Ewm,i (pm,i) =
α + β1 F Plm,i− 1 + β2 E(pm,i− 1) + um + εm,i.

 

An observation (Ewm,i (pm,i)) is the median popularity (pm,i) of the posts containing protomeme m on day i, or the score of the post. Since post scores are count data and distributed over a skewed distribution, we used a Poisson mixed model. Each observation has weight wm,i, or the number of posts containing m on day i, thus giving less weight to the ( presumably noisy) information on protomemes m that were not used very much on day i.

FPlm,i − 1 registers if protomeme m was on the front page on day i − 1. The parameter l is the number of posts hitting the front page each day. The default front page in Reddit includes 25 posts ( 30 for Hacker News). So, every day, at least 25 ( 30) posts hit the front page. However, users can increase the physical length of the front page. Moreover, as the day passes, front-page posts get replaced by other posts. As a result, there is no way to know how many posts hit any particular user’s front page on any given day (see the online appendix). For this reason, we ran the regression multiple times for different l values to test the robustness of our results for different front-page sizes.

E(pm,i− 1) denotes the protomeme’s popularity on the day before i, controlling for existing trends; um is a random effect of protomeme we used to control for the fact that different observations can refer to the same protomeme; and εm,i is the error term.

Figure 2 outlines our estimates of β1
for different values of l. The effect of
being on the front page is negative; the
protomeme is expected to have a lower
median score than on a business-as-
usual day. This expectation confirms
the theory of dissimilarity-driven suc-
ty; scores cluster around each pro-
tomeme’s average. Third, a
protomeme’s recent history might
explain this variation. If, for exam-
ple, a protomeme was getting de-
clining scores, we might expect it to
get even lower scores after a ran-
dom popularity spike. Finally, there
is a fat tail in score distributions, so
the average alone is not meaningful.

To give more solid evidence for the theory about viral connections, we tested the median popularity of a protomeme on a particular day using the following mixed model, or “MED Model”

Figure 1. Distributions of score and number of posts per day of the observed memes, overall, and focusing on only those created the day after the meme was among the 25 top-scoring posts; included is the average and 95% confidence intervals.

44 45 46 47 48 49 50 51 52

Overall After FP

A v g. D ai ly

Sco
r
e
Status

4. 3 4. 4 4. 5 4. 6 4. 7 4. 8 4. 9

5 5. 1 5. 2

Overall After FP

P os ts

Pe
rD
ay
Status

7 8 9 10 11 12 13 14

Overall After FP

A v g. D ai ly

Sc
o
re
Status

1.06 1.08 1. 1 1. 12 1. 14 1. 16 1. 18 1. 2 1. 22

Overall After FP

P o st sPe r

Da
y
Status

(a) (b)

(c) (d)

Figure 2. Evolution of β1 coefficients for increasing l in the model and in its associated null model; thin lines represent 95% confidence intervals.

-0.12 -0.1 -0.08 -0.06 -0.04 -0.02

0 0.02

20 30 40 50 60 70 80 90100 β

l Observation Null Model

-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05

0 0.05 0.1

30 40 50 60 70 80 90 100 β

l Observation Null Model

(a) (b)