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MATHmodels

Problem Chosen

2020

MCM/ICM

Summary Sheet

Team Control Number

2004647

Good Morning Sunshine:

A Rating and Review Based Analysis

Summary

The Review and Rating System has been playing a huge role during the evolu-

tion of E-commerce. Customers use it to help make the best purchase decisions,

while vendors can utilize it to collect opinions on how to make improvements.

Therefore, in a vendor’s perspective, it is of essential to learn to most efﬁciently

extract the most valuable information out of mountains of customers’ voices.

Firstly, based on the attributes we ﬁnd useful in the provided data sets, we pro-

pose the Rating and Review Based Score (RRBS) Model, which deﬁnes a product’s

score—a data measure based on information reﬁned from ratings and reviews—

that ﬁnely quantiﬁes and describes customers’ responses to a product. Based on

the RRBS Model, we further introduce the Reputation Model, which gives a time-

based quantiﬁcation of a product’s reputation over time periods. Our model eval-

uation results show that a quantiﬁed reputation has a strong correlation with the

corresponding product’s sales in terms of trend. This fact intuitively proves our

models’ correctness.

Then, in order to predict a product’s potential success or failure in the future,

we propose the the Successfulness Prediction Model, utilizing the knowledge ba-

sis established from our previously proposed models. Based on the premise that a

product’s success is closely connected to its sales, we are able to address the suc-

cessfulness prediction task by predicting a product’s future reputation with calcu-

lated reputation series, followed by comparison between the predicted values and

a pre-set threshold. As a result, the successfulness of products can be effectively

predicted.

Next, we evaluate star ratings’ incitement to custmoers’ speciﬁc reviews by record-

ing customers’ reviews right after a series of same ratings (either high or low), and

calculate the chance of them being either positive, negative or neutral. It turns out

a series of high ratings do incite more positive reviews; at the other end, we cannot

conﬁdently determine a series of low ratings’ incitement to negative reviews. Sub-

sequently, we discover the association between rating levels and speciﬁc quality

descriptors from review text by matching review contents with graded-words. The

results reveal strong connection between postive words and high ratings, and simi-

larly, negative words and low ratings.

Finally, to assist with Sunshine Company’s upcoming business, we propose our

devised marketing strategies and some important design features for each product.

Keywords: the RRBS Model; the Reputation Model; Correlation Analysis;

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Team # 2004647 Page 1 of 24

Contents

1 Introduction 2

1.1 Problem Restatement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Data Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Modeling Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Assumptions & Nomenclature 3

3 the RRBS Model 4

3.1 Model Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 the Rating Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.3 the Review Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3.1 The Review-based Measure Equation . . . . . . . . . . . . . . . . . . . . . 8

3.3.2 the Sentiment Polarity Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 the Reputation Model 10

4.1 Time Weight Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.2 Quantiﬁcation of Reputation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.3 Model Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.3.1 Trend Similarity between Quantiﬁed Reputation and Sales . . . . . . . . . 11

4.3.2 Kendall’s Tau Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 the Successfulness Prediction Model 13

5.1 Gaussian Process Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.2 Reputation Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3 Successfulness Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6 Results 16

6.1 Evaluation of Star Rating’s Incitement . . . . . . . . . . . . . . . . . . . . . . . . . 16

6.2 Association between Review Wording and Rating Levels . . . . . . . . . . . . . . 18

6.3 Our Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.3.1 Marketing Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

6.3.2 Important Design Features . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7 Sensitivity Analysis 20

8 Strengths and Weaknesses 20

8.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

8.2 Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

9 Conclusion 21

10 Our Letter 22

Appendices 25

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Team # 2004647 Page 2 of 24

1 Introduction

"Amazing things will happen when you listen to the consumer."

—Jonathan Midenhall, CMO of Airbnb

E-commerce has sprouted for the last few decades all over the world, and now it has be-

come one of the most prosperous and promising modern industries. During this process, the

Review and Rating System has been playing a huge role all along. Not only does it help cus-

tomers ﬁnd out what is best for them when making purchase decisions, but also it helps sellers

realize what problems their products have and thus things can be improved. Therefore, it is

signiﬁcant for companies to know how to make the most use of it and apply the knowledge to

improving product designs and marketing strategies.

