Hi Roger,<div><br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div style="margin:4px 4px 1px;font:10pt Tahoma"><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span class="Apple-style-span" style="font-family: &#39;Courier New&#39;; ">I have a quite lot of missing responses, and as you can see in the summary of the results, there are correlations between the “main” effects and the interaction.<span>  </span>But you say “not the fixed effect correlation”, so are you referring to a different correlation?</span></p>
</div></div></blockquote><div><br></div><div>I just meant that the specific numbers I gave were those of the correlations between the two variables (cor()). Fixed effect correlations are a somewhat complicated beast, so I wasn&#39;t talking about them, but usually when the correlations are high, the fixed effect correlations are high, too.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div style="margin:4px 4px 1px;font:10pt Tahoma"><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span class="Apple-style-span" style="font-family: &#39;Courier New&#39;; ">I haven’t done the model comparisons yet.<span>  </span>You said:</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">In any case, since ANOVA are omnibus test, you can get at least that by simple comparing the above model to a model without the interaction or without any of the simple (main) effects (using anova(model1, model2)). Model comparison is robust against collinearity.</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">I find it hard to conceptualize what the model comparisons tell me.<span>  </span>What can I conclude if the model with which I got the simple effect differs from a model without the interaction or without any of the simple effects?</font></span></p>
</div></blockquote><div><br></div><div>I had a somewhat hard time finding what you did in your code below, but I was thinking that you can just compare the models with and without a simple effect. if the comparison is significant, the simple effect matters. I put up some code that might be generally helpful at <a href="http://hlplab.wordpress.com/2009/12/18/some-r-code-to-understand-the-difference-between-treatment-and-sum-anova-style-coding/">http://hlplab.wordpress.com/2009/12/18/some-r-code-to-understand-the-difference-between-treatment-and-sum-anova-style-coding/</a>, but I didn&#39;t have time to clean things up. Let me know what you think.</div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div style="margin:4px 4px 1px;font:10pt Tahoma">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">My previous analyses were done with R 2.2.0.<span>  </span>I have now updated to 2.10.1 and suddenly, all the coefficients are different, which I find a bit worrying.<span>  </span>The p-values are now quite a bit larger, although the new R version doesn’t change any of the conclusions that I can draw from the data.</font></span></p>
</div></blockquote><div><br></div><div>wow. That is worrisome. I&#39;d be interested to hear what other people&#39;s experience with R 2.10.1 is. I haven&#39;t upgraded yet. </div><div><br></div><div>Btw, I had a quick look at your code below and I have two thoughts:</div>
<div><ul><li>you can treatment code automatically, by saying:</li><ul><li>contrasts(factor) &lt;- contr.treatment(numer_of_levels_of_factor)</li><li>e.g. contrasts(language) &lt;- contr.treatment(2)</li><li>the contrasts() command creates attributes to the variable which regression functions are sensitive to. i.e. if you put a factor into a regression function (such as lmer) the regression will use the contrast-coding specified by contrasts. to see what the contrasts are, simply enter contrasts(factor).</li>
<li>as a matter of fact, treatment coding is the default in R. so, if you just throw in a factor into a regression, R will treatment code it. </li></ul><li>an easy way to create a new variable that contains the contrast coding uses the ifelse statement:</li>
<ul><li>data$LanguageSwedish &lt;- ifelse(data$language == &quot;swe&quot;, 1, 0)</li></ul></ul><div>maybe useful?</div><div><br></div><div>Florian</div></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div style="margin:4px 4px 1px;font:10pt Tahoma">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Roger</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; library(lme4)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Loading required package: Matrix</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Loading required package: lattice</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim = read.table(&quot;forLME.txt&quot;, header=TRUE)<span>  </span># open data file</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; head(L2prim) # show first 6 lines</font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>  </span>LIST PID ITEM language prime score</font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>    </span>1<span>   </span>2<span>    </span>4<span>      </span>swe<span>    </span>do<span>     </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>    </span>1<span>   </span>2<span>    </span>7<span>      </span>swe<span>    </span>do<span>     </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>    </span>1<span>   </span>2<span>    </span>8<span>      </span>swe<span>    </span>pp<span>     </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>    </span>1<span>   </span>2<span>   </span>20<span>    </span><span>  </span>swe<span>    </span>pp<span>     </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>    </span>1<span>   </span>2<span>   </span>22<span>      </span>eng<span>    </span>pp<span>     </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>    </span>1<span>   </span>2<span>   </span>23<span>      </span>swe<span>    </span>pp<span>     </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # effect code vars so that they can be interpreted as main effects in ANOVAs</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim$langcent &lt;- scale(as.numeric(L2prim$language)) # effect code language</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim$primecent &lt;- scale(as.numeric(L2prim$prime))<span>  </span># effect code prime</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim$PID=as.factor(L2prim$PID)<span>  </span># convert subject no to factor</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim$ITEM=as.factor(L2prim$ITEM)<span>  </span># convert item no to factor</font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; head(L2prim)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>  </span>LIST PID ITEM language prime score<span>  </span>langcent<span>  </span>primecent</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>    </span>1<span>   </span>2<span>    </span>4<span>      </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>    </span>1<span>   </span>2<span>    </span>7<span>      </span>swe<span>    </span>do<span>     </span>0<span>  </span>1.008740 -0.9742244</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>    </span>1<span>   </span>2<span>    </span>8<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>    </span>1<span>   </span>2<span>   </span>20<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>    </span>1<span>   </span>2<span>   </span>22<span>      </span>eng<span>    </span>pp<span>     </span>0 -0.989767<span>  </span>1.0248334</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>    </span>1<span>   </span>2<span>   </span>23<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # mixed logit model with variables effect coded (main effects as in ANOVA)</font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; primanal=lmer(score ~langcent*primecent + (1|PID) + (1|ITEM), data=L2prim, family = &quot;binomial&quot;)</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; summary(primanal)</font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Generalized linear mixed model fit by the Laplace approximation </font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Formula: score ~ langcent * primecent + (1 | PID) + (1 | ITEM) </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>   </span>Data: L2prim </font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>   </span>AIC<span>   </span>BIC logLik deviance</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>650.5 677.2 -319.2<span>   </span><span> </span>638.5</font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Random effects:</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>Groups Name<span>        </span>Variance Std.Dev.</font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>ITEM<span>   </span>(Intercept) 1.9705<span>   </span>1.4037<span>  </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>PID<span>    </span>(Intercept) 2.2791<span>   </span>1.5097<span>  </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Number of obs: 632, groups: ITEM, 40; PID, 32</font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Fixed effects:</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>                   </span>Estimate Std. Error z value Pr(&gt;|z|)<span>  </span><span>  </span></font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">(Intercept)<span>        </span>-1.06339<span>    </span>0.37331<span>  </span>-2.849 0.004392 ** </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">langcent<span>            </span>0.01506<span>    </span>0.10822<span>   </span>0.139 0.889334<span>    </span></font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">primecent<span>           </span>0.36986<span>    </span>0.11024<span>   </span>3.355 0.000793 ***</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">langcent:primecent -0.10630<span>    </span>0.10898<span>  </span>-0.975 0.329365<span>    </span></font></span></p><div class="im">

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">---</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Signif. codes:<span>  </span>0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Correlation of Fixed Effects:</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>            </span>(Intr) lngcnt prmcnt</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">langcent<span>    </span>-0.001<span>              </span></font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">primecent<span>   </span>-0.028 -0.030<span>       </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">lngcnt:prmc<span>  </span>0.008 -0.055 -0.008</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # Analysis of simple effect of prime for Swedish (coded as 0)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[,2:3] # Outputs col 2 and 3 (to check no of rows)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>    </span>PID ITEM</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>     </span>2<span>    </span>4</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>     </span>2<span>    </span>7</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>     </span>2<span>    </span>8</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>     </span>2<span>   </span>20</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>     </span>2<span>   </span>22</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>     </span>2<span>   </span>23</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">629<span>  </span>34<span>   </span>35</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">630<span>  </span>34<span>   </span>36</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">631<span>  </span>34<span>   </span>37</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">632<span>  </span>34<span>   </span>38</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # create column for language that is treatment coded</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; x =c(1:632)<span>   </span># creates 632 rows of numbers</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; x[1:632] = 0<span>    </span># sets the numbers to 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; cbind(L2prim,x)<span>   </span># adds the 0s to L2prim</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>    </span>LIST PID ITEM language prime score<span>  </span>langcent<span>  </span>primecent x</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>      </span>1<span>   </span>2<span>    </span>4<span>     </span><span> </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>      </span>1<span>   </span>2<span>    </span>7<span>      </span>swe<span>    </span>do<span>     </span>0<span>  </span>1.008740 -0.9742244 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>      </span>1<span>   </span>2<span>    </span>8<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>      </span>1<span>   </span>2<span>   </span>20<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>      </span>1<span>   </span>2<span>   </span>22<span>      </span>eng<span>    </span>pp<span>     </span>0 -0.989767<span>  </span>1.0248334 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>      </span>1<span>   </span>2<span>   </span>23<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">629<span>    </span>4<span>  </span>34<span>   </span>35<span>      </span>eng<span>    </span>pp<span>     </span>1 -0.989767<span>  </span>1.0248334 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">630<span>    </span>4<span>  </span>34<span>   </span>36<span>      </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">631<span>    </span>4<span>  </span>34<span>   </span>37<span>      </span>eng<span>    </span>pp<span>     </span>1 -0.989767<span>  </span>1.0248334 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">632<span>    </span>4<span>  </span>34<span>   </span>38<span>      </span>eng<span>    </span>do<span>     </span>0 -0.989767 -0.9742244 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[L2prim[,4] ==&quot;swe&quot;,9] = 0<span>   </span># recodes swe (col 4) into 1 (col 9)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[L2prim[,4] ==&quot;eng&quot;,9] = 1<span>   </span># recodes eng (col 4) into 0 (col 9)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # create column for prime that is treatment coded</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; y =c(1:632)<span>   </span># creates 632 rows of numbers</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; y[1:632] = 0<span>    </span># sets the numbers to 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; cbind(L2prim,y)<span>   </span># adds the 0s to L2prim</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>    </span>LIST PID ITEM language prime score<span>  </span>langcent<span>  </span>primecent V9 y</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>      </span>1<span>   </span>2<span>    </span>4<span>      </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244<span>  </span>0 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>      </span>1<span>   </span>2<span>    </span>7<span>      </span>swe<span>    </span>do<span>     </span>0<span>  </span>1.008740 -0.9742244<span>  </span>0 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>      </span>1<span>   </span>2<span>    </span>8<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>0 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>      </span>1<span>   </span>2<span>   </span>20<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>0 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>      </span>1<span>   </span>2<span>   </span>22<span>    </span><span>  </span>eng<span>    </span>pp<span>     </span>0 -0.989767<span>  </span>1.0248334<span>  </span>1 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>      </span>1<span>   </span>2<span>   </span>23<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>0 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">629<span>    </span>4<span>  </span>34<span>   </span>35<span>      </span>eng<span>    </span>pp<span>     </span>1 -0.989767<span>  </span>1.0248334<span>  </span>1 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">630<span>    </span>4<span>  </span>34<span>   </span>36<span>      </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244<span>  </span>0 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">631<span>    </span>4<span>  </span>34<span>   </span>37<span>      </span>eng<span>    </span>pp<span>     </span>1 -0.989767<span>  </span>1.0248334<span>  </span>1 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">632<span>    </span>4<span>  </span>34<span>   </span>38<span>      </span>eng<span>    </span>do<span>     </span>0 -0.989767 -0.9742244<span>  </span>1 0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[L2prim[,5] ==&quot;do&quot;,10] = 1<span>   </span># recodes do (col 5) into 1 (col 10)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[L2prim[,5] ==&quot;pp&quot;,10] = 0<span>   </span># recodes pp (col 5) into 0 (col 10)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim$langtreat=as.factor(L2prim$V9) # convert language (v9) into factor</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim$primetreat=as.factor(L2prim$V10) # convert prime (v10) into factor</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[1:20,] # Outputs rows 1-20</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>   </span>LIST PID ITEM language prime score<span>  </span>langcent<span>  </span>primecent V9 V10 langtreat</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>     </span>1<span>   </span>2<span>    </span>4<span>      </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244<span>  </span>0<span>   </span>1<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>     </span>1<span>   </span>2<span>    </span>7<span>      </span>swe<span>    </span>do<span>     </span>0<span>  </span>1.008740 -0.9742244<span>  </span>0<span>   </span>1<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>     </span>1<span>   </span>2<span>    </span>8<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>     </span>1<span>   </span>2<span>   </span>20<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>     </span>1<span>   </span>2<span>   </span>22<span>      </span>eng<span>    </span>pp<span>     </span>0 -0.989767<span>  </span>1.0248334<span>  </span>1<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>     </span>1<span>   </span>2<span>   </span>23<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">20<span>    </span>1<span>   </span>3<span>   </span>10<span>      </span>eng<span>    </span>pp<span>     </span>0 -0.989767<span>  </span>1.0248334<span>  </span>1<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>   </span>primetreat</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>           </span>1</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>           </span>1</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>           </span>0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>           </span>0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>           </span>0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>           </span>0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">20<span>          </span>0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # mixed logit model with variables treatment coded</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; primanal=lmer(score ~langtreat*primetreat + (1|PID) + (1|ITEM), data=L2prim, family = &quot;binomial&quot;)</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; summary(primanal)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Generalized linear mixed model fit by the Laplace approximation </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Formula: score ~ langtreat * primetreat + (1 | PID) + (1 | ITEM) </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>   </span>Data: L2prim </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>   </span>AIC<span>   </span>BIC logLik deviance</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>650.5 677.2 -319.2<span>    </span>638.5</font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Random effects:</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>Groups Name<span>        </span>Variance Std.Dev.</font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>ITEM<span>   </span>(Intercept) 1.9705<span>   </span>1.4038<span>  </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>PID<span>    </span>(Intercept) 2.2791<span>   </span>1.5097<span>  </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Number of obs: 632, groups: ITEM, 40; PID, 32</font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Fixed effects:</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>                       </span>Estimate Std. Error z value Pr(&gt;|z|)<span>  </span></font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">(Intercept)<span>             </span>-0.7790<span>     </span>0.4155<span>  </span>-1.875<span>   </span>0.0608 .</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">langtreat1<span>               </span>0.1875<span>     </span>0.3022<span>   </span>0.621<span>   </span>0.5348<span>  </span></font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">primetreat1<span>             </span>-0.5251<span>     </span>0.3100<span>  </span>-1.694<span>   </span>0.0903 .</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">langtreat1:primetreat1<span>  </span>-0.4246<span>     </span>0.4354<span>  </span>-0.975 <span>  </span>0.3294<span>  </span></font></span></p>
<div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">---</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Signif. codes:<span>  </span>0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Correlation of Fixed Effects:</font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>            </span>(Intr) lngtr1 prmtr1</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">langtreat1<span>  </span>-0.364<span>              </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">primetreat1 -0.354<span>  </span>0.477<span>       </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">lngtrt1:pr1<span>  </span>0.262 -0.699 -0.703</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # primetreat is the simple effect of prime on Swedish</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # the sum of the estimates for primetreat and the interaction (0.9497) is the simple effect </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # of prime on English (no z and p values can be calculated)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # Analysis of simple effect of prime for English (coded as 0)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[,2:3] # Outputs col 2 and 3 (to check no of rows)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>    </span>PID ITEM</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>     </span>2<span>    </span>4</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>     </span>2<span>    </span>7</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>     </span>2<span>    </span>8</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>     </span>2<span>   </span>20</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>     </span>2<span>   </span>22</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>     </span>2<span>   </span>23</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">629<span>  </span>34<span>   </span>35</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">630<span>  </span>34<span>   </span>36</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">631<span>  </span>34<span>   </span>37</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">632<span>  </span>34<span>   </span>38</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; x =c(1:632)<span>   </span># creates 632 rows of numbers</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; x[1:632] = 0<span>    </span># sets the numbers to 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; cbind(L2prim,x)<span>   </span># adds the 0s to L2prim</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>    </span>LIST PID ITEM language prime score<span>  </span>langcent<span>  </span>primecent V9 V10 langtreat</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>      </span>1<span>   </span>2<span>    </span>4<span>      </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244<span>  </span>0<span>   </span>1<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>   </span><span>   </span>1<span>   </span>2<span>    </span>7<span>      </span>swe<span>    </span>do<span>     </span>0<span>  </span>1.008740 -0.9742244<span>  </span>0<span>   </span>1<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>      </span>1<span>   </span>2<span>    </span>8<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>      </span>1<span>   </span>2<span>   </span>20<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>      </span>1<span>   </span>2<span>   </span>22<span>      </span>eng<span>   </span><span> </span>pp<span>     </span>0 -0.989767<span>  </span>1.0248334<span>  </span>1<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>      </span>1<span>   </span>2<span>   </span>23<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">629<span>    </span>4<span>  </span>34<span>   </span>35<span>      </span>eng<span>    </span>pp<span>     </span>1 -0.989767<span>  </span>1.0248334<span>  </span>1<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">630<span>    </span>4<span>  </span>34<span>   </span>36<span>      </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244<span>  </span>0<span>   </span>1<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">631<span>    </span>4<span>  </span>34<span>   </span>37<span>      </span>eng<span>    </span>pp<span>     </span>1 -0.989767<span>  </span>1.0248334<span>  </span>1<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">632<span>    </span>4<span>  </span>34<span>   </span>38<span>      </span>eng<span>    </span>do<span>     </span>0 -0.989767 -0.9742244<span>  </span>1<span>   </span>1<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>    </span>primetreat x</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>            </span>1 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>            </span>1 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>            </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>         </span><span>   </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>            </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>            </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">629<span>          </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">630<span>          </span>1 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">631<span>          </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">632<span>          </span>1 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[L2prim[,4] ==&quot;swe&quot;,9] = 1<span>   </span># recodes swe (col 4) into 1 (col 9)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[L2prim[,4] ==&quot;eng&quot;,9] = 0<span>   </span># recodes eng (col 4) into 0 (col 9)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; y =c(1:632)<span>   </span># creates 632 rows of numbers</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; y[1:632] = 0<span>    </span># sets the numbers to 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; cbind(L2prim,y)<span>   </span># adds the 0s to L2prim</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>    </span>LIST PID ITEM language prime score<span>  </span>langcent<span>  </span>primecent V9 V10 langtreat</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>      </span>1<span>   </span>2<span>    </span>4<span>      </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244<span>  </span>1<span>   </span>1<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>      </span>1<span>   </span>2<span>    </span>7<span>      </span>swe<span>    </span>do<span>     </span>0<span>  </span>1.008740 -0.9742244<span>  </span>1<span>   </span>1<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>      </span>1<span>   </span>2<span>    </span>8<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>1<span>   </span>0<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>      </span>1<span>   </span>2<span>   </span>20<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>1<span>   </span>0 <span>        </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>      </span>1<span>   </span>2<span>   </span>22<span>      </span>eng<span>    </span>pp<span>     </span>0 -0.989767<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>      </span>1<span>   </span>2<span>   </span>23<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>1<span>   </span>0<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">629<span>    </span>4<span>  </span>34<span>   </span>35<span>      </span>eng<span>    </span>pp<span>     </span>1 -0.989767<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">630<span>    </span>4<span>  </span>34<span>  </span><span> </span>36<span>      </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244<span>  </span>1<span>   </span>1<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">631<span>    </span>4<span>  </span>34<span>   </span>37<span>      </span>eng<span>    </span>pp<span>     </span>1 -0.989767<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">632<span>    </span>4<span>  </span>34<span>   </span>38<span>      </span>eng<span>    </span>do<span>     </span>0 -0.989767 -0.9742244<span>  </span>0<span>   </span>1<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>    </span>primetreat y</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>            </span>1 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>    </span><span>        </span>1 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>            </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>            </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>            </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>            </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">628<span>          </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">629<span>          </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">630<span>          </span>1 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">631<span>          </span>0 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">632<span>          </span>1 0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[L2prim[,5] ==&quot;do&quot;,10] = 1<span>   </span># recodes do (col 5) into 1 (col 10)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[L2prim[,5] ==&quot;pp&quot;,10] = 