  A comprehensive understanding of data quality is the cornerstone of
measurement studies in social media research. This paper presents in-depth
measurements on the effects of Twitter data sampling across different
timescales and different subjects (entities, networks, and cascades). By
constructing complete tweet streams, we show that Twitter rate limit message is
an accurate indicator for the volume of missing tweets. Sampling also differs
significantly across timescales. While the hourly sampling rate is influenced
by the diurnal rhythm in different time zones, the millisecond level sampling
is heavily affected by the implementation choices. For Twitter entities such as
users, we find the Bernoulli process with a uniform rate approximates the
empirical distributions well. It also allows us to estimate the true ranking
with the observed sample data. For networks on Twitter, their structures are
altered significantly and some components are more likely to be preserved. For
retweet cascades, we observe changes in distributions of tweet inter-arrival
time and user influence, which will affect models that rely on these features.
This work calls attention to noises and potential biases in social data, and
provides a few tools to measure Twitter sampling effects.
