Discussion Paper No. 105
Investigating the Impacts of Customer Experienceand Attribute Performances on Overall Ratings
using Online Review Data: Nonlinear Estimation
and Visualization with a Neural Network
Toshikuni SatoNovember, 2019

Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research
Graduate School of Economic and Management
Tohoku University27-1 Kawauchi, Aobaku
Sendai 980-8576, JAPANInvestigating the Impacts of Customer Experience and Attribute
Performances on Overall Ratings using Online Review Data: Nonlinear
Estimation and Visualization with a Neural Network

Toshikuni Sato††

Graduate School of Economics and Management, Tohoku University

Abstract

This study investigates interpretable neural networks for marketing and consumer behavior
research using customer reviews instead of measurement scales to better understandcustomer experiences. Service attribute ratings are used to measure attribute performances
to compare the influence of customer experience and service performance on overallsatisfaction. Although many researchers have investigated word-of-mouth reviews and theirpractical applications, the detailed contents of those reviews were generally disregarded,
possibly because of their high dimensionality. To solve this problem, this study proposessome useful neural-network methods for specifying the expected assumptions based on
previous knowledge or theories in consumer behavior research. Because neural networks
help estimate nonlinear relationships between objective and predictive variables, a partial
dependence plot is used to visualize the estimated functions and marginal effects. Empiricalresults not only provide a highly accurate neural-network model, they also create better
marketing implications.
Keywords: Customer experience, Customer review, Neural networks, Interpretablemachine learning, Nonlinear measurement model1

1.

Introduction

Customer experience, as proposed by Schmitt (1990), has been applied to a wide range of marketingareas, from retail marketing to service design and customer journey (Verhoef et al. 2009; Grewal 2009;
Teixeira et al. 2012; Lemon & Verhoef 2016). Experiential marketing aims to provide the desired
experience for customers via goods or services based on SEMs (strategic experiential modules), which
are constructed around the five aspects of sense, feel, think, relate, and act (Schmitt 1999, p.60-63). To
create a better marketing experience, Schmitt (1990) explained the importance of utilizing ExPros(experience providers) that included variables of communications, visual and verbal identity andsignage, product presence, co-branding, spatial environments, electronic media, and people.
Measurement scales have been developed by several researchers (Bustamante & Rubio 2017; Pelleiter& Collier 2018; Bleier et al. 2019; Nikhashemi et al. 2019) to evaluate customer experience. Althoughmeasurement scales are useful to understanding customer experience, this study focuses on online
reviews obtained from websites and social network services, such as Amazon, Trip Adviser, Facebook,and Twitter.
Word-of-mouth (WOM) marketing is a powerful and important tool for diffusing information about
new products, sales, and marketing campaigns (Trusov et al. 2009, Kozinets et al. 2010). However,
online customer reviews (OCR) contain information related to customer experience when they consume
products and receive services (Chen & Xie 2008). To utilize this kind of free-form textual information,
several topic models based on latent dirichlet allocation (LDA) have been proposed for marketing areas(Tirunillai & Tellis 2014, Büschken & Allenby 2016). Deep-learning neural networks for natural
language process are also popular (Collobert et al. 2010). Most studies for review data have focused on
the relationships among words and terms, such that they adapt morphological analyses to divide text
into effective words. They then convert text into high dimensional word data, and machine-learning
methods are often used to analyze them. In contrast, many machine-learning methods have performed
complicated model estimations known as “black box” (Larasati et al. 2011). It is important to obtainreasonable interpretations from these techniques in social science.
2

The purpose of this study is to utilize the advantages of machine learning for online review data andto discuss the marketing interpretations of the results. We develop a marketing model for forecastingoverall satisfaction using the Rakuten travel dataset (Rakuten, Inc. 2016). For predictors, words in text
and attribute ratings are used to measure customer experience and attribute performance, respectively.
Additionally, the proposed model adopts the interaction of words, because they represent customer
experiences, including perceptions and feelings during travel. It is also important to specify the nonlinear
relationship between attribute performance and overall satisfaction (Finn 2011, Falk et al. 2010, Lin etal. 2010, Cheung & Lee 2009, Gómez et al. 2004, Matzler et al. 2004, Anderson & Mittal 2000, Mittal
et al. 1998, Brandt 1988).

2.

Related LiteratureThis section reviews two marketing research areas to introduce the role of customer experience inmarketing and consumer behavior. The first area includes customer experience studies, which conduct
developing measurement scales and testing consumer behavior models. The second area includes online
review studies that adopt review data for marketing models.

2.1.

Measurement Scales and Models for Customer Experience

Many researchers have measured customer experiences and have investigated its impact on consumer
behaviors. Table 1 summarizes representative studies in several areas, where researchers conceptualized
customer experience in various unique scopes. Those studies commonly focus on customer feelings,
emotions, perceptions, or mental states during their experiences.
Novak et al. (2000) discussed online experiences before Scimitt (1999) conceptualized experiential
marketing. Subsequently, the other researchers developed measurement scales based on experience
types. To define brand experiences, Brakus et al. (2009) extended three basic experience types: product,
shopping and service, and consumption (Hoch 2002, Hui & Bateson 1991, Krein et al. 1992, Holbrook3

& Hirschman 1982). For measurements, they defined brand experiences as subjective, internal consumer
responses, and behavioral responses. Although they specified four constructs (i.e., sensory, affective,
behavioral, and intellectual), Bustamante and Rubio (2017) improved the work of Brakus et al. (2009)by measuring social constructs.

Table 1: Customer experience studies

Author (year)

Type of CX

Constructs

Novak et al. (2000)

Online Experience

Flow, Arousal, Challenge, Control, Focused Attention, Interactivity,
Speed, Involvement, Importance, Skill, Telepresence, Time
Distortion

Brakus et al. (2009)

Brand Experience

Sensory, Affective, Behavioral, Intellectual

Klaus & Maklan (2012; 2013) Service Experience

Product experience, Outcome focus, Moments-of-truth, Peace-ofmind

Khan & Rahman (2016)

Retail Brand
Experience

Brand name influence, Customer billing, order & application forms,
Mass media impression, Point-of-sales assistance, Recommendation
by a salesperson, Emotional event experience, Brand stories
connectedness

Bustamante & Rubio (2017)

In-Store Customer
Experience

Cognitive, Affective, Physical, Interaction with customers,
Interaction with employees, Social

Pelletier & Collier (2018)

Experiential
Purchases

Fun, Escapism, Servicescape quality, Social congruence, UniquenessFor consumer behavior models, many researchers have investigated the relationship between
customer experience and satisfaction and loyalty, proposing two different approaches (Bustamante &Rubio 2017). Klaus and Mklan (2012; 2013) examined service experience quality using a formativemodel and estimated indirect effects of sub-experiential dimensions on satisfaction. Brakus et al. (2009)
and Khan and Rahman (2016) assumed direct effect of an essential component of sub-experiential
dimensions using a reflective model. Although these methods differed, both approaches leveraged
customer experience to derive satisfaction directly or indirectly.
4

