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I've run an experiment where 120 participants (PP) viewed 40 quotes (Item) each (presented in Facebook format) and were asked to rate them on a scale (1 to 7) (Rating is my DV).

The variable Font (2 levels: Hard, Easy) denotes in what font the quotes were presented. This was between subjects, so participants only viewed one type of font (equally split into two groups).

The 40 quotes were of two types - QuoteType (2 levels: Good, Bad) across both Font conditions, so every participant was exposed to both types.

Lastly, the Metrics variable (2 levels: High, Low) denoted the amount of endorsement on each quote. This was also across both Font conditions.

In sum, I created a total of 160 variations of stimuli (40 items (20 Good + 20 Bad) x 2 Font x 2 Metrics). Four exposures were created to allow the Metrics variable to be counterbalanced and avoid a participant having to see the same quote listed with each Metric manipulation.

My assumption is that this is a nested design due to the Font variable. My hypothesis is that the Hard Font can reduce ratings on the Bad QuoteType, so I'm looking for a Font*QuoteType interaction. A secondary hypothesis is looking for a significant effect of Metrics (High should get higher ratings than Low). I used a linear mixed-effects model using R's lmer.

My original model was specified like so:

lmer.model=lmer(Rating~Font*QuoteType + Metrics + (1+QuoteType|PP) + (1|Item), data = myData)

I'm also uncertain about how I have specified the random effects. I assume that every participant has a different intercept for QuoteType, since all participants viewed all 40 items and therefore both quote types, hence (1+QuoteType|PP). I don't think this can be said for Font as participants only viewed one type of font. I also assumed that Item would have its own random effect.

Is this a nested design and if so, should I change the way my model is currently specified?

Thanks in advance.

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My assumption is that this is a nested design due to the Font variable.

Font is a fixed effect, so is not involved in whether it the random effects are crossed or nested.

I've run an experiment where 120 participants viewed 40 quotes each ...and were asked to rate them on a scale

So scale is the measured variable (the response in the model). Since each quote was seen by all participant, quote is not nested in participant. Since each participant viewed each quote, participant is not nested in quote. Therefore this is a fully crossed design. See this question and answers regarding crossed vs nested random effects.

(1+QuoteType|PP) specifies that random intercepts will be fited for PP, which I assume is participant though this isn't stated in the question, and also that the fixed effect for QuoteType will be allowed to vary for each PP

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  • $\begingroup$ Thank you very much for clarifying, it makes much more sense now. Is it correct to assume that the DV can be predicted by the interaction as specified in the model? $\endgroup$
    – NickB
    Jul 13, 2020 at 11:26
  • $\begingroup$ No worries. Yes, from your description that maks sense although you might also want to consider an interaction with Metrics too (if you expect the 2 way interaction to vary at the different levels of Metrics) $\endgroup$
    – Robert Long
    Jul 13, 2020 at 11:36

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