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Whenever I read about repeated measures or within-subjects design in different books and on webpages, the example that always is brought up is some kind of longitudinal or repeated measures design (e.g. people are measured on the same scale several times during the day). For my experiment, I have showed people a number of different pictures in random order, and then grouped these pictures into different categories. Is this an example of a repeated measures or within-subjects design, that is, can I use a repeated measures (within-subjects) ANOVA on my data (given that it satisfies all the basic assumptions)?

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    $\begingroup$ You appear to have TWO forms of dependence here: By person and by category. So you probably need a multilevel model to account for both $\endgroup$
    – Peter Flom
    Mar 3, 2012 at 15:36
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    $\begingroup$ @PeterFlom can you give a lecture about how exactly to do this multilevel mixed linear regression on YouTube? Or for example, write some blog posts about it? Or give me some paper or link that explains it? The normal mixed model with subjects as the sole dependence (and random effects) is rather straightforward. But when the repeated measures is added to the mixed model (2-dimensional dependence), it gets somehow confusing to decide if the repeated measurements (for example, photomanipulated images in this question) should be treated as random effects or fixed effects. Thanks a lot. $\endgroup$
    – Vic
    Jul 5, 2023 at 23:57
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    $\begingroup$ I have pretty much retired, sorry. $\endgroup$
    – Peter Flom
    Jul 6, 2023 at 0:38
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    $\begingroup$ @PeterFlom , So sad to hear it; your explanations were always the best. $\endgroup$
    – Vic
    Jul 6, 2023 at 10:13

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Traditionally, yes, your design can be treated as a repeated-measures design where you treat person as a unit of repeated observation and you treat the pictures in each category as homogenous replications of one another, collapsing them to a mean and treating category as a within-Ss variable.

However, as Peter Flom notes, it's possible (likely?) that the intra-category variability in your pictures is worth accounting for, in which case you will want to move to a mixed effects modelling context where you will treat category as a fixed effect and both person and category token as crossed random effects. See Baayen et al 2008 for explanation.

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    $\begingroup$ @Spledosa, With regards to sphericity/homoscedasticity, yes it is generally the case that these are not concerns in mixed effects modelling. $\endgroup$ Mar 5, 2012 at 12:11
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    $\begingroup$ @Vic hm, nothing comes to mind in terms of content to suggest that addresses your questions specifically; the way I like to think of it these days is that whenever you have something in your data that isn’t quantifies by a number with a meaningful value (either ratio, ordinal or interval), but does have a unique identity that’s encoded as a “label” (so, a nominal variable), it’s usually useful to account for the influence of a collection of such named-things as a hierarchy (aka treating it as a “random effect”) where each named thing has its own influence but the collection of said influences… $\endgroup$ Jul 6, 2023 at 18:43
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    $\begingroup$ … has a distribution with parameters you estimate (folks usually choose a normal, thereby estimating the mean influence and variability of influences). You’ll sometimes see this not being done if there are only a small number of named-things in a given collection, and folks instead still model the influence of each thing as truly independent, without the higher-level distribution-of-influences part (aka treating the things as “fixed effects”), but often that is a holdover from frequentist modelling realms where the absence of priors make for more fragile estimation of the distribution… $\endgroup$ Jul 6, 2023 at 18:51
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    $\begingroup$ … parameters amidst too few names-things being modelled as derived from a distribution. Note that this framing of hierarchy/random-effects is about using all the information at hand. In theory there is some collection of truly numeric data that would more fully capture the expected influence of a given named-thing, but we simply haven’t done the work to identify and measure those things, and instead are relying on the information of difference implied by the fact we’ve given things different names. If you can derive meaningful numbers associated with each named thing, those numbers would … $\endgroup$ Jul 6, 2023 at 18:59
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    $\begingroup$ … then be useful as “fixed-effects” in the model. It can make sense to keep the hierarchical/random-effects model structure if you aren’t confident you’ve extracted all the meaningful numbers associated with each thing, but as you increasingly account for more of the properties of each thing relevant to its influence, the utility of keeping the hierarchical structure will diminish (but never “hurt” per se). $\endgroup$ Jul 6, 2023 at 19:02

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