Ordinal Regression as a Model for Signal Detection | R-bloggers

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Ordinal Regression as a Model for Signal Detection
Posted on October 5, 2022 by R on Stat's What It's All About in R bloggers | 0 Comments
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Preface
I was basically done with this blog post when I came across Matti Vuorre’s post on the same exact topic . Matti goes into all the details, and really the present post can be seen as a brief account of all the cool things the probit-approach-to-SDT can do. I’m only posting this here because I really like my plots ????
Previously , we’ve seen that for data from a binary decision signal detection task, we can use a probit binomial regression model (like a logistic regression, but with a probit link function) to estimate the two main parameters of signal detection theory (SDT): the sensitivity and the bias.
In this post I would like to show how this idea can be extended to multiple response SDT tasks by using an ordinal probit regression model.
The Data
Imagine the following task: after being presented with 20 images of dogs, you are presented with 300 new images of dogs, and you have to decide for each dog if it appeared in the training set (“Old”) or not (“New”).
In a binary decision task, you would simply indicate “New” or “Old”, but in this task you have multiple response options – from 1 to 6, with 1 = “Feels New” and 6 = “Feels Old”. We can call this scale a “feelings numbers” scale .
After going over all 30 photos, you have
STD_data ## # A tibble: 12 × 3 ## Truth Response N ##
## 1 New Confidence1 35 ## 2 New Confidence2 31 ## 3 New Confidence3 26 ## 4 New Confidence4 22 ## 5 New Confidence5 19 ## 6 New Confidence6 17 ## 7 Old Confidence1 14 ## 8 Old Confidence2 20 ## 9 Old Confidence3 22 ## 10 Old Confidence4 27 ## 11 Old Confidence5 32 ## 12 Old Confidence6 35
Where N is the number of responses in each condition and response level.
Modeling with Classic SDT
We can use Siegfried Macho ’s R code to extract the SDT parameters. In this case, they are:
Sensitivity – The distance between the two (latent) normal distributions. The further they are, the more “distinguishable” the Old and New images are from each other.
5 Threshold – One between each pair of consecutive possible responses. Perceived “stimulation” above each threshold leads to a decision in that category.
(These will probably make sense when we present them visually below.)
First, we’ll model this with classical SDT:
SDT_equal