<br>Hi Roger,<div><br></div><div>sorry for the prolonged silence. deadlines ...</div><div><br></div><div><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"><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span class="Apple-style-span" style="font-family: 'Times New Roman'; font-size: medium; ">The correlation between my two independent variables (language and prime) is very low (after treatment coding):</span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">> cor(L2prim$LangSwe, L2prim$PrimePP) </font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">[1] 0.00292528</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">Does this make sense?</font></font></span></p></div></blockquote><div><br></div><div>yes, the independent variables themselves won't be correlated within a balanced data set. They will, however, be correlated with their interaction</div>
<div><br></div><div>cor<span class="Apple-style-span" style="font-family: 'Times New Roman'; font-size: medium; ">(L2prim$LangSwe, L2prim$LangSwe * L2prim$PrimePP)</span></div><div><font class="Apple-style-span" face="'Times New Roman'"><span class="Apple-style-span" style="font-size: medium;"><span class="Apple-style-span" style="font-family: arial; font-size: small; "><div>
cor<span class="Apple-style-span" style="font-family: 'Times New Roman'; font-size: medium; ">(L2prim$PrimePP, L2prim$LangSwe * L2prim$PrimePP)</span></div><div><font class="Apple-style-span" face="'Times New Roman'"><span class="Apple-style-span" style="font-size: medium;"><br>
</span></font></div><div><font class="Apple-style-span" face="'Times New Roman'"><span class="Apple-style-span" style="font-size: medium;">should be high.</span></font></div><blockquote class="gmail_quote" style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0.8ex; border-left-width: 1px; border-left-color: rgb(204, 204, 204); border-left-style: solid; padding-left: 1ex; ">
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<div style="margin:4px 4px 1px;font:10pt Tahoma"><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman"><span> </span>Given that there is no correlation, I can perhaps just report the analyses with treatment coding.<span> </span>But you said that it should be around .33, and somehow it’s much lower.<span> </span>I guess I still don’t understand what you meant.</font></font></span></p>
</div></blockquote><div><br></div><div>does the above help? </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><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">I have done the model comparisons as you suggest.<span> </span>When I use the following model:</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">primanaleng=lmer(score ~LangEng+LangEng:PrimePP + (1|PID) + (1|ITEM), data=L2prim, family = "binomial")</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">I appear to get both simple effects (simple effect of prime on English LangEng0:PrimePP2, and simple effect on Swedish LangEng1:PrimePP2).<span> </span>See APPENDIX 1.</font></font></span></p>
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<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">I then compare this model with:</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">primanalengnoint=lmer(score ~LangEng+PrimePP + (1|PID) + (1|ITEM), data=L2prim, family = "binomial")</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">The comparison shows that the models don’t significantly differ (APPENDIX 2).<span> </span>So I think I should conclude that the model with the simple effects is no better than without.</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">My question is: The model with the simple effects contains BOTH simple effects (effect of prime on English, and effect on Swedish).<span> </span>But I’d like to know whether ONE of the simple effects is significant/improves the model (e.g., effect of prime on English only).<span> </span>How do I get this with a model comparison?</font></font></span></p>
</div></blockquote><div><br></div><div>hmmm, verflixt ;). I gotta admit the ANOVA approach is more intuitive to me for this question, too. After I thought about it some more (though probably still not long enough), I know think that another way is better, though I hope other people may chime in (for practical purposes you may consider just running the analyses on the half-data sets and presenting this to the reviewers since the whole thing doesn't really make that much sense given that you don't have any sign of an interaction).</div>
<div><br></div><div>you could just code a contrast that only contrasts the simple effect, e.g.</div><div><br></div><div><div>d$lang0prim <- ifelse(d$lang == 0, ifelse(d$prim == 0, -1, 1), 0)</div><div><br></div><div>now what I am not so sure of is, if you would want to include the main effect that you're not interested in. so whether it should be</div>
<div><br></div><div>l.lang0prim <- lmer(score ~ lang + lang0prim + (1|s) + (1|i), d, family="binomial")</div><div>compared against</div><div><div>lmer(score ~ lang + (1|s) + (1|i), d, family="binomial")</div>
<div><br></div></div><div>or</div><div><br></div><div>l.lang0prim <- lmer(score ~ lang0prim + (1|s) + (1|i), d, family="binomial")</div><div>compare against</div><div><div>lmer(score ~ 1 + (1|s) + (1|i), d, family="binomial")</div>
<div><br></div></div><div>in the test I run they come out pretty much the same, but that isn't really satisfying. unfortunately, i don't have to time to go back to look at the logic of simple effects right so as compare the results to see whether any of what i say above makes a grain of sense (it's late in the year, you know). but if you feel like it you could use my code below and add the stuff above and compare it against a simple effect anova analyses (for a continuous variable). and hopefully some other people have some thoughts, too. sorry to have given you probably misleading information before! I think about it some more after my next deadline, but i didn't want to wait forever to answer =).</div>
</div><div><br></div><div>here's some code that I used to create data like yours. it may be useful in order to understand the relation between sum and treatment coding, though I now think it's not relevant to your question.</div>
<div><div><br></div><div># number of items and subjects</div><div>ni= 32</div><div>ns= 40</div><div><br></div><div># predictors</div><div>s= sort(rep(1:ns, ni))</div><div>l= rep(c(rep(1,ni), rep(2,ni), rep(3,ni), rep(4,ni)), ns/4)</div>
<div>i= rep(1:ni, ns)</div><div>lang=rep(c(1,0),(ni/2)*ns)</div><div>prim=rep(c(1,1,0,0),(ni/4)*ns)</div><div><br></div><div># noise</div><div>snoise= rnorm(ns, sd=2.5^0.5)</div><div>inoise= rnorm(ni, sd=2.3^0.5)</div><div>