In addition to service experience quality, Klaus and Mklan (2012; 2013) explained the differencesof perceived service quality as an overall judgment for excellence or superiority (Parasuraman et al.
1988). They defined customer experience as “a customer’s cognitive and affective assessment of all
direct and indirect encounters with a firm relating to their purchasing behavior, triggering an experiential
quality” (Klaus & Mklan 2013, p.228; Klaus & Mklan 2012, p.10). Hence, measuring service experienceand quality should be distinguished from the measurement scales of perceived service quality(Parasuraman et al. 1985; 1988, Cronin & Tayler 1982) or customers’ evaluation of specific services.
Following Klaus and Mklan (2012; 2013), we specify that customer experience and quality are
different measurements from attribute ratings, and they are predictors of overall satisfaction.
Additionally, the attribute rating score is used to measure attribute performance, and it is an essential
factor of overall satisfaction (Arbore & Busacca 2009, Matzler et al. 2004, Mittal & Kamakura 2001,
Mittal et al. 1998, Brandt 1988). Hence, we assume that customer experience can be measured from
review texts as cognitive and affective statements of customer experiences, and that attribute ratings for
specific services take the place of attribute performances. Figure 1 shows the proposed conceptualized
model.

Customer Experience/Quality(Words in Review Text)
Overall Rating

Attribute Performance(Attribute Ratings)

Figure 1: Conceptualized Model

5

2.2.

Measurements of Online Reviews

Table 2 summarizes several studies that investigated the influence of online reviews as marketing
variables. Three variables of valance, volume, and variance were used to adopt online review data formarketing models (Kostyra et al. 2016, p.12-13). Chintagunta et al. (2010) investigated the impact of
online user reviews on box-office performance using valance, volume, and variance as averages,
numbers, and variances, respectively, for movie ratings. They found significant effects of valence;
however, they also indicated that volume and variance were not effective predictors. Marchand et al.
(2016) measured valence and volume from Twitter WOMs as a microblog and Amazon reviews as an
OCR website for video games. They found that OCRs had long-term effects on sales, whereas microblog
WOMs were effective during pre-release periods.

Table 2: WOM and OCR studies
Author (year)

Data Category

Type of WOM Variable

Objective Variable

Method/Model

Chintagunta et al. (2010)

Movie (Yahoo! Movies
website)Valence/Volume/VarianceTotal opening
earnings

Multiple Regression estimated by
GMM (generalized method of
moments)

Gopinath et al. (2014)

Cell Phone (Howard
Forums)Categorized by Attribute/Emotion/
Recommendation with Score (-2~+2
for negative to positive contents)

Sales

DHLM (dynamic hierarchicallinear modeling)

Ma et al. (2015)

Company in Fortune 500(Twitter)Categorized (Compliments/Neutral/
Complaints)

Voicing Decision(positive/neutral/neg
ative/no voicing)

HMM (hidden-Markov mode)

Kostyra et al. (2016)

eBook Reader (not real
data)

Categorized by Valence/Volume/
Variance

Choice Probability

Laboratory Experiment andConjoint Analysis by MMNLM(mixed multinomial logit model)

Marchand et al. (2017)

Video Game
(Twitter/Amazon)

Valence/Volume

Sales

OLS & 3SLS (three-stage leastsquares regression)

Wang & Chaudhry (2018)

Hotel (TripAdvisor/
Expedia/ Hotels.com/
Orbits)Categorized by Negative/Positive

RatingDID (deference in differences)

Some studies measured online reviews as a categorical variable. Ma et al. (2014) and Wang and
Chaudhry (2018) labeled WOMs as positive, negative, or neutral, based on the rating (e.g., less than 4star = negative) or WOM contents. They investigated the influence of manager responses (MR), defined6

as the act of managers publicity replying to online reviews (Wang & Chaudhry 2018, p.163). Ma et al.
(2014) indicated that MRs sometimes created negative effects. Additionally, Wang and Chaudhry (2018)
recommended managing negative reviews rather than positive ones, because they found that MRs to
positive reviews had negative impacts on later ratings. Kostyra et al. (2016), on the other hand,
performed a conjoint experiment to analyze choice probability for eBook readers using categorized
averages of ratings (valence), number of reviews (volume), and variance of ratings (variance). Theirresults indicated that valence and volume had positive effects on the choice probability and willingnessto-pay. Additionally, large level variance had a negative effect. They also found the OCRs decreased theeffect of product attributes (e.g., brand, price, and technical features) by comparing two groups: reviewprovided and other.
Apart from the three measurements and categorizing methods, Gopinath et al. (2014) introduced
scoring for WOM contents. They graded WOMs on a scale of −2 to 2 points, based on three aspects:
attribute, emotion, and recommendation, following the texts. They found significant effects of thesepredictors with cell-phone sales. Their results also indicated the importance of paying attention tocontents and not just focusing on WOM volume.

2.3.

Customer Experience and Online Review Measures

We reviewed the methods of treating online reviews as marketing variables in a previous section, finding
three issues in the preset methods. First, volume and variance were not effective in some cases(Chintagunta et al. 2010). Second, many researchers did not consider the detailed contents of online
reviews (Gopinath et al. 2014), although, some researchers categorized texts by positive and negative
content (Ma et. 2014; Wang & Chaudhry 2018). Third, there were no exact methods used to judge thetext contents and words. It is sometimes inconvenient to check all words without using effective
guidelines. However, many researchers showed interest in the impact of online reviews and developing
better methods to measure them.

7In contrast, our research measures customer experience using online reviews. On the other hand,perceived attribute performance is measured using attribute ratings, assuming that the text informationin online reviews and their ratings represent a different construct. One possible problem is that the WOM
behaviors are driven by customer satisfaction (Klaus & Maklan 2012; 2013). However, the customer
describes an event at a point in time when perceptions of their experiences are fresh. Concretely, we
prepare two example reviews, as follows:i.

“I was very satisfied, because the dinner was delicious, and I also like the buffet breakfast.
Additionally, the staff was very kind to me.”ii.

“Bad services” (lowest rating).

These reviews mainly indicate descriptions of experiences, sometimes including a reason. Izogo andJayawardhena (2018) investigated Facebook WOMs using Netnography, a qualitative researchmethodology, to study cultures and communities emerging through computer-mediated communications(Kozinets 2002). They indicated that several constructs related to customer experience could be
conjectured from WOM sentence expressions. Therefore, we use word information directly from
reviews to measure customer experience. Although Sridhar and Srinivasan (2012) adapted a similar
method and model as our concept, our study investigates the effects of word frequency on overall ratingsand compares them with the effects of each attribute rating.

3.

Methods and Model

3.1.

Basic Procedure

Our research procedure is as follows:i.

Make a frequent-term text matrix based on morphological analysis.

ii.

Compare several neural-network models.

iii.

Visualize and estimate the marginal effects of each predictor.

8

We first adapt morphological analysis to divide text samples into words and count the frequencies of
each. Second, we propose interpretable neural-network models and compare their accuracy using
training and testing datasets. Finally, we use a partial dependence plot (PDP) (Hastie et al. 2009) toinvestigate marginal effects and to discuss marketing implications.

