<html lang=en> <meta http-equiv="content-type" content="text/html;charset=utf-8" /> <body bgcolor="FFFFFF" fgcolor="000000"> <h1> <table width = "99%"> <tr> <td width="25%">Program:</td> <td width="75%" align="right">HLM 7 Hierarchical Linear and Nonlinear Modeling</td> </tr> <tr> <td width="25%">Authors:</td> <td width="75%" align="right">Stephen Raudenbush, Tony Bryk, & Richard Congdon</td> </tr> <tr> <td width="25%">Publisher:</td> <td width="75%" align="right">Scientific Software International, Inc. (c) 2010</td> </tr> <tr> <td /> <td align="right"> techsupport@ssicentral.com<br />www.ssicentral.com </td> </tr> </table> <hr /> </h1> <h2> <table width = "50%"> <tr> <td width="25%">Module:</td> <td width="75%" align="right">HLM2.EXE (7.00.21103.1002)</td> </tr> <tr> <td width="25%">Date:</td> <td width="75%" align="right">25 October 2017, Wednesday</td> </tr> <tr> <td width="25%">Time:</td> <td width="75%" align="right">16:53:25</td> </tr> </table> <hr /> </h2> <br /> <br> <h2>Specifications for this HLM2 run</h2> Problem Title: no title<br> <br> The data source for this run = popular2.mdm<br> The command file for this run = D:\Dropbox\MLMbook\book2\New or Corrected Data\2 Basic Model\popular.hlm<br> Output file name = D:\Dropbox\MLMbook\book2\New or Corrected Data\2 Basic Model\hlm2.html<br> The maximum number of level-1 units = 2000<br> The maximum number of level-2 units = 100<br> The maximum number of iterations = 100<br> <br> Method of estimation: full maximum likelihood<br> <br> The outcome variable is POPULAR <h3>Summary of the model specified</h3> <h4>Level-1 Model</h4> <i>POPULAR</i><sub><small><i>ij</i></small></sub> = <i>β</i><sub><small><i>0j</i></small></sub> + <i>β</i><sub><small><i>1j</i></small></sub>*(<i>EXTRAV</i><sub><small><i>ij</i></small></sub>) + <i>β</i><sub><small><i>2j</i></small></sub>*(<i>SEX</i><sub><small><i>ij</i></small></sub>) + <i>r</i><sub><small><i>ij</i></small></sub> <br> <h4>Level-2 Model</h4> <i>β</i><sub><small><i>0j</i></small></sub> = <i>γ</i><sub><small><i>00</i></small></sub> + <i>γ</i><sub><small><i>01</i></small></sub>*(<i>TEXP</i><sub><small><i>j</i></small></sub>) + <i>u</i><sub><small><i>0j</i></small></sub><br> <i>β</i><sub><small><i>1j</i></small></sub> = <i>γ</i><sub><small><i>10</i></small></sub> + <i>u</i><sub><small><i>1j</i></small></sub><br> <i>β</i><sub><small><i>2j</i></small></sub> = <i>γ</i><sub><small><i>20</i></small></sub> <br> <h4>Mixed Model</h4> <i>POPULAR</i><sub><small><i>ij</i></small></sub> = <i>γ</i><sub><small><i>00</i></small></sub> + <i>γ</i><sub><small><i>01</i></small></sub>*<i>TEXP</i><sub><small><i>j</i></small></sub> <br> + <i>γ</i><sub><small><i>10</i></small></sub>*<i>EXTRAV</i><sub><small><i>ij</i></small></sub> <br> + <i>γ</i><sub><small><i>20</i></small></sub>*<i>SEX</i><sub><small><i>ij</i></small></sub> <br> + <i>u</i><sub><small><i>0j</i></small></sub> + <i>u</i><sub><small><i>1j</i></small></sub>*<i>EXTRAV</i><sub><small><i>ij</i></small></sub> + <i>r</i><sub><small><i>ij</i></small></sub><br> </tbody></table> <h2>Final Results - Iteration 9</h2><b>Iterations stopped due to small change in likelihood function</b><br> <br> σ<sup>2</sup> = 0.55181<br> <br> Standard error of σ<sup>2</sup> = 0.01837<br> <br> τ<table border=0 cellpadding=0><tbody><tr><td>INTRCPT1,<i>β</i><sub><small><i>0</i></small></sub> </td><td align=right> 1.28143</td><td align=right> -0.18475</td></tr><tr><td> EXTRAV,<i>β</i><sub><small><i>1</i></small></sub> </td><td align=right> -0.18475</td><td align=right> 0.03392</td></tr></tbody></table> <br> Standard errors of τ<table border=0 cellpadding=0><tbody><tr><td>INTRCPT1,<i>β</i><sub><small><i>0</i></small></sub> </td><td align=right> 0.28119</td><td align=right> 0.04655</td></tr><tr><td> EXTRAV,<i>β</i><sub><small><i>1</i></small></sub> </td><td align=right> 0.04655</td><td align=right> 0.00833</td></tr></tbody></table> <br> τ (as correlations)<table border=0 cellpadding=0><tbody><tr><td>INTRCPT1,<i>β</i><sub><small><i>0</i></small></sub> </td><td align=right> 1.000</td><td align=right> -0.886</td></tr><tr><td> EXTRAV,<i>β</i><sub><small><i>1</i></small></sub> </td><td align=right> -0.886</td><td align=right> 1.000</td></tr></tbody></table><br> <table border=1 cellpadding=3 style='border-collapse:collapse;border:none'> <tr> <td align=left style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>Random level-1 coefficient</td> <td style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> Reliability