I am running an experiment in which participants respond to various words that appear rotated on the screen. I would like to analyze their reaction times using a linear mixed-effects model, but I am not sure how to classify some of the independent variables.
The degree of rotation is the effect of interest, so intuitively it should be a fixed variable. However, I'm not sure it satisfies the criteria of fixed variables (according to: Statistical methods for psychology; Howell, 2010), since the levels of rotation used in the experiment (0, 35, 70 degrees) do not exhaust all possible levels, and may change between replications of the experiment (except for 0 which stands for no rotation).
In addition, the words in the experiment are of different lengths (4,5,6 letters). Not so much because I wanted to manipulate the length, but because I had constraints on word selection and could not find enough words of the same length. So, length is a nuisance variable and may change from one replication of the study to another, but it has a limited set of values it can get.
Can you help me decide whether these variables are fixed or random?
Thanks,
Chen
I presume that you have a repeated measures two-level structure with occasions nested within individuals so that there unexplained random effects at both levels. I would then initially treat both 3 factor category predictors as fixed effects to get at their mean effect (may be need interactions) and then allow their effects to be diffentially variable by individual an/or or by occasion.
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp
http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/repeated-measures.pdf
From the information you have given, I would say its a fixed effect, however, a variable can be fixed and a random in the same model. the fixed effect in these cases are estimating the population level coefficients, while the random effects can account for individual differences in response to an effect.
Thank you, Kelvyn and Jessica, for your answers!
Indeed I have a repeated measures structure, though I'm not sure I would call it nested (all individuals are tested on all words in all rotation levels).
How can I, technically, use the same variable as both fixed and random in the same model? Did you mean something like (Rotation|Individual) as a random effect of rotation level on the individual level? (in Wilkinson-Rogers notation)
Thanks,
Chen
"Indeed I have a repeated measures structure, though I'm not sure I would call it nested (all individuals are tested on all words in all rotation levels)."
You could do a non-nested cross classified model in which there are four sets of random effcets : individuals, occasions, word, rotatations
http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#nonhier
but on the latter two you have very few observations to esimate a variance and thereby generalize to the wide 'population' of words and rotations. You are not evaluating at all rotation levels but at three specific ones - as you note in your orginal post So the key from me is the random effects of the nested structure of occasions and individuals ( you do not want to infer to specific individuals and specific occasions) and then possibility at each of these two levels of a variance function based on the fixed classifications of words and rotations to model the possible variance heterogeneity of the response variable around its means.
There is a lot on confusion around using the terms fixed and random
http://andrewgelman.com/2005/01/25/why_i_dont_use/
I find it much easier to spell out the equations that are being estimated , and that is why I like MLwiN's equation interface.
http://www.bristol.ac.uk/cmm/software/mlwin/features/equation.html
You may want to look at my answers to this previous question:
https://www.researchgate.net/post/Can_random_effects_apply_continuous_variables
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