3.2.

Neural Network as Mental Processing

This section introduces the basic feed-forward neural-network model and its use as a measurement
model for mental processing. Figure 2 indicates the neural network as a regression model.

Figure 2: Feed-forward neural-network model

Let 𝑙 = 1, … , 𝐿 represent the number of layers. The top layer (𝑙 = 𝐿) in the network is express asyi  f  xi ;   β zi
L

l 1

 c  ,L(1)

where 𝑖 is the discrete individual, 𝑦𝑖 is the objective variable (output), 𝛃(𝐿) is the vector of
regression coefficients (weight parameters), z𝑖 is the vector of latent variables, and 𝑐 (𝐿) is the constant(𝐿−1)term (bias parameter). 𝛃(𝐿) and z𝑖are thus given byβ L   1  , 2  , 3  ,
L

L

L

9

,  p L   ,

(2)

zi

   z1 L 1 , z2 L 1 , z3 L 1 ,


L 1

  g  u1

 L 1 , g u, z pL 1 

 , g u

 L 1
2

 L 13(𝑙−1)

where g is an activation function (e.g., sigmoid), and 𝑢𝑗
L 1
u1 L 1  b1 ,1   L 1    L 1u2  b2 ,1
  L 1    L 1u3   b3 ,1   L 1  
u p  b L 1 i  p ,1

(𝐿−1)

Hence, 𝑢𝑗

b1 ,2 L 1

b1 ,3 b2 ,2 L 1b2 ,3 b3 ,2 L 1b3 ,3 bp ,2 bp ,3 , g  u pL 1  ,(3)i(𝑗 = 1, … , 𝑝) is given byb1 ,q    z1 L  2   c1 L 1 
   L  2    L 1 L 1b2 , q    z2
  c2    L 1 
L

2


L 1
b3 , q    z3
   c3  .
   L  2   L 1   c p  bpL,q1   zq
i 


L 1

L 1

L 1
L 1

L 1

,

i

L 1

(4)

is a latent variable (unit) formed by former latent variables transformed using theactivation function. Rewriting Eq. (4), we obtain a simple expression,

Ui

L 1

 B L1 ziL 2 c L1 .

(5)

In the lowest latent layer (𝑙 = 0), similarly, we obtain the following equations,u11   b1 ,1 1   1
u2   b2 ,1 1   1
u3    b3 ,1   1  u p  b1  i  p ,1
1

b1 ,21

b1 ,3b2 ,21b2 ,3b3 ,21b3 ,3bp ,2bp ,31

b1 ,q   x1 0   c11 
   0    1 
1b2 ,q   x2  c2    0    1 
1b3 ,q   x3   c3  .
   0   1  bp1,q   xq  i c p 

1

1

1

1

1

(6)

Then,

Ui   B1 xi   c1 .
1

0

(7)

where 𝒙𝑖 is a vector of observable predictors (inputs). Eq. (7) indicates a formative model specification.
Therefore, the neural network can be regarded as a type of measurement model in consumer behavior
research if we predict some assessments or scores for the psychological constructs of related predictors.

3.3.

Skip-Layer Neural Network

Several related networks are used for machine leaning. Skip-layer networks (SLNet) and residual
learning networks (ResNet) are modeled as follows:10f  xi ;   x1,i β1 (1) Skip-Layerf  xi ;  

NN  x ; i(2) Fully connected networkxIi(1) Make residual between
input and output,NN  x ; i(2) Fully connected network

(8)

,

(9)

where 𝐈 is a vector whose elements are all ones. ResNet (Eq. 9) is a helpful network used for learning
deep neural networks (He et al. 2016). The network of the second term learns the residuals between theobjective and predictive variables (𝑦𝑖 − 𝒙𝑖 𝐈). The important difference of these two models and thenext three semiparametric models is that the second term contains all predictors. Hence, these twomodels offer more complicated interpretations.

3.4.

Semiparametric Neural Network

The essential problem of neural networks is their interpretability. Generally, network parameters cannot
be identified, although the neural network provides better functional approximations. This is known as
weight–space symmetry (Bishop 2006), indicating that it is nearly impossible to find unique solutions
for parameters. However, Crane–Droesch (2017; 2018) focused on the approximation properties of feedforward networks and proposed a semiparametric neural network. Let 𝑓 be a regression function; let
𝑁𝑁 be a function specified by a fully connected network containing latent variables; let 𝒙𝑖 be thepredictor (input) matrix; and let 𝜽 be all parameters containing constant terms and regression
coefficients. Crane–Droesch (2017; 2018)’s model (Figure 3) is thus given byf  xi ;  

x β

1,i 1
(1) Specified withlinear parameters NN  x2,i ; 2  ,(2) Fully connected
network except X1(10)where 𝒙1,𝑖 and 𝒙2,𝑖 are sub-vectors of 𝒙𝑖 , and 𝛃1 and 𝜽2 = 𝜽 ∖ 𝛃1 are parameters corresponding
to 𝒙1,𝑖 and 𝒙2.𝑖 , respectively. This is similar specification using a partially linear regression model(Robinson 1988); hence, we call this model as partially linear network (PLNet). Crane–Droesch (2017)
investigated the estimates for 𝛃1 using a Monte Carlo simulation, showing its unbiasedness andconsistency. Note that the linear part does not contain an intercept, because it cannot be identified
separately from the nonlinear function, 𝑁𝑁 , similar to the partially linear model (Klemelä 2014).
11

Additionally, Crane–Droesch (2017; 2018) adopted this model for panel data analysis and indicated its
better prediction compared with ordinal fixed effect models, lasso regression, random forest, and fully
connected neural networks.

Figure 3: PLNet

In our research, we extend PLNet to a nonlinearity of part or all of 𝒙1,𝑖 and propose an additivemodel learning network (AMNet) (Figure 4), as follows:f  xi ; d    NN d  xd ,i , xd2,i ,
K

d 1



, xdM,i  ; d ,(11)where 𝑑 = 1, ⋯ , 𝐾 represents the number of predictors; 𝑚 = 1, ⋯ , 𝑀 is the degree of thepolynomial; and 𝑁𝑁𝑑 is an independent network of predictor 𝑑. This model learns the independent
networks constructed by a single predictor with polynomial transformation and approximates theobjective variable using the sum of the independent nonlinear faction, 𝑁𝑁𝑑 . Thus, AMNet is a kind ofadditive model (Hastie & Tibshirani 1986). In practice, it is possible to combine AMNet, PLNet, andfully connected networks using independent predictors. Similar to the additive model, only one 𝑁𝑁𝑑
contains the intercept, but another 𝑁𝑁𝑑 does not.

12

Figure 4: AMNet

If we know the relationship of some predictors from existing knowledge or theories, AMNet can beextended as follows:

f xi ;  g    NN gGg 1

 x , x , , x  ;   ,
g
1,i

g
2,i

g
k g  , i

g

(12)

where 𝑔 = 1, … , 𝐺 is the number of independent predictor groups. For our setting, the review texts andattribute ratings represent a different construct. Thus, this model learns two networks constructed
separately of words and rating scores (see Figure 5). This becomes a grouped AMNet (G-AMNet).
Finally, Table 3 summarizes those models and their interpretability.