estimate</td> <tbody> <tr><td style='border:none;padding:0in 5.4pt 0in 5.4pt'> INTRCPT1,<i>β</i><sub><small><i>0</i></sub></small><td align=center style='border:none;padding:0in 5.4pt 0in 5.4pt'>0.633</td></tr> <tr><td style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> EXTRAV,<i>β</i><sub><small><i>1</i></sub></small><td align=center style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>0.564</td></tr> </tbody></table> The value of the log-likelihood function at iteration 9 = -2.406403E+003<br> <h4> Final estimation of fixed effects:<br> </h4><table border=1 cellpadding=3 style='border-collapse:collapse;border:none'> <tr> <td align=left style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>Fixed Effect</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> Coefficient</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> Standard<br> error</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> <i>t</i>-ratio</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> Approx.<br><i>d.f.</i></td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> <i>p</i>-value</td> </tr> <tbody> <tr><td align=left colspan=6 style='border:none;padding:0in 5.4pt 0in 5.4pt'> For INTRCPT1, <i>β</i><sub><small><i>0</i></small></sub> </td></tr> <tr><td style='border:none;padding:0in 5.4pt 0in 5.4pt'> INTRCPT2, <i>γ</i><sub><small><i>00</i></small></sub> </td><td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.738568</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.195209</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 3.783</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'>98</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'><0.001</td> </tr><tr><td style='border:none;padding:0in 5.4pt 0in 5.4pt'> TEXP, <i>γ</i><sub><small><i>01</i></small></sub> </td><td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.090813</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.008598</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 10.563</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'>98</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'><0.001</td> </tr><tr><td align=left colspan=6 style='border:none;padding:0in 5.4pt 0in 5.4pt'> For EXTRAV slope, <i>β</i><sub><small><i>1</i></small></sub> </td></tr> <tr><td style='border:none;padding:0in 5.4pt 0in 5.4pt'> INTRCPT2, <i>γ</i><sub><small><i>10</i></small></sub> </td><td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.452641</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.024478</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 18.491</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'>99</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'><0.001</td> </tr><tr><td align=left colspan=6 style='border:none;padding:0in 5.4pt 0in 5.4pt'> For SEX slope, <i>β</i><sub><small><i>2</i></small></sub> </td></tr> <tr><td style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> INTRCPT2, <i>γ</i><sub><small><i>20</i></small></sub> </td><td align=right valign=bottom style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> 1.252470</td> <td align=right valign=bottom style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> 0.036554</td> <td align=right valign=bottom style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> 34.263</td> <td align=right valign=bottom style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>1799</td> <td align=right valign=bottom style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'><0.001</td> </tr></tbody></table> <br> <h4> Final estimation of fixed effects<br> (with robust standard errors) </h4><table border=1 cellpadding=3 style='border-collapse:collapse;border:none'> <tr> <td align=left style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>Fixed Effect</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> Coefficient</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> Standard<br> error</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> <i>t</i>-ratio</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> Approx.<br><i>d.f.