Temporal Distribution of Tweets
Period: January 01, 2018 to April 21, 2021
Number of tweets 2,601,702
Keywords: “vaccine” OR “vaccines” OR “vaccinate” OR “vaccination” OR “vaccineswork” OR “antivax” OR “vaccinesdontwork” OR “provax” OR “vaxwithme” OR “antivaxxers” OR “immunization”
Period: January 01, 2020 to April 21, 2021
Number of tweets 2,409,522
Period: January 01, 2020 to September 30, 2020
Number of tweets: 374,084
Proportion: 15,5% of total number of tweets
Period: October 01, 2020 to April 21, 2021
Number of tweets: 2,035,438
Proportion: 84,5% of total number of tweets
3.1 Overall Time Series
Event study
We used an Event study approach.
In order to perform this type of analysis, financial specialists use the return, volume or volatility of stocks. It is about quantifying the economic impact of an event in so-called abnormal returns. For our study, we chose to use the number of tweets per day to detect anomalies.
We performed an anomaly detection on all tweets from the beginning of the pandemic (January 01, 2020 to April 21, 2021), which corresponds to 2,409,522 tweets.
We noticed an acceleration of the conversation on Twitter about vaccination starting on October 1, 2020. So we decided to split the tweets into two parts:
- Part 1: January 01, 2020 to September 30, 2020
- Number of tweets: 374,084
- Part 2: October 01, 2020 to April 21, 2021
- Number of tweets: 2,035,438
For each part we performed a new anomaly detection.
Part 1 (01-01-2020 to 30-09-2020): Anomaly performed with the following parameters:
- alpha = 0.05 or 5% of outlier data
- max_anoms = 0.2 or 20% of anomalies allowed.
Part 2 (01-10-2020 to 21-04-2021): Anomaly performed with adjusted parameters:
- alpha = 0.3
- max_anoms = 0.05
We have grouped the anomalies by sub periods.
- Part 1: We have identified 5 sub periods
- Part 2: We have observed 6 sub periods.
Time interval of each sub Period:
- Start of the intverval: date 1st anomaly - 3 days (period_start)
- End of the interval: last anomaly date + 3 days (period_end)
Sub-periods of anomalies for the 1st part of the pandemic period
Sub-periods of anomalies for the 2nd part of tweets
3.2 Thematic Model
3.2 Thematic Model
Part 1 Period 1 (March 13-19, 2020)
Part 1 Period 1 (March 13-19, 2020). Topic 8 & 9 respectively.
Part 2 Period 6 (April 10-16, 2021)
Part 2 Period 6 (April 10-16, 2021). Topic 7 & 6 respectively.
3.3 Cosine similarity
- Document similarity (or distance between documents) is one of the central themes in Information Retrieval. How humans usually define how similar are documents? Usually documents treated as similar if they are semantically close and describe similar concepts. [@selivanov_dselivanovtext2vec_2021]
Classical approach from computational linguistics is to measure similarity based on the content overlap between documents. For this documents are presented as bag-of-words, so each document will be a sparse vector. And measure of overlap will be defined as angle between vectors:
similarity(doc1,doc2)=cos(θ)=doc1doc2|doc1||doc2|
By cosine distance/dissimilarity we assume following:
distance(doc1,doc2)=1−similarity(doc1,doc2)
It is important to note, however, that this is not a proper distance metric in a mathematical sense as it does not have the triangle inequality property and it violates the coincidence axiom.
We calculated the cosine similarity between the tweets of each 11 sub periods and the New York Times (NYT) articles for the same periods.
First, we collected all the NYT articles using the dates of each sub period (see the following table).
Second, we filtered the collected NYT articles per sub periods to only keep those that contained at least one of the following words:
- “vaccine” OR “vaccines” OR “vaccinate” OR “vaccination” OR “vaccineswork” OR “antivax” OR “vaccinesdontwork” OR “provax” OR “vaxwithme” OR “antivaxxers” OR “immunization”.
The following table display the number of articles remaining after the filtering.
