Social Media Mining: An Introduction

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10.1 Individual Behavior 277

which the phenomenon is guaranteed to be removed. We assume CAUSALITY

the phenomenon has happened when the measurements on the sub- TESTING

samples are different from the ones on the original dataset. Another

approach is to usecausality testingmethods. Causality testing meth-

ods measure how a feature can affect a phenomenon. A well-known

causality detection technique is calledgranger causalitydue to Clive GRANGER

W. J. Granger, the Nobel laureate in economics. CAUSALITY

Definition 10.1. Granger Causality. Assume we are given

two temporal variables X={X 1 ,X 2 ,...,Xt,Xt+ 1 ,...}and Y=

{Y 1 ,Y 2 ,...,Yt,Yt+ 1 ,...}. Variable X “Granger causes” variable Y

when historical values of X can help better predict Y than just using

the historical values of Y.

Consider a linear regression model outlined in Chapter 5. We can pre-

dictYt+ 1 by using eitherY 1 ,...,Ytor a combination ofX 1 ,...,Xt

andY 1 ,...,Yt.

Yt+ 1 =

∑t

i= 1

aiYi+ 

1 , (10.1)

Yt+ 1 =

∑t

i= 1

aiYi+

∑t

i= 1

biXi+ 

2 , (10.2)

where 

1 and 

2 are the regression model errors. Now, if 

2 <

 1 ,it

indicates that usingXhelps reduce the error. In this case,XGranger

causesY.

10.1.2 Individual Behavior Modeling

Similar to network models, models of individual behavior can help con-

cretely describe why specific individual behaviors are observed in social

media. In addition, they allow for controlled experiments and simulations

that can help study individuals in social media.

As with other modeling approaches (see Chapter 4), in behavior mod-

eling, one must make a set of assumptions. Behavior modeling can be

performed via a variety of techniques, including those from economics,

game theory, or network science. We discussed some of these techniques in

earlier chapters. We review them briefly here, and refer interested readers

to the respective chapters for more details.

 Threshold models (Chapter 8).When a behavior diffuses in a net-

work, such as the behavior of individuals buying a product and

referring it to others, one can use threshold models. In threshold