Figure 5: G-AMNet

13

Table 3: Neural Networks and Interpretability

Model

References

Interpretability
parameterfunction

Skip-Layer Network (SLNet)

Velten (2009),
Venables & Ripley (2002)

impossible

complicatedResdual Learning Network (ResNet)

He et al. (2016)

impossible

complicatedPartially Linear Neural Network (PLNet)

Crane-Droesch (2017; 2018)

partially

partially linear

Aditive Model Learing Network (AMNet)

This study

partially

partially linear
partially nonlinear

3.5.

Partial Dependence Function and Marginal Effect

The previous section introduced a few interpretable neural networks. However, it is still necessary toinvestigate the complicated multivariate function or fully connected network in cases such as G-AMNet.
Estimating a partial dependence function is useful to solving this problem. The partial dependence
function and PDP have been discussed to visualize the results given by some machine-learning methods(e.g., decision trees, random forests, and boosted regression) (Becker et al. 1996; Friedman 2001; Hasite
et al. 2009; Greenwell 2017). Klemalä (2014) also discussed PDP in line with nonparametric regressions(Klemalä 2014, p.298-299).
Let 𝒙 = (𝑥1 , ⋯ , 𝑥𝑑 ) represent the predictors of a regression model whose prediction is 𝑓(𝒙). If
we divide 𝒙 into an interest set, 𝑧𝑆 , and its compliment, 𝑧𝐶 = 𝒙 ∖ 𝑧𝑆 , then the “partial dependence” ofthe response on 𝑧𝑆 is defined asf S  zS   E  f  zS , zC    f  zS , zC  p C  zC  dzC ,(13)

where 𝑝𝐶 (𝑧𝐶 ) is the marginal probability of 𝑧𝐶 : 𝑝𝐶 (𝑧𝐶 ) = ∫ 𝑝(𝐱) 𝑑𝑧𝑆 . Eq. (14) can be estimated froma set training data byn1fˆS  zS    fˆ  zS , zi ,C ,
n i 114(14)

where 𝑧𝑖,𝐶 (𝑖 = 1,2, … , 𝑛) are the values of 𝑧𝐶 occurring in the training sample. Thus, it averages
over the effects of all the other predictors in the model.
To estimate the marginal effect, let 𝑧𝑖,𝑧 (𝑖 = 1,2, … , 𝑛) denote the estimates ordered points at
which the regression function is evaluated. Applying a finite-difference estimate of the derivative to𝑓̂𝑆 (𝑧𝑆 ), we obtain

dfˆS  zi , S 
dzi , SfˆS  zi , S   fˆS  zi 1, S zi , S  zi 1, S

.

(15)

Because it is inconvenient to calculate the derivative from the neural network, we simply estimate themarginal effect from the above equation, like in cases of some nonparametric regressions (Cameron &Trivedi 2005). The partial dependence function indicates an averaged 𝑓(𝒙) with respect to 𝑧𝐶 at any
data points of 𝑧𝑆 . Thus, Eq. (15) indicates an averaged change of 𝑓(𝒙) when 𝑧𝑆 is changed. For
example, assuming a simple linear regression, 𝑓(𝒙) = 𝑎 + 𝑏1 𝑥1 + 𝑏2 𝑥2 + ⋯ + 𝑏𝑑 𝑥𝑑 , we obtain𝑓𝑠 (𝒙) = 𝑎 + 𝑏𝑑 𝑥𝑑 and 𝑑𝑓𝑠 (𝒙)⁄𝑑𝑥𝑑 = 𝑏𝑑 for 𝑧𝑆 = 𝑥𝑑 . In this case, the marginal effect of Eq. (15) is
the same as the analytical solution. Assuming 𝑓(𝒙) = 𝑎 + 𝑔1 (𝑥1 ) + 𝑔2 (𝑥2 ) + ⋯ + 𝑔2 (𝑥2 ), which is a
simple expression of AMNet, we obtain 𝑓𝑠 (𝒙) = 𝑎 + 𝑔𝑑 (𝑥𝑑 ) for 𝑧𝑆 = 𝑥𝑑 , and the marginal effect canbe calculated with Eq. (15). Hence, PLNet and AMNet provide a more amenable interpretationcompared to the fully connected network.

4.

Empirical Applications

4.1.

Data Description

The data were provided by Rakuten, Inc. and contains customer reviews and ratings aboutaccommodations in Japan, posted from January 1997 to November 2015 (Rakuten, Inc. 2016). We
randomly selected 100,000 samples from the latest 2015 data, because the total sample (over 5 million)
was too large. Additionally, we deleted samples missing values and lacking reviews. We finally used
80,000 samples for training data, and the remaining 16,761 were used for test data.
15

In morphological analysis, we selected the words based on parts-of-speech tags and truncatingwords whose total frequency was less than 100 to remove unusual words. Outliers (e.g., “am,” “is,”“are,” “do,” or “does”) were also deleted. As a result, a total of 684 words were gathered, including 112
adjectives, 113 adverbs, and 459 verbs. Their frequencies were used to measure customer experience.
For attribute performance, the six variables of attribute rating scores (5 scales) were Location, Room,Meal, Bathroom (or Hot spring), Service, and Facility and Amenity (F&A). However, Meal, Bathroom,
and F&A scales contain 0 for the guests who did not use those services or for hotels not providing suchservices. We then make dummy variables (e.g., no_Meal, no_Bathroom, and no_F&A) that take 1 when
the ratings of Meal, bathroom, or F&A take 0, respectively. Additionally, because of these dummy
variables, Meal, Bathroom, and F&A contain a coefficient dummy variable that takes 1 when no_Meal,
no_Bathroom, and no_F&A are 0, respectively, and take 1 otherwise.
For the other predictors, purpose (Business, Leisure, and other) and companion (Alone, Family,
Colleague, Couple, and other) dummy variables are available. Additionally, we extracted the room typefrom room names in the dataset and created a Japanese-styled room dummy variable (J_room), whichtakes 1 for Japanese-styled rooms. Similarly, month dummies were created using character strings ofposted dates in the dataset. Table 4 displays our arranged dataset.

Table 4: Dataset arrangement

User1
User2
User3
User4
User5
User6
・
・
・

・・・

Word1 Word2
0
0
1
0
0
2
0
0
0
1
0
0
・
・
・

・・・

Word684 Location
0
4
0
4
0
4
0
5
0
5
1
5

・
・
・

・
・
・

Alone Family Colleague
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
・
・
・

・
・
・

・
・
・

Friend
0
0
1
0
0
0
・
・
・

・
・
・

Room

Meal
3
3
5
4
3
4

0
3
4
5
0
5

・
・
・

・
・
・

Bathroom Service A & F Business Leisure
3
3
3
0
1
2
3
3
1
0
4
5
4
0
1
4
4
4
0
1 ・・・
3
3
3
0
0
4
5
5
0
1
・
・
・

・
・
・

Couple no_Meal no_Bath no_A & F J_room
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
・
・
・

・
・
・

・
・
・

16

・
・
・

・
・
・

・
・
・

Jan

・
・
・

・・・

Feb
1
0
0
0
0
0
・
・
・

・
・
・

0
0
1
0
0
0
・
・
・

Oct Overall（Y）
0
4
0
3
0
4
0
5
0
4
0
5
・
・
・

・
・
・

4.2.

