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I do quasi-experimental individual differences psychology research. I examine how people who differ in a cognitive ability (that I measure) perform on another task that always at least involves within-subject manipulations (and sometimes between-subject)–DVs are usually response time and/or accuracy. For this question I'd like to focus on response times (let's assume they are normally distributed). I then infer from the ability-task relations what it means theoretically for the cognitive ability. The nature of this work is correlational and involves repeated measures where each subject completes many task trials(mostly I’m not interested in changes over time, just the overall difference).

Researchers in my field often create categorical variables from the cognitive ability scores and compare the upper and lower quartiles of the distribution with a repeated-measures ANOVA. Because the cognitive ability is measured continuously, I am looking for an analytic strategy that treats the cognitive ability in this way. I’ve recently been investigating mixed-models, thinking that I can treat the people as a random effect grouping variable and the cognitive ability score as a random effect nested within people. I would like to examine interactions between this nested random effect (cognitive ability) and the fixed effects of the experimental treatments by doing model comparisons.

Does this seem like a reasonable analytic strategy? Am I thinking about this right? What are some other ways (the simpler, the better) that I can take advantage of repeated measures -remove experimental subject variance- while also maintaining the cognitive ability measure as a continuous measure? Any citations or examples in R are appreciated.

In a typical experiment, I would expect there to be anywhere from 1-3 categorical IVs with 2-4 levels(measured by multiple trials), and 1 continuous IV(cognitive ability). The exact nature of the categorical variables changes from study to study. The designs are fully crossed.

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  • $\begingroup$ It seems that you're on the right track but you might want to look at the interaction between cognitive ability and your other predictors. $\endgroup$ – John Jan 4 '11 at 20:42
  • $\begingroup$ @John that's exactly what I want to do. Are you suggesting that I'm not able to do that with mixed-models? $\endgroup$ – Matt Jan 4 '11 at 21:01
  • $\begingroup$ not at all... I'm suggesting that what you want to find is an interaction between cognitive ability and your other predictors. All you need to do is add them to the model. $\endgroup$ – John Jan 5 '11 at 3:39
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    $\begingroup$ I think it would be great if you could provide a few example of the exact nature of the independent variables (i.e., how many factors and how many levels). I think you can get pretty far with traditional GLM depending on the exact nature of your designs. $\endgroup$ – Henrik Jan 5 '11 at 10:16
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    $\begingroup$ @Matt If you have two levels on a within subject variable you can use the difference as dv (no need to go for repeated measures models). The same logic applies if you have two two-level within subject variables. The interaction is the difference of the differences (avoiding repeated measure models). However, if one of your within-variables has more than two levels, this approach does not work anymore, but you have to go multilevel. I recommend you read the special issue of the Journal of Memory and Language referred to in chl's answer: J. Mem. Language, 2008 59(4): Emerging Data Analysis $\endgroup$ – Henrik Jan 7 '11 at 9:41
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There were already some useful comments, that are probably waiting for some updates in the question, so I will just drop some general online references:

Examples using R may be found on Doug Bates' lme4 - Mixed-effects models project.

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