1.1 Problem Restatement

Sunshine Company is about to launch three new products in the marketplace, including a mi-

crowave, a baby paciﬁer and a hair dryer. Data of customer-supplied reviews and ratings for

microwave ovens, baby paciﬁers and hair dryers sold on Amazon.com are supplied, each of

which has a time label on. Analysis of customers’ ratings and reviews of other companies’s

competing products is required in order to ﬁgure out the optimal online marketing strategies

and possible design features they can employ to make their products more desirable to cus-

tomers.

To achieve our goals, speciﬁcally, we need to:

• Identify the most informative data measures based on reviews and ratings for Sunshine

Company to track, once they launch their three new products in the online marketplace.

• Discover time-based measures and patterns that can suggest a product’s reputation’s

trend of increase or decrease.

• Combine text-based measures and rating-based measures to discover measures that best

indicate a product’s potential success or faliure.

• Find out whether speciﬁc star ratings incite more reviews.

• Find out whether rating levels and speciﬁc quality descriptors of text-based reviews are

strongly associated.

1.2 Literature Review

Early work have proposed several methods for utilizing reviews and ratings of online prod-

ucts. In 2009, Koren et al. [4] proposed Latent Factor Models (LFM) to address the rating

prediction task. In 2013, McAuley et al. [5] took advantage of the abundunt information in

reviews using Latent Dirichlet Allocation (LDA) to achieve topic distributions. Later in 2016,

Tan et al. [8] proposed the Rating-Boosted Latent Topics (RBLT) Framework, combining tex-

tual reviews with users’ sentiment orientations, and thus recommendations are made more

accurate.

However, some of the valuable information in reviews is not fully utilized in the introduced

works, such as varying text lengths of different reviews and the sentiment intensity of speciﬁc

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Team # 2004647 Page 4 of 24

Asm. 1 Provided data do not include spam reviews, either from competitors or mischievous

customers.

Asm. 2 Contents of every review are legitimate and unbiased.

Asm. 3 The number of review records of a product equals to the sales of the same product

aggregated since it was launched, i.e., there are no missed or excluded records in any of

the provided data sets.

Asm. 4 Customers’ reviews and ratings were posted the same day they purchased the prod-

ucts, i.e., the time consumption of procedures such as packaging, delivery and users’

conﬁrmation of quality is neglected.

Asm. 5 Each customer has at most one review and rating record on one type of product (either

a microwave, a paciﬁer or a hair dryer).

We have a list of the main notations we deﬁne during our modeling, as shown in Table 1.

3 the RRBS Model

In this section, we propose the RRBS Model (viz., the Rating and Review Based Score Model) to

serve as a data measure, combining star ratings and textual information from reviews. When

determining the quantiﬁcation process, we take into account nearly all inﬂuencing attributes

from the provided data. As a result, a highly informative data measure is presented for Sun-

shine Company to track, once their three new products are launched.

Table 1: Notations we use in future discussion.

Symbol Description

i Product type (either Microwaves, Paciﬁers or Hair dryers), i = 1, 2, 3

k Unique model identiﬁer of a type of products

t Timestamp identiﬁer (unit: Month)

n Number of rating and review records of a model within a speciﬁc month

score

(t)

i,k

Measure for customer responses a product model receives

α Rating vector—an n-dimensional row vector

β Review vector—an n-dimensional column vector

λ Rating weight parameter

A Sentiment polarity matrix—an n-by-n diagonal matrix

Φ Review-quantifying vector—an n-dimensional column vector

Vine factor

Sentiment intensity factor

Validity factor

Helpfulness-rating factor

Review-length factor

Correction term

score Time series of a model’s scores

Rep

(t)

i,k

Quantiﬁed reputation

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