</i></td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> <i>p</i>-value</td> </tr> <tbody> <tr><td align=left colspan=6 style='border:none;padding:0in 5.4pt 0in 5.4pt'> For INTRCPT1, <i>β</i><sub><small><i>0</i></small></sub> </td></tr> <tr><td style='border:none;padding:0in 5.4pt 0in 5.4pt'> INTRCPT2, <i>γ</i><sub><small><i>00</i></small></sub> </td><td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.738568</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.199352</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 3.705</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'>98</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'><0.001</td> </tr><tr><td style='border:none;padding:0in 5.4pt 0in 5.4pt'> TEXP, <i>γ</i><sub><small><i>01</i></small></sub> </td><td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.090813</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.008711</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 10.425</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'>98</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'><0.001</td> </tr><tr><td align=left colspan=6 style='border:none;padding:0in 5.4pt 0in 5.4pt'> For EXTRAV slope, <i>β</i><sub><small><i>1</i></small></sub> </td></tr> <tr><td style='border:none;padding:0in 5.4pt 0in 5.4pt'> INTRCPT2, <i>γ</i><sub><small><i>10</i></small></sub> </td><td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.452641</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.024561</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'> 18.430</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'>99</td> <td align=right valign=bottom style='border:none;padding:0in 5.4pt 0in 5.4pt'><0.001</td> </tr><tr><td align=left colspan=6 style='border:none;padding:0in 5.4pt 0in 5.4pt'> For SEX slope, <i>β</i><sub><small><i>2</i></small></sub> </td></tr> <tr><td style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> INTRCPT2, <i>γ</i><sub><small><i>20</i></small></sub> </td><td align=right valign=bottom style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> 1.252470</td> <td align=right valign=bottom style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> 0.034903</td> <td align=right valign=bottom style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> 35.884</td> <td align=right valign=bottom style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>1799</td> <td align=right valign=bottom style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'><0.001</td> </tr></tbody></table> <br> <h4>Final estimation of variance components</h4> <table border=1 cellpadding=3 style='border-collapse:collapse;border:none'> <tr> <td align=left style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>Random Effect</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>Standard<br> Deviation</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>Variance<br> Component</td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> <i>d.f.</i></td> <td align=center style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>χ<sup><small>2</small></sup></td> <td align=right style='border:none;border-top:solid windowtext 1.5pt;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'><i>p</i>-value</td> </tr> <tbody> <tr><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'> INTRCPT1, <i>u</i><sub><small><i>0</i></small></sub></td><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'> 1.13200</td><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'> 1.28143</td><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'> 98</td><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'> 288.64116</td><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'><0.001</td></tr> <tr><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'> EXTRAV slope, <i>u</i><sub><small><i>1</i></small></sub></td><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.18417</td><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'> 0.03392</td><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'> 99</td><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'> 237.61747</td><td align=right style='border:none;padding:0in 5.4pt 0in 5.4pt'><0.001</td></tr> <tr><td align=right style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'>level-1, <i>r</i></td><td align=right style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> 0.74284</td><td align=right style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> 0.55181</td><td style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> </td><td style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> </td><td style='border:none;border-bottom:solid windowtext 1.5pt;padding:0in 5.4pt 0in 5.4pt'> </td></tr> </tbody></table> <h4>Statistics for the current model</h4> Deviance = 4812.806967<br> Number of estimated parameters = 8<br> </body></html>