0<span>   </span># recodes pp (col 5) into 0 (col 10)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim$langtreat=as.factor(L2prim$V9)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim$primetreat=as.factor(L2prim$V10)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; L2prim[1:20,] # Outputs rows 1-20</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>   </span>LIST PID ITEM language prime score<span>  </span>langcent<span>  </span>primecent V9 V10 langtreat</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>     </span>1<span>   </span>2<span>    </span>4<span>      </span>swe<span>    </span>do<span>     </span>1<span>  </span>1.008740 -0.9742244<span>  </span>1<span>   </span>1<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>     </span>1<span>   </span>2<span>    </span>7<span>      </span>swe<span>    </span>do<span>     </span>0<span>  </span>1.008740 -0.9742244<span>  </span>1<span>   </span>1<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>     </span>1<span>   </span>2<span>    </span>8<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>1<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>     </span>1<span>   </span>2<span>   </span>20<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>1<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>     </span>1<span>   </span>2<span>   </span>22<span>      </span>eng<span>    </span>pp<span>     </span>0 -0.989767<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>     </span>1<span>   </span>2<span>   </span>23<span>      </span>swe<span>    </span>pp<span>     </span>0<span>  </span>1.008740<span>  </span>1.0248334<span>  </span>1<span>   </span>0<span>         </span>1</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">20<span>    </span>1<span>   </span>3<span>   </span>10<span>      </span>eng<span>    </span>pp<span>     </span>0 -0.989767<span>  </span>1.0248334<span>  </span>0<span>   </span>0<span>         </span>0</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>   </span>primetreat</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">1<span>           </span>1</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">2<span>           </span>1</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">3<span>           </span>0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">4<span>           </span>0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">5<span>           </span>0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">6<span>           </span>0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">20<span>          </span>0</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; primanal=lmer(score ~langtreat*primetreat + (1|PID) + (1|ITEM), data=L2prim, family = &quot;binomial&quot;)</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; summary(primanal)</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Generalized linear mixed model fit by the Laplace approximation </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Formula: score ~ langtreat * primetreat + (1 | PID) + (1 | ITEM) </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>   </span>Data: L2prim </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>   </span>AIC<span>   </span>BIC logLik deviance</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>650.5 677.2 -319.2<span>    </span>638.5</font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Random effects:</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>Groups Name<span>        </span>Variance Std.Dev.</font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>ITEM<span>   </span>(Intercept) 1.9705<span>   </span>1.4038<span>  </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span> </span>PID<span>    </span>(Intercept) 2.2791<span>   </span>1.5097<span>  </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Number of obs: 632, groups: ITEM, 40; PID, 32</font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Fixed effects:</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>                       </span>Estimate Std. Error z value Pr(&gt;|z|)<span>   </span></font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">(Intercept)<span>             </span>-0.5915<span>     </span>0.4153<span>  </span>-1.424 <span> </span>0.15435<span>   </span></font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">langtreat1<span>              </span>-0.1875<span>     </span>0.3022<span>  </span>-0.621<span>  </span>0.53489<span>   </span></font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">primetreat1<span>             </span>-0.9496<span>     </span>0.3095<span>  </span>-3.068<span>  </span>0.00215 **</font></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">langtreat1:primetreat1<span>   </span>0.4244<span>     </span>0.4354<span>   </span>0.975<span>  </span>0.32973<span>   </span></font></span></p>
<div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">---</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Signif. codes:<span>  </span>0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">Correlation of Fixed Effects:</font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New"><span>            </span>(Intr) lngtr1 prmtr1</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">langtreat1<span>  </span>-0.363<span>              </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">primetreat1 -0.354<span>  </span>0.507<span>       </span></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">lngtrt1:pr1<span>  </span>0.247 -0.699 -0.702</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # primetreat is the simple effect of prime on English</font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # the sum of the estimates for primetreat and the interaction (0.5252) is the simple effect </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Courier New">&gt; # of prime on Swedish (no z and p values can be calculated)</font></span></p><div class="im"><br>

    <p>
      The University of Dundee is a registered Scottish charity, No: SC015096
    </p>
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</blockquote></div><br></div>