Library and notebooks for schizophrenia-induced emotion mismapping analysis.
- Sum the squares of the fine grained emotions for each coarse emotion:
- $\tilde{p}{coarseEmotion,trialNumber}:=\sum{fineEmotion \in coarseEmotion} s_{fineEmotion, trialNumber}^{2}$
- Normalize the coarse emotions so they sum to 1 for each trial
- $p_{coarseEmotion,trialNumber} = \tilde{p}{coarseEmotion,trialNumber} / \sum{coarseEmotion^{\prime}} \tilde{p}_{coarseEmotion^{\prime},trialNumber}$
- From here on I'll use:
-
$i$ subject -
$j$ stimulus -
$k$ coarse emotion -
$n_{e}=4$ the number of emotions -
$n_{s}=14$ the number of stimuli -
$n_{p}=?$ the number of subjects
-
- For each stimulus
$j$ we have a vector$r_{j}$ of length$n_{e}$ which is a normative distribution over emotions for that stimulus (elements a between 0 and 1 and sum to 1) - skipping details and grotesquely abusing notations, define
$\mathscr{N}_{i}\left(x \right)$ to be a noised representation of the distribution over emotions$x$ that includes both a trial specific pure noise component and a subject level random effect -
$\beta$ is an$n_{e}$ by$n_{e}$ matrix representing how much of each emotion is piped to each other emotion. Each row (column??) is a distribution - We observe
- $\mathscr{N}{i}\left(r{j} \right)$ for HCs
- $\mathscr{N}{i}\left(\beta^{\prime} r{j} \right)$ for SZs
Imagine that each stimulus emits par