Disappearing errors in a conversion model

TL;DR

This paper discusses a differential equation-based conversion model applied to various fields, focusing on how measurement errors diminish over time, with empirical predictions of public opinion shifts based on Twitter data during a crisis.

Contribution

It introduces a method to analyze how measurement errors in conversion models fade over time, with practical application to opinion dynamics using social media data.

Findings

Errors in message measurements diminish over time.

The model accurately predicted Toyota's opinion shifts during a crisis.

Prediction uncertainty was quantified using formal statistics.

Abstract

The same basic differential equation model has been adapted for time-dependent conversions of members of a population among different states. The conversion model has been applied in different contexts such as epidemiological infections, the Bass model for the diffusion of innovations, and the ideodynamic model for public opinion. For example, the ideodynamic version of the model predicts changes in public opinions in response to persuasive messages extending back to an indefinite past. All messages are measured with error, and this chapter discusses how errors in message measurements disappear with time so that predicted opinion values gradually become unaffected by past measurement errors. Prediction uncertainty is discussed using formal statistics, sensitivity analysis and bootstrap variance calculations. This chapter presents ideodynamic predictions for opinion time series about the Toyota car manufacturer calculated from daily Twitter scores over two and half years. During this time, there was a sudden onslaught of bad news for Toyota, and the model could accurately predict the accompanying drop in favorable Toyota opinion and rise in unfavorable opinion.