Roger,<div><br></div><div>I agree with you that a simple effect seems out of place here. To get at simple effects, there are two options:</div><div><br></div><div>1) run the model without only primecent as a predictor on the halves of the data (loosing power).</div>
<div><br></div><div>2) recode your variables using treatment coding. To be overly explicit (since treatment coding is the default in R):</div><div><span class="Apple-style-span" style="font-family: Tahoma; font-size: 13px; border-collapse: collapse; "><p class="MsoNormal" style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; ">
<font class="Apple-style-span" face="'Times New Roman'"><span class="Apple-style-span" style="font-size: medium;"><br></span></font></p><p class="MsoNormal" style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; ">
<span lang="EN-US"><font size="3"><font face="Times New Roman">> contrasts(L2prim$lang) <- contr.treatment(L2prim$lang)</font></font></span></p><p class="MsoNormal" style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; ">
<font class="Apple-style-span" face="'Times New Roman'"><span class="Apple-style-span" style="font-size: medium;"><span class="Apple-style-span" style="font-family: Tahoma; font-size: 13px; "></span></span></font></p>
<font class="Apple-style-span" face="'Times New Roman'"><p class="MsoNormal" style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; "><span lang="EN-US"><font size="3"><font face="Times New Roman">> contrasts(L2prim$prime) <- contr.treatment(L2prim$prime)</font></font></span></p>
<p class="MsoNormal" style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 0pt; margin-left: 0cm; "><font class="Apple-style-span" face="'Times New Roman'"><span class="Apple-style-span" style="font-size: medium;">> primanal=lmer(score ~lang*prime + (1|PID) + (1|ITEM), data=L2prim, family = "binomial")</span></font></p>
<div><font class="Apple-style-span" face="'Times New Roman'"><span class="Apple-style-span" style="font-size: medium;"><br></span></font></div></font></span><font class="Apple-style-span" face="'Times New Roman'"></font><p>
</p></div><div>In such a model, the "main" effects are actually simple (main) effects. For example, the coefficient of lang will give give you the effect of Lang if Prime == 0, where as the effect of Lang for Prime == 1 corresponds to the sum of the interaction coefficient and the coefficient of Lang. Now, the problem, of course, is that treatment coding leads to collinearity between the "main" effects and the interaction (even in a balanced sample). In a perfectly balanced sample, the correlation (not the fixed effect correlation) will be .33, which is still ok. As long as unbalance due to data exclusion is pretty much random, this correlation should not go up much beyond .38 (I did some simulation).<br>
</div><div><br></div><div>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.</div>
<div><br></div><div>HTH,</div><div><br></div><div>Florian</div><div><br></div><div><br><div class="gmail_quote">On Wed, Dec 16, 2009 at 7:27 AM, Roger van-Gompel <span dir="ltr"><<a href="mailto:r.p.g.vangompel@dundee.ac.uk">r.p.g.vangompel@dundee.ac.uk</a>></span> wrote:<br>
<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 style="font-size:10pt;font-family:'Courier New'">Hi there,</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span style="font-size:10pt;font-family:'Courier New'"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span style="font-size:10pt;font-family:'Courier New'">I have a 2 (language: Swe vs. Eng) x 2 (prime: pp vs. do) design and was wondering how I do simple effects in mixed logit models.<span> </span>I could delete one level of a variable and then analyse the other level of a variable (e.g., Swe pp vs. Swe do), but I suspect that that’s not the appropriate way of doing it.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span style="font-size:10pt;font-family:'Courier New'"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span style="font-size:10pt;font-family:'Courier New'">I have attached my analyses and output. Note that my variables are effect coded.<span> </span>I don’t have an interaction and so strictly speaking, I shouldn’t analyse simple effects, but reviewers have asked us to.</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span style="font-size:10pt;font-family:'Courier New'"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span style="font-size:10pt;font-family:'Courier New'">Thanks a lot for any help!</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span style="font-size:10pt;font-family:'Courier New'"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span style="font-size:10pt;font-family:'Courier New'">Roger van Gompel</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span style="font-size:10pt;font-family:'Courier New'"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span style="font-size:10pt;font-family:'Courier New'"> </span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">> library(lme4)</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">> L2prim = read.table("forLME.txt", header=TRUE)</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">> L2prim$langcent <- scale(as.numeric(L2prim$language)) </font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">> L2prim$primecent <- scale(as.numeric(L2prim$prime))</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">> L2prim$PID=as.factor(L2prim$PID)</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">> L2prim$ITEM=as.factor(L2prim$ITEM)</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">> head(L2prim)</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"><span> </span>LIST PID ITEM language prime score<span> </span>langcent<span> </span>primecent</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">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></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">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></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">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></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">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></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">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></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">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></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">> primanal=lmer(score ~langcent*primecent + (1|PID) + (1|ITEM), data=L2prim, family = "binomial")</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">> summary(primanal)</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">Generalized linear mixed model fit using PQL </font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">Formula: score ~ langcent * primecent + (1 | PID) + (1 | ITEM) </font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"><span> </span>Data: L2prim </font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"><span> </span>Family: binomial(logit link)</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"><span> </span>AIC<span> </span>BIC<span> </span>logLik deviance</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"><span> </span>559.0337 590.1759 -272.5168 545.0337</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">Random effects:</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"><span> </span>Groups Name<span> </span>Variance Std.Dev.</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"><span> </span>ITEM<span> </span>(Intercept) 2.2551<span> </span>1.5017<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"><span> </span>PID<span> </span>(Intercept) 2.5343<span> </span>1.5919<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"># of obs: 632, groups: ITEM, 40; PID, 32</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">Estimated scale (compare to 1)<span> </span>0.880811 </font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">Fixed effects:</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"><span> </span>Estimate Std. Error<span> </span>z value Pr(>|z|)<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">(Intercept)<span> </span>-0.946211<span> </span>0.393646 -2.40371 0.016230 * </font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">langcent<span> </span>0.012060<span> </span>0.108898<span> </span>0.11075 0.911818<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">primecent<span> </span>0.337744<span> </span>0.110732<span> </span>3.05010 0.002288 **</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">langcent:primecent -0.099484<span> </span>0.109631 -0.90744 0.364172<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">---</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">Signif. codes:<span> </span>0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 </font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">Correlation of Fixed Effects:</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman"><span> </span>(Intr) lngcnt prmcnt</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">langcent<span> </span>-0.001<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">primecent<span> </span>-0.025 -0.033<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font face="Times New Roman" size="3">lngcnt:prmc<span> </span>0.007 -0.048 -0.005</font></span></p><br>
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