Solved – How should I analyze repeated-measures individual differences experiments

repeated measures

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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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:

Practical Data Analysis for the Language Sciences with R, Baayen (2008)
Categorical data analysis: Away from ANOVAs (transformation or not) and towards logit mixed models, Jaeger (J. Mem. Language 2008 59(4))

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

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Solved – Using lmer for repeated-measures linear mixed-effect model

I think that your approach is correct. Model m1 specifies a separate intercept for each subject. Model m2 adds a separate slope for each subject. Your slope is across days as subjects only participate in one treatment group. If you write model m2 as follows it's more obvious that you model a separate intercept and slope for each subject

m2 <- lmer(Obs ~ Treatment * Day + (1+Day|Subject), mydata)

This is equivalent to:

m2 <- lmer(Obs ~ Treatment + Day + Treatment:Day + (1+Day|Subject), mydata)

I.e. the main effects of treatment, day and the interaction between the two.

I think that you don't need to worry about nesting as long as you don't repeat subject ID's within treatment groups. Which model is correct, really depends on your research question. Is there reason to believe that subjects' slopes vary in addition to the treatment effect? You could run both models and compare them with anova(m1,m2) to see if the data supports either one.

I'm not sure what you want to express with model m3? The nesting syntax uses a /, e.g. (1|group/subgroup).

I don't think that you need to worry about autocorrelation with such a small number of time points.

Solved – repeated-measures linear mixed-effect model

Is it correct to consider this as a nested two-level repeated measures ANOVA?

No, it is a linear mixed effects model.

Is it correct to use the following R syntax?

m1 <- lmer(CO2~days*treatment+(days|replicates),mydata)

It is correct if you wish to account for clustering, ie repeated measures, within each replicate, and allow the slope of days to vary between replicates.

Is this a random intercept and slope model with replicates nested in treatment?

It is a random intercept and slope model, but observations are nested within replicates.

Is it correct to say that this model accounts for:

the main effect of treatment and time and

the interaction between the two?

Yes, these are modeled as fixed effects.

What would be the difference between m1 and m2?

m2 <- lmer(CO2~days*treatment+(1|replicates),mydata)

m2 is a random intercept model, it accounts for clustering (repeated measures) but the slopes, are assumed to be constant for east replicate. m1 allows the slope for days to vary between clusters (replicates in your case).

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Solved – Using lmer for repeated-measures linear mixed-effect model

Solved – repeated-measures linear mixed-effect model

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