Comparative Models and Optimization

We compared the following five models using ordinal linear regression without the words.

f FCNet  NN Words684 , Attribtes6 , DummyVariables 21  ,(16)

f PLNet  NN Words684   Attributes6 β1  DummyVariables 21 β2 ,(17)

f P  PLNet  NN Words 684   k 1 Attributek 1 ,1  Atributek2 1 ,2 
6kk Attributek9 1 ,9k(18)

 DummyVariables 21 β 2 ,f I  AMNet  NN 0 Words 684   k 1 NN k  Attriubtek , Attributek2 ,6, Attributek7 (19) DummyVariables 21 β 2
fG  AMNet  NN 0 Words 684   NN1  Attributes 6 
 DummyVariables 21 β 2 .

fG AMNet 0  NN1  Attributes6   DummyVariables 21 β2 .

(20)

(21)

For simplicity, we note purpose, companion, no meal, no bathroom, no F&A, J_room, and month asdummy variables in the above models. FCNet is a standard feed-forward network, and PLNet sets linear
parameters for attribute ratings and dummy variables. P-PLNet contains ninth-degree polynomial terms
for each attribute rating, whereas the independent AMNet (I-AMNet) has six networks constructed byseventh-degree polynomial variables for each attribute rating with the word network. Grouped AMNet(G-AMNet) specifies the two networks as customer experience and attribute performance, constructedwith words and attribute ratings, respectively. G-AMNet0 is set without the word network to check theimportance of words as predictors.
The neural network optimization method uses Adam (Kingma & Ba 2015), and all of the necessary
pre-parameter settings follow the default values from the original paper (see Appendix II for a detailedalgorithm). This method achieves faster convergence of optimization by adjusting the learning rate withthe first and second moments of the gradients. To tune the units, we changed their number from 1 to 10,17and from 10 to 100 by 10s. Then, we chose the unit number for minimum mean squared error (MSE),
comparing the MSEs of training and test datasets among the different numbers of units. After unit tuning,
we added the latent layer and tuned the unit again. We repeated this process until the MSE stopped
improving. Using PLNet, we fixed the units and layers of the word network for the other models. Wechanged the degree of the polynomial for each attribute rating from 2 to 15 jointly and compared theMSEs. Although each predictor was normalized by dividing each maximum value for efficient learning,
we reported the results based on non-normalized parameter estimates. Table 11 in Appendix I
summarizes the details of each final network.

4.3.

Model and Coefficient Comparison

Table 5 reports the training and test MSEs for each model, showing that G-AMNet achieves the lowest
MSE, although, FCNet also shows better prediction when training MSE. Additionally, I-AMNet showsa slightly better prediction capability than P-AMNet.
Table 6 reports the estimates of linear parameters in each model. Note that the blanks in Table 6
indicate the parameter that cannot be identified from the nonlinear part. However, there is a large
difference in the estimates for the coefficients of “companion” (i.e., alone, family, colleague, couple).
Therefore, we investigate the estimates of G-AMNet to check validity. We repeated the estimation 50
times using different initial values generated from the standard normal distribution and evaluated theseries of estimates via mean and standard deviation. The results of the validation for G-AMNet are
shown in the G-AMNet (V) column of each Table. From Table 5, G-AMNet provides stable forecasting;however, we found that the estimates for the coefficients of companion depend on the initial values inTable 6.

18

Table 5: MSE

Model

LR

FCNet

PLNet

P-PLNet I-AMNet G-AMNet0 G-AMNet

G-AMNet (V)Training

0.247300.203270.22452

0.219420.21579

0.214510.203210.20188 (0.001)

Test

0.24367

0.22260

0.227940.220630.21785

0.211360.20704

0.20655 (0.001)

Table 6: Coefficient Estimates

PLNet P-PLNet I-AMNet G-AMNet0 G-AMNet
Intersept
Location
Room
Meal
BathroomService
F&A
Business
LeisureAlone
FamilyColleague
FriendCoupleno_Mealno_Bathroom
no_F & A
J_room
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct

0.116
0.256
0.139
0.087
0.269
0.095
0.014
0.024
-0.160-0.177-0.156-0.144-0.165
0.525
0.284
0.148
-0.007
0.010
0.014
0.005
-0.006
0.020
0.020
0.012
0.009
0.007
0.012

-0.002
0.011
0.066
0.054
0.078
0.090
0.074
0.910
0.766
0.034
-0.003
0.015
0.022
0.010
0.002
0.021
0.025
0.014
0.011
0.008
0.015

-0.0030.010-0.006-0.016
0.006
0.023
0.002
0.684
0.485
0.396
0.000
0.014
0.018
0.010
-0.001
0.022
0.023
0.013
0.009
0.008
0.011

G-AMNet (V)

0.001
0.006
0.117
0.099
0.131
0.143
0.125

-0.004
0.004
0.162
0.145
0.177
0.183
0.167

0.003 (0.005)
0.011 (0.005)
0.020 (0.125)
0.004 (0.124)
0.031 (0.126)
0.043 (0.125)
0.024 (0.125)-0.008
0.009
0.016
0.010
0.002
0.019
0.024
0.016
0.008
0.006
0.007

-0.011
0.012
0.020
0.012
0.004
0.017
0.025
0.013
0.009
0.006
0.010

-0.011 (0.001)
0.012 (0.001)
0.020 (0.002)
0.011 (0.002)
0.003 (0.002)
0.018 (0.002)
0.023 (0.002)
0.013 (0.002)
0.009 (0.001)
0.008 (0.001)
0.009 (0.001)

Without Words-0.166 (0.023) ***0.586 (0.012) ***1.418 (0.012) ***0.775 (0.012) ***0.445 (0.011) ***1.635 (0.013) ***0.445 (0.014) ***0.022 (0.009) **0.016 (0.008) *0.045 (0.020) *0.012 (0.020)
0.056 (0.022) **0.054 (0.021) **0.027 (0.021)
0.588 (0.010) ***0.290 (0.012) ***0.075 (0.021) ***-0.011 (0.005) *0.002 (0.009)
0.010 (0.009)
0.004 (0.009)-0.009 (0.009)
0.024 (0.008) **0.027 (0.008) **0.019 (0.008) *0.011 (0.008)
0.007 (0.008)
0.014 (0.008) .
R2
0.7217‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1

19

Adj.R20.7216RSE
0.4974

4.4.

