My first Jupyter notebook¶
A little bit late,huh. Let's start by generating some data.
In [1]:
#First, generate some fake categorization data, under a logistic model
set.seed(1234)
#Set parameters
gmean = 0
cat = .1
block = .3
catblock = .3
#Create design
cats = 0:1
blocks = 0:9
design = expand.grid(cats, blocks)
design$Var3 = design[, 1]*design[, 2]
#Generate data with normal noise
design = cbind(design, Var4 = as.matrix(design) %*% array(c(cat, block, catblock), dim = c(3, 1)) + gmean)
replicates = 30
data = do.call('rbind', sapply(1:replicates, function(x) data.frame(sub = x, design[, 1:2], logodds = design[, 4]+rnorm(nrow(design), 0, sd = .5)), simplify = F))
#calculate probabilities
data$prob = 1/(1+exp(-data$logodds))
names(data) = c('subject', 'category', 'block', 'logodds', 'pcorrect')
summary(data)
subject category block logodds pcorrect Min. : 1.0 Min. :0.0 Min. :0.0 Min. :-1.3661 Min. :0.2032 1st Qu.: 8.0 1st Qu.:0.0 1st Qu.:2.0 1st Qu.: 0.8078 1st Qu.:0.6916 Median :15.5 Median :0.5 Median :4.5 Median : 1.8169 Median :0.8602 Mean :15.5 Mean :0.5 Mean :4.5 Mean : 2.0644 Mean :0.8084 3rd Qu.:23.0 3rd Qu.:1.0 3rd Qu.:7.0 3rd Qu.: 2.9696 3rd Qu.:0.9512 Max. :30.0 Max. :1.0 Max. :9.0 Max. : 6.7079 Max. :0.9988
Visualize the data.
In [2]:
require(ggplot2)
ggplot(data, aes(x = block, y = pcorrect, colour = as.factor(category))) +
geom_line(aes(group = interaction(category, subject)), alpha = .1) +
stat_summary(fun.data = 'mean_se', geom = 'line') +
theme_bw() + labs(x = 'Block', y = 'Proability Correct', colour = 'Category')
Loading required package: ggplot2 Warning message: "package 'ggplot2' was built under R version 4.2.3"
Tweak the qnorm function to adjust perfect proportions (0 and 1).
In [3]:
adj_qnorm = function(p, adj = min(p[p!=0])/2){
p[p == 0] = p[p == 0]+adj
p[p == 1] = p[p == 1]-adj
return(qnorm(p))
}
Here's the trick: we have to designate a target category (our task is not really a 2AF, because it presents a single stimulus). So, S and N trials are defined taking the target category into account. Let's use category 0 as the reference.
In [4]:
#Transformation of p(correct) of the non-target category to false alarms (1-p(correct))
data$sdt = ifelse(data$category == 0, data$pcorrect, 1-data$pcorrect)
#Now transform
data$zsdt = adj_qnorm(data$sdt)
#The final step involves the calculation of d prime, as z(H)-z(FA)
dtable = data[data$category == 0, ]
dim(dtable) #half the data is here
dtable$dprime = dtable$zsdt-data$zsdt[data$category == 1] #note how we use the other half of the data
#Similarly, we can calculate bias as -[z(H)+z(FA)]/2
dtable$criterion = -(dtable$zsdt+data$zsdt[data$category == 1])/2
summary(dtable)
- 300
- 7
subject category block logodds pcorrect
Min. : 1.0 Min. :0 Min. :0.0 Min. :-1.3661 Min. :0.2032
1st Qu.: 8.0 1st Qu.:0 1st Qu.:2.0 1st Qu.: 0.5815 1st Qu.:0.6414
Median :15.5 Median :0 Median :4.5 Median : 1.3552 Median :0.7950
Mean :15.5 Mean :0 Mean :4.5 Mean : 1.3350 Mean :0.7518
3rd Qu.:23.0 3rd Qu.:0 3rd Qu.:7.0 3rd Qu.: 2.0673 3rd Qu.:0.8877
Max. :30.0 Max. :0 Max. :9.0 Max. : 3.5128 Max. :0.9710
sdt zsdt dprime criterion
Min. :0.2032 Min. :-0.8301 Min. :-1.316 Min. :-0.4082
1st Qu.:0.6414 1st Qu.: 0.3622 1st Qu.: 1.160 1st Qu.: 0.1819
Median :0.7950 Median : 0.8238 Median : 2.321 Median : 0.3549
Mean :0.7518 Mean : 0.7826 Mean : 2.259 Mean : 0.3470
3rd Qu.:0.8877 3rd Qu.: 1.2143 3rd Qu.: 3.331 3rd Qu.: 0.5383
Max. :0.9710 Max. : 1.8964 Max. : 4.740 Max. : 0.9529 Finally, plot the SDT indexes
In [5]:
ggplot(dtable, aes(x = block, y = dprime, group = subject)) + geom_line(colour = 'red', alpha = .1) + geom_line(aes(y = criterion), colour = 'blue', alpha = .1) +
stat_summary(aes(group = NA), fun = 'mean', geom = 'line', colour = 'red') +
stat_summary(aes(y = criterion, group = NA), fun = 'mean', geom = 'line', colour = 'blue') + theme_bw() + labs(x = 'Block', y = "d' (red), criterion (blue)")
And that's it!