To illuminate and motivate: a fuzzy-trace model of the spread of information online

Abstract

We propose, and test, a model of online media platform users’ decisions to act on, and share, received information. Specifically, we focus on how mental representations of message content drive its spread. Our model is based on fuzzy-trace theory (FTT), a leading theory of decision under risk. Per FTT, online content is mentally represented in two ways: verbatim (objective, but decontextualized, facts), and gist (subjective, but meaningful, interpretation). Although encoded in parallel, gist tends to drive behaviors more strongly than verbatim representations for most individuals. Our model uses factors derived from FTT to make predictions regarding which content is more likely to be shared, namely: (a) different levels of mental representation, (b) the motivational content of a message, (c) difficulty of information processing (e.g., the ease with which a given message may be comprehended and, therefore, its gist extracted), and (d) social values.

Appendix

This Appendix contains details of our model fitting methodologies.

1.1 Linear regression

We first identified 1388 tweets that had been retweeted at least once. These tweets were used for subsequent analyses.

1.1.1 Bidirectional stepwise elimination

We implemented Bidirectional stepwise elimination using the R Project for Statistical Computing version 3.5.1. Specifically, we used the step function in R. The starting model contained main effects for the following features:

• 1. All 50 topic proportions (logit transformed)

• 2. Dummy variables for media and user verification

• 3. All three PCA dimensions for text complexity in Table 3

• 4. All three PCA dimensions for emotion in Table 4

• 5. tweet sentiment (positive, negative, or neutral)

Given this initial model, the step function successively added interaction terms (specifically between tweet sentiment, topic proportion, and text complexity) and removed other terms already in the model until AIC reached a local minimum. The resulting model is shown in Table 9.

Table 9 Linear regression model derived via bidirectional stepwise elimination minimizing AIC and explaining number of retweets per follower for tweets with at least one retweet

1.1.2 LASSO regression

In parallel, we used LASSO regression to fit a model with the same predictors as above (including two- and three-way interactions between topic proportions, topic sentiment, and readability). We held out one third of our 1,388 datapoints, keeping the remaining data for training and test. LASSO regression was implemented using the scikit-learn package in Python 2.7. Specifically, we used the LassoCV function with 10,000 iterations and with eps=1e-4. The resulting model is shown in Table 10.

Table 10 Linear model derived via LASSO regression and predicting number of retweets per follower for tweets with at least one retweet

1.1.3 Model concordance

Although the bidirectional and LASSO models have several similarities, they also have many differences. We therefore fit a second pair of OLS models using only those covariates that appeared in both the bidirectional and LASSO models (see Table 11). Finally, we removed all covariates that were not significant after multiple comparisons using the Holm-Bonferroni procedure to generate our final model, shown in Table 5.

Table 11 OLS regression model using covariates that appeared in both LASSO and bidirectional models, and explaining number of retweets per follower for tweets with at least one retweet

1.2 Logistic regression

We next compared the 1388 tweets that had been retweeted at least once to the remaining tweets in our sample—i.e., those that had not been retweeted.

1.2.1 Bidirectional stepwise elimination

We once again implemented Bidirectional stepwise elimination using the step function in R. The starting model contained the same main effects and scope as in the linear regression model. The resulting model is shown in Table 12.

Table 12 Logistic regression model derived via bidirectional stepwise elimination minimizing AIC and explaining number of retweets per follower for tweets with at least one retweet

1.2.2 $L_1$-norm regularization

In parallel, we used $L_1$-norm regularization to fit a model with the same predictors as above (including two- and three-way interactions between topic proportions, topic sentiment, and readability). We retained the 1,388 datapoints that had been retweeted at least once and randomly sampled another 1,388 datapoints from the remaining data to account for class imbalance. We held out one third of this combined dataset, keeping the remaining data for training and test. Logistic regression with $L_1$-norm regularization was implemented using the scikit-learn package in Python 2.7. Specifically, we used the LogisticRegressionCV function with 4,000 iterations and the liblinear solver. The resulting model is shown in Table 13.

Table 13 Logistic regression model derived via $L_1$-norm regularization and predicting number of retweets per follower for tweets with at least one retweet

1.2.3 Model concordance

We once again resolved differences between the two models by fitting a second pair of logistic regression models using only those covariates that appeared in both the bidirectional and $L_1$-norm models (see Table 14). Finally, we removed all covariates that were not significant after multiple comparisons using the Holm-Bonferroni procedure to generate our final model, shown in Table 7.

Table 14 Standard logistic regression model using covariates that appeared in both $L_1$-norm and bidirectional models, and explaining likelihood of at least one retweet