Backstory of the model:
This model is based on networks, so I’ll use some of the language and techniques from the study of networks to analyze the data.This peer review model creates a directed and weighted network. In other words, the ‘scientists’ (nodes) are connected (via edges) to other scientists (other nodes). The connections (edges) have a direction (how ‘scientist A’ feels toward ‘B’) and weight (-3, negatively). The book-keeping for this model is an adjacency matrix.
Where denotes the an edge from i to j with a given weight. In this model, it is the mood that scientist i has toward scientist j . (Some other texts do the reverse convention).
A measurement for this sort of matrix is incoming and outgoing node strength. The outgoing strength of scientists i — how scientist i feels about all other scientists — can be denoted as:
And can be calculated by summing rows. The incoming strength of scientists i — how all other scientists feel about scientist i — can be denoted as:
And can be calculated by summing columns. (for reference, my previous post showed time series plots of the mean of incoming weights, similar to the strength metric we are talking about here ).
Signed reviewers can be polarizing — weights can quickly become very negative and/or very positive. So the strengths ( and ) will be a sum of extreme positives and negatives — this is not very descriptive because it can lead to 0 strength. Instead I want to look at the range of incoming and outgoing weights, or:
which denotes the maximum outgoing weight minus the minimum outgoing weight.
which denotes the maximum incoming weight minus the minimum incoming weight.
Now let’s now look at some model results, and , for each scientist.
- Both types of reviewers have similar — they tend to have a similar range in their opinions about the scientists in the discipline.
- Signed reviewers tend to have a larger — the range of feelings that other scientists have toward the signed reviewers — compared to those who do not sign reviews. Scientists tend to either like or dislike signed reviewers more strongly that unsigned reviewers.
An added feedback is coming….
Some inspiration for this work comes from:
- Newman, M. (2010). Networks: an introduction. Oxford University Press.
- Squartini, T., Picciolo, F., Ruzzenenti, F., & Garlaschelli, D. (2013). Reciprocity of weighted networks. Scientific Reports, 3, Article number: 2729 https://doi.org/10.1038/srep02729