[R-sig-ME] Using mixed-effects modelling to estimate between- and within-Ss variance in an effect

[Mike Lawrence]

To illustrate the measures I'm seeking, here's how I'd obtain them
normally (code alternatively downloadable at http://drop.io/qumwtvp):

library(ez)
data(ANT)

#simplify the data to a 2x2x2 for demonstration purposes
ANT = ANT[
	ANT$cue %in% c('No Cue','Center Cue')
	& ANT$flanker %in% c('Congruent Flanker','Incongruent Flanker')
	& ANT$group %in% c('Control','Treatment')
	,
]

#use bootstrap resampling to generate distributions of effects from
which the within- and between-Ss variance will be estimated
bootstrap_iterations = 10 #obviously for publication, use a much larger number!
boot = ldply(
	.data = 1:bootstrap_iterations
	, .fun = function(x){
		resampled_ANT = ddply(
			.data = ANT
			, .variables = .(sid,group,cue,flanker)
			, .fun = function(x){
				to_return = x[ sample( 1:nrow(x) , nrow(x) , replace=T ) , ]
				return(to_return)
			}
		)
		resampled_ANT_scores = ddply(
			.data = resampled_ANT
			, .variables = .(sid,group)
			, .fun = function(x){
				cue_eff = mean(x$acc[x$cue=='No Cue']) - mean(x$acc[x$cue=='Center Cue'])
				flank_eff = mean(x$acc[x$flanker=='Incongruent Flanker']) -
mean(x$acc[x$flanker=='Congruent Flanker'])
				to_return = data.frame(
					eff = c('cue','flank')
					, value = c(cue_eff,flank_eff)
				)
				return(to_return)
			}
		)
		resampled_ANT_scores$iteration = x
		return(resampled_ANT_scores)
	}
	, .progress = 'text'
)

within_variance = ddply(
	.data = boot
	, .variables = .(sid,group,eff)
	, .fun = function(x){
		to_return = data.frame(
			value = var(x$value)
		)
		return(to_return)
	}
)

within_variance_stats = ddply(
	.data = within_variance
	, .variables = .(group,eff)
	, .fun = function(x){
		to_return = data.frame(
			Mean = mean(x$value)
			, SD = sd(x$value)
		)
		return(to_return)
	}
)
print(within_variance_stats)


between_variance_per_iteration = ddply(
	.data = boot
	, .variables = .(iteration,group,eff)
	, .fun = function(x){
		to_return = data.frame(
			value = var(x$value)
		)
		return(to_return)
	}
)
between_variance_stats = ddply(
	.data = between_variance_per_iteration
	, .variables = .(group,eff)
	, .fun = function(x){
		to_return = data.frame(
			Mean = mean(x$value)
			, SD = sd(x$value)
		)
		return(to_return)
	}
)
print(between_variance_stats)