Crossed random effects

Effects may berequired in models when the data being analyzed have been obtained by recordingoutcomes for a sample of participants responding to a sample of stimuli.  In arepeated-measures design study, where all participants respond to all stimuli,observations are nested both by participants (there are multiple responseobservations per participant) and by stimulus items (there are multipleresponse observations per item).  It is therefore sensible to focus on thevariation in coefficients due to random effects: variance in intercepts orslopes due to differences in both participants and items.

See Fixed effects, Random effects