Partial Dependence Functions and Marginal Effects

Table 7 and Figure 6 in Appendix I report the estimated partial dependence functions and marginal
effects for the attribute ratings by G-AMNet (V). Table 7 shows that nearly all estimates are stable,
although some (e.g., Meal, no_Meal, no_bathroom, and no_F&A) depend on initial values. Hence, weplan to address their instability in future studies.
From the results in Table 7 and Figure 6, we found the nonlinear relationships between attribute
ratings and overall rating so that the marginal effects of attribute ratings are not constant. The marginal
effect decreases until the rating changes to four points in Room, Meal, Bathroom, and Service. It also
keeps decreasing in F&A, whereas it increases in Location. When the rating changes from four to five,the marginal effect increases in the former four attributes (Room, Meal, Bathroom, and Service).
However, it may not provide large contributions to overall rating.

Table 7: Details of estimated marginal effects

Location

Room

Meal

BathroomService

F&A

Partially Dependence Function (PDF)
1 3.760 (0.034)
2.987 (0.051)
2 3.862 (0.022)
3.610 (0.031)
3 3.955 (0.022)
3.920 (0.023)
4 4.062 (0.021)
4.123 (0.021)
5 4.186 (0.020)
4.338 (0.022)

3.620 (0.174)
3.886 (0.177)
4.074 (0.172)
4.223 (0.176)
4.395 (0.174)

3.749 (0.077)
3.938 (0.039)
4.053 (0.029)
4.132 (0.034)
4.241 (0.030)

2.606 (0.045)
3.555 (0.042)
3.937 (0.023)
4.109 (0.022)
4.338 (0.022)

3.665 (0.055)
3.882 (0.028)
4.026 (0.021)
4.120 (0.021)
4.210 (0.022)

Marginal Effect
1-2 0.102 (0.025)
2-3 0.093 (0.007)
3-4 0.106 (0.005)
4-5 0.125 (0.004)

0.266 (0.069)
0.188 (0.012)
0.150 (0.011)
0.172 (0.009)

0.189 (0.053)
0.115 (0.015)
0.079 (0.012)
0.109 (0.015)

0.949 (0.040)
0.381 (0.034)
0.172 (0.012)
0.229 (0.010)

0.217 (0.038)
0.143 (0.016)
0.094 (0.008)
0.090 (0.010)

no_Mealno_Bathroom

no_F & A

Partially Dependence Function (PDF)
01

3.962 (0.168)
4.376 (0.415)

4.065 (0.028)
4.449 (0.448)

4.078 (0.020)
4.583 (0.109)

Marginal Effect
0-1

0.414 (0.582)

0.385 (0.466)

0.505 (0.110)

0.623 (0.036)
0.310 (0.019)
0.204 (0.008)
0.215 (0.007)

20

Table 8: Top-50 negative and positive marginal effects when the word frequency changes to one from zero

Negative
POS
never again
Adverbunfavorable
Adjective
sting
Verb
somehow/manage toAdverbthrowVerbbelieveVerbraise/wake
Verb
pay
Verb
sink
Verb
returnVerbarriveVerbnoisy
Adjective
stand/get
Verb
black
Adjective
give upVerblower/reduce
Verb
offer
Verb
lukeworm
Adjectiveraise/increase
Verb
dry
Verb
pay
Verb
peel off
Verb
wake
Verb
hurry
Verb
make a niseVerbstrange/suspicious
Adjective
horrible
Adjective
be cut off
Verb
go to/visit
Verb
float
Verb
somehow/manage toAdverbcloud/mistVerbbuild up
Verb
stop
Verb
divideVerb
dirty
Adjective
have a shower/bathVerbat least
Adverbclog up/chokeVerb
probably
Adverbtell
Verbsmell bad
Adjective
with effort
Adverbserious/heavy
Adjective
together/at the same time Adverb
connectVerbdecreaseVerbthin/weak
Adjective
fall
Verb
later
Adverbterm

Marginal Effects max-0.505 (0.030)
2-0.196 (0.029)
3-0.170 (0.023)
2-0.142 (0.026)
2-0.142 (0.016)
3-0.135 (0.013)
2-0.134 (0.020)
3-0.131 (0.021)
3-0.127 (0.013)
2-0.124 (0.017)
3-0.124 (0.016)
2-0.124 (0.009)
3-0.122 (0.011)
2-0.120 (0.020)
2-0.119 (0.014)
3-0.119 (0.013)
2-0.116 (0.014)
2-0.116 (0.010)
2-0.113 (0.015)
2-0.112 (0.017)
2-0.112 (0.018)
9-0.111 (0.013)
2-0.111 (0.012)
2-0.110 (0.017)
3-0.109 (0.009)
2-0.108 (0.019)
2-0.108 (0.013)
5-0.107 (0.015)
2-0.106 (0.015)
2-0.105 (0.016)
2-0.104 (0.013)
2-0.102 (0.023)
2-0.102 (0.022)
3-0.101 (0.024)
1-0.100 (0.008)
2-0.099 (0.010)
4-0.099 (0.016)
4-0.098 (0.011)
2-0.097 (0.022)
2-0.095 (0.015)
1-0.095 (0.009)
5-0.091 (0.006)
7-0.091 (0.007)
3-0.090 (0.012)
3-0.090 (0.012)
2-0.090 (0.017)
3-0.087 (0.013)
2-0.084 (0.006)
3-0.084 (0.012)
4-0.082 (0.018)
2

21

term
utilize/use
savesuitable/exactly
elaborate
not crowded
rathernever
really/please
completely
excel
smooth/slippy
apparently
lightsimmerboil
spreadfuthermore
stretchmostlyso/that muchreally/please
contrary
bring/report
forcibly
get bored/tired
face/touchtakenarrow/limit
entirelypretty/cutetake out
pleasecan staty
alwayssufficiently
read
pass
stick/keep tosometimes
watch
shrinkinteresting/funsqueeze
relatively
quick
rememberequip/have
unexpectedly
keep
can get/have

Positive
Marginal Effects max
POS
Verb
0.144 (0.023)
2
Verb
0.124 (0.021)
2
Adverb0.120 (0.013)
2
Verb
0.111 (0.017)
1
Verb
0.108 (0.015)
2
Adverb
0.103 (0.016)
1
Adverb
0.097 (0.012)
2
Adverb
0.096 (0.006)
2
Adverb
0.093 (0.012)
2
Verb
0.093 (0.009)
2
Adverb
0.091 (0.011)
3
Adverb
0.090 (0.011)
2
Adjective 0.085 (0.013)
2
Verb
0.083 (0.014)
2
Verb
0.080 (0.013)
3
Verb
0.079 (0.014)
1
Adverb
0.077 (0.013)
2
Verb
0.077 (0.010)
3
Adverb
0.077 (0.013)
2
Adverb
0.077 (0.010)
2
Adverb
0.076 (0.004)
3
Adverb
0.072 (0.019)
1
Verb
0.070 (0.014)
2
Adverb
0.070 (0.007)
2
Verb
0.069 (0.007)
2
Verb
0.069 (0.016)
3
Verb
0.069 (0.014)
3
Verb
0.068 (0.013)
1
Adverb
0.068 (0.016)
1
Adjective 0.066 (0.010)
3
Verb
0.065 (0.016)
3
Adverb
0.065 (0.004)
2
Verb
0.065 (0.003)
3
Adverb
0.064 (0.007)
2
Adverb
0.063 (0.007)
2
Verb
0.063 (0.013)
3
Verb
0.063 (0.019)
2
Verb
0.062 (0.015)
3
Adverb
0.062 (0.009)
2
Verb
0.061 (0.012)
5Verb
0.061 (0.013)
3
Adjective 0.057 (0.007)
2
Verb
0.057 (0.011)
4Adverb
0.056 (0.008)
2
Adjective 0.056 (0.014)
2
Verb
0.056 (0.016)
3
Verb
0.055 (0.014)
2
Adverb
0.055 (0.008)
2
Verb
0.055 (0.011)
2
Verb
0.055 (0.006)
2

