04954 -2.294 0.024 ------------------------------------------------------------------------------ Latent Variable Regression: Comparison of Original and Adjusted Coefficients ------------------------------------------------------------------------------ Outcome Predictor Original Adjusted Difference Standard Coefficient Coefficient Error of Difference ------------------------------------------------------------------------------ TIME3/INTRCPT2,B10 INTRCPT3 12.40280 -4.19957 16.60237 33.27177 AC 4.59834 4.56636 0.03198 0.11491 NEWST1 0.58591 1.23515 -0.64924 1.31551 NEWST2 -0.10991 0.14373 -0.25364 0.53027 NEWST3 -1.27970 -1.29383 0.01413 0.12539 NEWST5 -6.60358 -6.68233 0.07875 0.19714 NEWST6 -3.98248 -4.40841 0.42593 0.86448 LOGITPR -2.35802 -2.41734 0.05932 0.13830 TIME3SQ/INTRCPT2,B20 INTRCPT3 -1.75200 67.93144 -69.68344 30.37371 AC -2.48584 -2.35160 -0.13424 0.40455 NEWST1 4.58398 1.85900 2.72498 1.44047 NEWST2 2.61867 1.55411 1.06456 0.78572 NEWST3 3.05014 3.10945 -0.05931 0.51335 NEWST5 3.90662 4.23715 -0.33053 0.51636 NEWST6 1.53218 3.31990 -1.78772 0.96802 LOGITPR -0.14275 0.10621 -0.24896 0.31592 ------------------------------------------------------------------------------ Var(u*) TIME3 TIME3SQ INTRCPT2 INTRCPT2 14.97104 -5.55407 -5.55407 9.58541