<br></div><div># assumed effects under sum-coding</div><div><a href="http://sum.int">sum.int</a> = -0.95</div><div>sum.lang = 0.0</div><div>sum.prim = 0.34</div><div>sum.lp = -0.1</div><div><br></div><div># get effects for dummy coding</div>
<div># under assumption of perfectly balanced sample</div><div><a href="http://dum.int">dum.int</a>= <span class="Apple-tab-span" style="white-space:pre"> </span><a href="http://sum.int">sum.int</a> - sum.lang - sum.prim + sum.lp</div>
<div>dum.lang= <span class="Apple-tab-span" style="white-space:pre"> </span>2 * sum.lang - 2 * sum.lp</div><div>dum.prim= <span class="Apple-tab-span" style="white-space:pre"> </span>2 * sum.prim - 2 * sum.lp</div><div>dum.lp= <span class="Apple-tab-span" style="white-space:pre"> </span>2 * sum.lp</div>
<div><br></div><div>fixed= <a href="http://dum.int">dum.int</a> + dum.lang * lang + dum.prim * prim + dum.lp * lang * prime</div><div>score= rbinom(ns*ni, 1, plogis(fixed + snoise[s] + inoise[i]))</div><div><br></div><div>
# test</div><div>lapply(split(score, paste("x=",lang,",z=",prime)), mean)</div><div><br></div><div># dataframe</div><div>d <- as.data.frame(cbind(s,i,lang,prim,score))</div><div>d$s= as.factor(d$s)</div>
<div>d$i= as.factor(d$i)</div><div>d$lang = as.factor(d$lang)</div><div>d$prim = as.factor(d$prim)</div><div><br></div><div># analysis</div><div>library(lme4)</div><div>contrasts(d$lang) <- c(-1,1)</div><div>contrasts(d$prim) <- c(-1,1)</div>
<div>l.sum <- lmer(score ~ lang * prim + (1|s) + (1|i), d, family="binomial")</div><div>summary(l.sum)</div><div><br></div></div><div><div><br></div><div>contrasts(d$lang) <- c(0,1)</div><div>contrasts(d$prim) <- c(0,1)</div>
<div>l.treat <- lmer(score ~ lang * prim + (1|s) + (1|i), d, family="binomial")</div><div>summary(l.treat)</div><div><br></div></div><div><br></div><div><br></div><div><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
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<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">I have to admit that I don’t quite understand why treatment coding results in an analysis of simple effects.<span> </span>I am sure you are right, but it’s difficult for me to conceptualise.</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">Thanks for all your help.</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman"></font></font></span> </p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">Roger</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">APPENDIX 1</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">primanaleng=lmer(score ~LangEng+LangEng:PrimePP + (1|PID) + (1|ITEM), data=L2prim, family = "binomial")</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">summary(primanalengnoint)</font></font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">Generalized linear mixed model fit by the Laplace approximation </font></font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">Formula: score ~ LangEng + LangEng:PrimePP + (1 | PID) + (1 | ITEM) </font></font></span></p><div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><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><font size="3"><font face="Times New Roman"><span> </span>AIC<span> </span>BIC logLik deviance</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman"><span> </span>650.5 677.2 -319.2<span> </span>638.5</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">Random effects:</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><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><font size="3"><font face="Times New Roman"><span> </span>ITEM<span> </span>(Intercept) 1.9705<span> </span>1.4038<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman"><span> </span>PID<span> </span>(Intercept) 2.2791<span> </span>1.5097<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">Number of obs: 632, groups: ITEM, 40; PID, 32</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">Fixed effects:</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman"><span> </span>Estimate Std. Error z value Pr(>|z|)<span> </span></font></font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">(Intercept)<span> </span>-0.5915<span> </span>0.4153<span> </span>-1.424<span> </span>0.15437<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">LangEng2<span> </span>-0.1875<span> </span>0.3022<span> </span>-0.621<span> </span>0.53486<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">LangEng0:PrimePP2<span> </span>-0.9496<span> </span>0.3095<span> </span>-3.068<span> </span>0.00215 **</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">LangEng1:PrimePP2<span> </span>-0.5252<span> </span>0.3100<span> </span>-1.694<span> </span>0.09026 . </font></font></span></p>
<div class="im">
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">---</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><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><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">Correlation of Fixed Effects:</font></font></span></p>
</div><p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman"><span> </span>(Intr) LngEn2 LE0:PP</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">LangEng2<span> </span>-0.363<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">LngEn0:PPP2 -0.354<span> </span>0.507<span> </span></font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">LngEn1:PPP2 -0.008 -0.477<span> </span>0.012</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font size="3"><font face="Times New Roman">APPENDIX 2</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><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">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">Models:</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">primanalengnoint: score ~ LangEng + PrimePP + (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">primanaleng: score ~ LangEng + LangEng:PrimePP + (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>Df<span> </span>AIC<span> </span>BIC<span> </span>logLik<span> </span>Chisq Chi Df Pr(>Chisq)</font></font></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span lang="EN-US"><font size="3"><font face="Times New Roman">primanalengnoint<span> </span>5 649.33 671.57 -319.66<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">primanaleng<span> </span>6 650.46 677.15 -319.23 0.8714<span> </span>1<span> </span>0.3506</font></span></p>
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<p class="MsoNormal" style="margin:0cm 0cm 0pt"><span><font face="Times New Roman" size="3"> </font></span></p><br>
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