Table 8 summarizes the top-50 words ordered by the magnitudes of negative and positive marginal
effects when the word frequency increases from zero to one. Figure 7 in Appendix I picks up the twowords, “unfavorable” and “light,” which are the top negative and positive words among adjectives,
respectively. Additionally, the details of estimates for partial dependence functions and marginal effects
are reported in Table 9.
In Table 8, we find the asymmetry effect between negative and positive words, so that the marginal
effects of negative words are larger than that of positive words. This result indicates that managing thenegative customer reviews is more important. This was a similar conclusion of Wang and Chaudhry(2018). Figure 7 and Table 9 indicate that the positive and negative marginal effects decrease withincreasing frequencies of “unfavorable” and “light,” respectively. Note that these marginal effects are
estimated based on overall rating. For negative words, a negative effect is estimated, because the wordmight be used frequently in customer reviews with lower overall ratings. Therefore, some words might
appear unreasonable.

Table 9: Illustrations of partial dependence functions and marginal effect for words

Unfavorable

0
1
2
3
4
5

PDF
4.082 (0.020)
3.886 (0.036)
3.682 (0.064)
3.541 (0.084)
3.461 (0.094)
3.415 (0.100)

Light

Marginal Effect
0-1
1-2
2-3
3-4
4-5

0
1
2
3
4
5

-0.196 (0.029)-0.205 (0.036)-0.141 (0.028)-0.081 (0.022)-0.045 (0.017)

PDF
4.082 (0.020)
4.167 (0.023)
4.223 (0.034)
4.257 (0.046)
4.279 (0.057)
4.293 (0.066)

Marginal Effect
0-1
1-2
2-3
3-4
4-5

0.085 (0.013)
0.055 (0.017)
0.035 (0.016)
0.022 (0.013)
0.014 (0.010)

Comparing the marginal effects of attribute ratings and words, the overall ratings seem to be more
affected by attribute service performance. However, we found that word frequency was important when
the attribute ratings achieved higher points (3–5). Because we assume the review texts represents acustomer experience, managers should pay attention to customer experiences, even if they obtain better22

service attribute assessments. Additionally, it is effective to overall customer satisfaction to keep
providing better experiences so that the customers willingly write positive reviews. Therefore, it is usefulto realize improvement by investigating the review text based on the negative words estimated by GAMNet.
Finally, we select the most effective two words (i.e., “never again” and “unfavorable”) and illustrate
an example for a 2-dimensional partial dependence plot. The results are reported in Table 10 and Figure
8. When the frequency of the phrase, “never again,” changes from zero to one, the marginal effects of“unfavorable” decreases. Similarly, increasing the frequency of “unfavorable,” the marginal effect of“never again” decreases. Focusing on the interaction effect, a “never again” and an “unfavorable” easily
promote decreasing overall ratings. However, it needs four “unfavorables” to reduce the overall ratingby the same magnitude as without a “never again.” For illustration purposes, compare the color of theheat map and the two line graphs in Figure 8. These 2-dimensional PDPs should help obtaining a properinterpretation for interaction effects.

Table 10: Illustrations of 2-dimensional partial dependence functions and marginal effects

0
1
2
3
4
5

0
1
2
3
4
5

5.

Conclusions and Future Research-0.507 (0.031)-0.425 (0.036)-0.280 (0.056)-0.169 (0.065)-0.104 (0.064)-0.067 (0.058)

Never_again (fixed)01

Unfavorable

Never_again
0-1

Unfavorable

Never_again
01
4.084 (0.020)
3.577 (0.034)
3.888 (0.036)
3.463 (0.046)
3.683 (0.064)
3.402 (0.067)
3.542 (0.084)
3.372 (0.081)
3.461 (0.094)
3.357 (0.091)
3.416 (0.100)
3.348 (0.096)

Marginal Effect

Unfavorable (fixed)

Partial Dependence Function

0-1
1-2
2-3
3-4
4-5

-0.197 (0.029)-0.205 (0.036)-0.141 (0.028)-0.081 (0.022)-0.045 (0.017)-0.115-0.060-0.030-0.016-0.008(0.039)(0.028)(0.018)(0.012)(0.008)This study proposed a marketing model to estimate the impact of customer experience using a
constrained neural network to process online review data. We investigated the relationship of overallratings with customer experience and attribute performance. G-AMNet achieved better performance23

than a fully connected neural network, indicating that different variables types should need to be treatedseparately when applying neural networks. We attribute this to a technique called “dropout,” which
randomly drops units and their connections from the fully connected neural network during training.
This makes it possible to improve the accuracy while avoiding overfitting (Srivastava et al. 2014). GAMNet and the other semiparametric neural networks can be regarded as special cases of dropout.
Social science data is often handled differently from those of natural science or machine learning.
Thus, it might be important to consider the model-driven approach of machine-learning algorithms forsocial science applications. In this study, we assumed that customer reviews and attribute ratings
represented a different construct, then the G-AMNet learns the variables as separate networks.
Additionally, the PDP estimated by this model provides natural interpretations for customer experienceand attribute performance. The results indicate that the impactful words are useful to finding
implementations of customer experience and services, and the negative words are especially important,because the customer might be more sensitive to the negative experience than the positive one.
For future research, there are three main limitations and issues. First, it is necessary to develop ameasuring and validation method to specify the psychological variables from the text data posted bycustomers. According to Izogo and Jayawardhera (2018), customer reviews and experiences have astrong relationship. However, there are no systematic methods to measure the constructs from the textual
data. Toubia et al. (2019) estimated latent topics based on psychological theory, and Humphreys andWang (2018) called the latent topic a construct and discussed the applications of LDA in social science.
For neural networks, CR and AVE (Sato 2019, Fornell & Larcker 1981) can be extended, because Sato(2019) proposed the construct validation for a nonlinear measurement model and discussed thereliability coefficient with the marginal effect estimation.
Second, the setting of our conceptualized model requires more strict causal relationships, because
our model is very simple. For example, the relationship between customer experience and attribute
performance should be estimated. However, we did not achieve this with our neural network. Moreover,past reviews might provide customer expectations or ideal points, affecting customer experience.
24

Therefore, specifying causal relationships among predictors and introducing dynamic effects in the
network should improve the accuracy and validity of our model. The heterogeneity of consumers, hotels,
and regions having high dimensional word data is an important remaining issue. Additionally, it requires
specifying the context of the words and discussing how to find and visualize important interaction effects
among the words.
Third, we should investigate the theoretical property of neural networks and apply it to the Bayesianneural-network method (e.g., Gaussian process regression model (Lee et al. 2018)). Because someestimates were unstable in G-AMNet, discovering this reason is very important for neural network
interpretations in the social sciences. Additionally, the stochastic model for high dimensional data, such
as Gaussian process regression, provides probabilistic inferences for the estimated parameters andfunctions. This is an advantage of the Bayesian neural network. Combining other Bayesian methods, we
expect to resolve the sparsity of marketing data, which does not contain enough data when sorted byindividuals.

