<div dir="ltr">Hey Bob,<br><br>yes, if you sum-code (aka contrast code) the main effects, the way you describe it below, you will be all set (at least for balanced data; for unbalanced data, you may want to center the variable). The interaction just multiplies the value of the two main predictors (leading to the values you give below), and -for balanced data- the interaction should be orthogonal to the main effects. The fitted coefficients will indeed differ from the default dummy coding (which is 0 vs. 1 coding, which is *not* centered). <br>
<br>HTH,<br>Florian<br><br><div class="gmail_quote">On Fri, Sep 5, 2008 at 4:27 PM, Bob Slevc <span dir="ltr"><<a href="mailto:slevc@rice.edu">slevc@rice.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
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<div>Hi there R-language-gurus,</div><div><br></div><div>I have what I think is a simple question – maybe even a stupid question (and there are too stupid questions) – that's related to recent discussions on this list. Imagine, if you will, that I have a full-factorial design, and want to set up a set of orthogonal contrasts rather than using R's default dummy coding. For a simple 2x2 design, I want something like this, where contrasts 1 and 2 are the main effects for A and B, and contrast 3 is the interaction:</div>
<div><br></div><div><span style="white-space: pre;"> </span>a1<span style="white-space: pre;"> </span>a1<span style="white-space: pre;"> </span>a2<span style="white-space: pre;"> </span>a2<br></div><div><span style="white-space: pre;"> </span>b1<span style="white-space: pre;"> </span>b2<span style="white-space: pre;"> </span>b1<span style="white-space: pre;"> </span>b2<br>
</div><div>contrast1<span style="white-space: pre;"> </span>1<span style="white-space: pre;"> </span>1<span style="white-space: pre;"> </span>-1<span style="white-space: pre;"> </span>-1</div><div>contrast2<span style="white-space: pre;"> </span>1<span style="white-space: pre;"> </span>-1<span style="white-space: pre;"> </span>1<span style="white-space: pre;"> </span>-1</div>
<div>contrast3<span style="white-space: pre;"> </span>1<span style="white-space: pre;"> </span>-1<span style="white-space: pre;"> </span>-1<span style="white-space: pre;"> </span>1</div><div><br></div><div>I haven't found any contrast function (e.g., contr.poly / contr.sum / etc.) that'll automatically create a matrix for this kind of contrast, but can I just specify the individual factor contrasts and assume that R will just multiply them to give nice orthogonal interaction contrasts? For example, if my factors are called A and B, and I say:</div>
<div><br></div><div><div style="margin: 0px;"><font size="3" face="Monaco">contrasts</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">(</font><font size="3" face="Monaco">datafile</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">$</font><font size="3" face="Monaco">A</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">) <- </font><font size="3" face="Monaco">c</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">(</font><font style="color: rgb(20, 81, 25);" color="#145119" size="3" face="Monaco">1</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">,-</font><font style="color: rgb(20, 81, 25);" color="#145119" size="3" face="Monaco">1</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">)</font></div>
<div style="margin: 0px;"><font size="3" face="Monaco">contrasts</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">(</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco"><span style="color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px;"><font size="3" face="Monaco">datafile</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">$</font><font size="3" face="Monaco">B</font></span>) <- </font><font size="3" face="Monaco">c</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">(</font><font style="color: rgb(20, 81, 25);" color="#145119" size="3" face="Monaco">1</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">,-</font><font style="color: rgb(20, 81, 25);" color="#145119" size="3" face="Monaco">1</font><font style="color: rgb(0, 26, 153);" color="#001a99" size="3" face="Monaco">)</font></div>
<div style="margin: 0px;"><br></div></div><div>and then run a model (on log(RTs) apparently):</div><div><br></div><div><font size="3" face="Monaco"><span style="font-size: 11px;">model <- lmer(log(RT) ~ A*B + (1|subj) + (1|item), data=datafile)</span></font></div>
<div><br></div><div>Then am I set? I'm a little unsure, partially because it gives me slightly different results than the default dummy coding does (though it does seem to be orthogonal as the correlations between fixed effects are all zero...)</div>
<div><br></div><div>Thanks much,</div><div>Bob</div><br><div> <span style="border-collapse: separate; border-spacing: 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><span style="border-collapse: separate; border-spacing: 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><div>
---</div><div>L. Robert (Bob) Slevc, Ph.D.</div><div style="margin: 0px;">Rice University, Dept. of Psychology • 6100 Main Street • Houston, TX 77005</div><div><a href="http://www.ruf.rice.edu/%7Eslevc/" target="_blank">http://www.ruf.rice.edu/~slevc/</a></div>
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<br></blockquote></div><br></div>