<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>FAQ/ManovaCov</title><revhistory><revision><revnumber>11</revnumber><date>2014-04-23 12:25:05</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>10</revnumber><date>2014-04-23 12:24:29</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>9</revnumber><date>2014-04-23 12:21:08</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>8</revnumber><date>2014-04-23 12:19:10</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>7</revnumber><date>2014-04-23 12:17:23</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>6</revnumber><date>2014-04-23 11:55:23</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>5</revnumber><date>2014-04-23 11:36:48</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>4</revnumber><date>2014-04-23 11:32:06</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>3</revnumber><date>2014-04-23 11:31:39</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>2</revnumber><date>2014-04-23 11:25:19</date><authorinitials>PeterWatson</authorinitials></revision><revision><revnumber>1</revnumber><date>2014-04-23 11:24:51</date><authorinitials>PeterWatson</authorinitials></revision></revhistory></articleinfo><section><title>Comparison of handling a varying covaruate (within subject) using SPSS MANOVA and SPSS MIXED</title><para>We illustrate using the data below with one time factor df() with three time points wach with a different covariate value cv() </para><screen><![CDATA[data list list
  / sub group dv1 dv2 dv3 cv1 cv2 cv3.
begin data.
1 1  3  4  7  3 1 2
2 1  6  8 12  9 3 1
3 1  7 13 11 11 8 4
4 1  0  3  6  6 2 1
5 2  5  6 11  7 8 3
6 2 10 12 18 15 9 5
7 2 10 15 15 14 8 6
8 2  5  7 11  9 2 8 
end data.]]></screen><para>Using MANOVA </para><screen><![CDATA[manova dv1 dv2 dv3 by group(1,2) with cv1 cv2 cv3
  /wsfactors trial (3)
  /wsdesign trial
  /design]]></screen><para>we obtain </para><para>Tests of Significance for T1 using UNIQUE sums of squares </para><informaltable><tgroup cols="11"><colspec colname="col_0"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3"/><colspec colname="col_4"/><colspec colname="col_5"/><colspec colname="col_6"/><colspec colname="col_7"/><colspec colname="col_8"/><colspec colname="col_9"/><colspec colname="col_10"/><tbody><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> <emphasis role="strong">Source</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">SS</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">DF</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">MS</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">F</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> Sig of F </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> WITHIN+RESIDUAL </para></entry><entry colsep="1" rowsep="1"><para> 33.81 </para></entry><entry colsep="1" rowsep="1"><para> 5 </para></entry><entry colsep="1" rowsep="1"><para> 6.76 </para></entry><entry colsep="1" rowsep="1"/><entry colsep="1" rowsep="1"/></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> REGRESSION </para></entry><entry colsep="1" rowsep="1"><para> 173.11 </para></entry><entry colsep="1" rowsep="1"><para> 1 </para></entry><entry colsep="1" rowsep="1"><para> 173.11 </para></entry><entry colsep="1" rowsep="1"><para> 25.60 </para></entry><entry colsep="1" rowsep="1"><para> .004 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> GROUP </para></entry><entry colsep="1" rowsep="1"><para> 5.09 </para></entry><entry colsep="1" rowsep="1"><para> 1 </para></entry><entry colsep="1" rowsep="1"><para> 5.09 </para></entry><entry colsep="1" rowsep="1"><para> .75 </para></entry><entry colsep="1" rowsep="1"><para> .425 </para></entry></row></tbody></tgroup></informaltable><itemizedlist><listitem override="none"><para>- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Regression analysis for WITHIN+RESIDUAL error term --- Individual Univariate .9500 confidence intervals Dependent variable .. T4 </para></listitem></itemizedlist><informaltable><tgroup cols="14"><colspec colname="col_0"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3"/><colspec colname="col_4"/><colspec colname="col_5"/><colspec colname="col_6"/><colspec colname="col_7"/><colspec colname="col_8"/><colspec colname="col_9"/><colspec colname="col_10"/><colspec colname="col_11"/><colspec colname="col_12"/><colspec colname="col_13"/><tbody><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para> <emphasis role="strong">COVARIATE</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">B</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">Beta</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">Std. Err.</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">t-Value</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> Sig of t </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">Lower -95%</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">CL-Upper</emphasis> </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_6" namest="col_0" rowsep="1"><para> T4 </para></entry><entry colsep="1" rowsep="1"><para> 1.398 </para></entry><entry colsep="1" rowsep="1"><para> 1.054 </para></entry><entry colsep="1" rowsep="1"><para> 0.276 </para></entry><entry colsep="1" rowsep="1"><para> 5.06 </para></entry><entry colsep="1" rowsep="1"><para> .004 </para></entry><entry colsep="1" rowsep="1"><para> 0.6878 </para></entry><entry colsep="1" rowsep="1"><para> 2.108 </para></entry></row></tbody></tgroup></informaltable><para>Tests involving 'TRIAL' Within-Subject Effect.  </para><itemizedlist><listitem override="none"><para>AVERAGED Tests of Significance for dv using UNIQUE sums of square </para></listitem></itemizedlist><informaltable><tgroup cols="11"><colspec colname="col_0"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3"/><colspec colname="col_4"/><colspec colname="col_5"/><colspec colname="col_6"/><colspec colname="col_7"/><colspec colname="col_8"/><colspec colname="col_9"/><colspec colname="col_10"/><tbody><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> <emphasis role="strong">Source</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">SS</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">DF</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">MS</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">F</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> Sig of F </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> WITHIN+RESIDUAL </para></entry><entry colsep="1" rowsep="1"><para> 24.51 </para></entry><entry colsep="1" rowsep="1"><para> 11 </para></entry><entry colsep="1" rowsep="1"><para> 2.23 </para></entry><entry colsep="1" rowsep="1"/><entry colsep="1" rowsep="1"/></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> REGRESSION </para></entry><entry colsep="1" rowsep="1"><para> .33 </para></entry><entry colsep="1" rowsep="1"><para> 1 </para></entry><entry colsep="1" rowsep="1"><para> .33 </para></entry><entry colsep="1" rowsep="1"><para> .15 </para></entry><entry colsep="1" rowsep="1"><para> .709 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> TRIAL </para></entry><entry colsep="1" rowsep="1"><para> 45.94 </para></entry><entry colsep="1" rowsep="1"><para> 2 </para></entry><entry colsep="1" rowsep="1"><para> 22.97 </para></entry><entry colsep="1" rowsep="1"><para> 10.31 </para></entry><entry colsep="1" rowsep="1"><para> .003 </para></entry></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> GROUP BY TRIAL </para></entry><entry colsep="1" rowsep="1"><para> 3.27 </para></entry><entry colsep="1" rowsep="1"><para> 2 </para></entry><entry colsep="1" rowsep="1"><para> 1.63 </para></entry><entry colsep="1" rowsep="1"><para> .73 </para></entry><entry colsep="1" rowsep="1"><para> .502 </para></entry></row></tbody></tgroup></informaltable><para>We then need to reformat the data into 'long format' using the varstocases syntax and then fit the repeated measures data with varying covariate as a mixed model. </para><screen><![CDATA[compute cvone=cv1.
]]><![CDATA[
varstocases
 /make dv from dv1 dv2 dv3
 /make cv from cv1 cv2 cv3
 /index = trial.
        
mixed dv by group trial with cv
  /fixed= group trial group*trial cv
  /repeated= trial | subject(sub) covtype(cs).]]></screen><informaltable><tgroup cols="11"><colspec colname="col_0"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3"/><colspec colname="col_4"/><colspec colname="col_5"/><colspec colname="col_6"/><colspec colname="col_7"/><colspec colname="col_8"/><colspec colname="col_9"/><colspec colname="col_10"/><tbody><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> <emphasis role="strong">Source</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">Num df</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">Denom DF</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">F</emphasis> </para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">Sig of F</emphasis> </para></entry><entry colsep="1" rowsep="1"/></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> Intercept </para></entry><entry colsep="1" rowsep="1"><para> 1 </para></entry><entry colsep="1" rowsep="1"><para> 12.80 </para></entry><entry colsep="1" rowsep="1"><para> 27.75 </para></entry><entry colsep="1" rowsep="1"><para> .000 </para></entry><entry colsep="1" rowsep="1"/></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> group </para></entry><entry colsep="1" rowsep="1"><para> 1 </para></entry><entry colsep="1" rowsep="1"><para> 5.881 </para></entry><entry colsep="1" rowsep="1"><para> 2.177 </para></entry><entry colsep="1" rowsep="1"><para> .191 </para></entry><entry colsep="1" rowsep="1"/></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> trial </para></entry><entry colsep="1" rowsep="1"><para> 2 </para></entry><entry colsep="1" rowsep="1"><para> 10.858 </para></entry><entry colsep="1" rowsep="1"><para> 12.708 </para></entry><entry colsep="1" rowsep="1"><para> .001 </para></entry><entry colsep="1" rowsep="1"/></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> group by trial </para></entry><entry colsep="1" rowsep="1"><para> 2 </para></entry><entry colsep="1" rowsep="1"><para> 10.287 </para></entry><entry colsep="1" rowsep="1"><para> 0.704 </para></entry><entry colsep="1" rowsep="1"><para> .517 </para></entry><entry colsep="1" rowsep="1"/></row><row rowsep="1"><entry colsep="1" nameend="col_5" namest="col_0" rowsep="1"><para> cv </para></entry><entry colsep="1" rowsep="1"><para> 1 </para></entry><entry colsep="1" rowsep="1"><para> 12.24 </para></entry><entry colsep="1" rowsep="1"><para> 0.081 </para></entry><entry colsep="1" rowsep="1"><para> .780 </para></entry><entry colsep="1" rowsep="1"/></row></tbody></tgroup></informaltable><para>The results using the two approaches are similar except for the group main effect which although non-significant in both has a lower significance level for the MANOVA. </para></section></article>