References
Anderson, Eugene W. and Mary W. Sullivan (1993), The Antecedents and Consequences of Customer
Satisfaction for Firms, Marketing Science, 12(2), 125-143.
Anderson, Eugene W. and Vikas Mittal (2000), Strengthening the Satisfaction-Profit Chain, Journal ofService Research, 3(2), 107-120.
Arbore, Alessandro and Bruno Busacca (2009), Customer Satisfaction and Dissatisfaction in Retail
Banking: Exploring the asymmetric impact of attribute performance, Journal of Retailing andConsumer Services, 16(4), 271-280.
Becker, Richard A., William S. Cleveland, and Ming–Jen Shyu (1996), The Visual Design and Controlof Trellis Display, Journal of Computational and Graphical Statistics, 5(2), 123-155.
Bishop, Christopher M. (2006), Pattern Recognition and Machine Learning, Springer.
25

Bleier, Alexander, Colleen M. Hormeling, and Robert W. Palmatier (2019), Creating Effective Online
Customer Experiences, Journal of Marketing, 83(2), 98-119.
Brandt, D. Randall (1988), How Service Marketers Can Identify Value-Enhancing Service Elements,
Journal of Service Marketing, 2(3), 35-41.
Brakus, J. Josko, Brend H. Schmitt, and Lia Zarantonello (2009), Brand Experience: What Is It? How
Is It Measured? Does It Affect Loyalty?, Journal of Marketing, 73(3), 53-68.
Büschken, Joachim and Greg M. Allenby (2016), Sentence-Based Text Analysis for Customer Reviews,
Marketing Science, 35(6), 953-975.
Bustamante, Juan Carlos and Natalia Rubio (2017), Measuring Customer Experience in Physical Retail
Environments, Journal of Service Management, 28(5), 884-913.
Cameron, A. Colin and Pravin K. Trivedi (2005), Microeconometrics: Methods and Applications,Cambridge University Press.
Chen, Yubo and Jinhong Xie (2008), Online Consumer Review: Word-of-Mouth as a New Element ofMarketing Communication Mix, Management Science, 54 (3), 477-491.
Cheung, Christy M. K. and Matthew K. O. Lee (2009), User Satisfaction with an Internet‐Based Portal:
An asymmetric and nonlinear approach, Journal of the American Society for Information Scienceand Technology, 60(1), 111-122.
Chintagunta, Pradeep K., Shyam Gopinath, and Sriram Venkataraman (2010), The Effect of Online User
Reviews on Movie Box Office Performance: Accounting for Sequential Rollout and Aggregation
Across Local Markets, Marketing Science, 29(5), 944-957.
Collobert, Ronan, Jason Weston, Léon Bottou, Michael Karlen, Koray Kavukcuoglu, and Pavel Kuksa(2011), Natural Language Processing (Almost) from Scratch, Journal of Machine Learning
Research, 12, 2493-2537.
Crane–Droesch, Andrew (2017), Semiparametric panel data models using neural networks,
arXiv:1702.06512v2, 1-15.

26

Crane–Droesch, Andrew (2018), Machine Learning Methods for Crop Yield Prediction and Climate
Change Impact Assessment in Agriculture, Environmental Research Letters, 13(11), 1-12.
Cronin, Joseph J. and Steven A. Taylor (1992), Measuring Service Quality: A Reexamination andExtension, Journal of Marketing, 56(3), 55-68.
Falk, Tmas, Maik Hammerschmidt, and Jeroen J. L. Schepers (2010), The Service Quality-Satisfaction
Link Revisited: Exploring Asymmetries and Dynamics, Journal of the Academy of Marketing
Science, 38(3), 288-302.
Finn, Adam (2011), Investigating the Non-linear Effects of E-Service Quality Dimensions on Customer
Satisfaction, Journal of Retailing and Consumer Services, 18, 27-37.
Fornell, Claes, and David F. Larcker (1981), Evaluating Structural Equation Models with Unobservable
Variables and Measurement Error, Journal of Marketing Research, 18(1), 39-50.
Friedman, Jerome H. (2001), Greedy Function Approximation: A Gradient Boosting Machine, The
Annals of Statistics, 29(5), 1189-1232.
Gómez, Miguel I., Edward W. McLaughlin, Dich R. Wittink (2004), Customer Satisfaction and Retail
Sales Performance: An empirical investigation, Journal of Retailing, 80(4), 265-278.
Goodfellow, Ian, Y. Benigo, and A. Courville (2016), Deep Learning, The MIT Press.
Gopinath, Shyam, Jacquelyn S. Thomas, and Lakshman Krishnamurthi (2014), Investigating theRelationship Between the Content of Online Word of Mouth, Advertising, and Brand Performance,
Marketing Science, 33(2), 241-258.
Greenwell, Brandon M. (2017), pdp: An R Package for Constructing Partial Dependence Plots, The R
Journal, 9(1), 421-436.
Grewal, Dhruv, Mchael, Levy, and V. Kumar (2009), Customer Experience, Management in Retailing:
An Organizing Framework, Journal of Retailing, 85(1), 1-14.
Hastie, Trevor and Robert Tibshirani (1986), Generalized Additive Models, Statistical Science, 1(3),297-318.

27

Hastie, Trevor, Robert Tibshirani, and Jerome Friedman (2009), The Elements of Statistical Learning:
Data Mining, Inference, and Prediction Second Edition, Springer.
He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sum (2016), Deep Residual Learning for Image
Recognition, 2016 IEEE Conference on Computer Vision and Pattern Recognition, 771-778
Hoch, Stephen J. (2002), Product Experience is Seductive, Journal of Consumer Research, 29(3), 448454.
Hoffman, Donna L. and Thomas P. Novak (1996), Marketing in Hypermedia Computer-MediatedEnvironments: Conceptual Foundations, Journal of Marketing, 60(3), 50-68.
Holbrook, Morris B. and Elizabeth C. Hirschman (1982), The Experiential Aspects of Consumption:
Consumer Fantasies, Feelings, and Fun, Journal of Consumer Research, 9(2), 132-140.
Hui, Michael K. and John E. G. Bateson (1991), Perceived Control and the Effects of Crowding andConsumer Choice on the Service Experience, Journal of Consumer Research, 18(2), 174-184.
Humphreys, Ashlee, and Rebecca Jem–Hui Wang (2018), Automated Text Analysis for Consumer
Research, Journal of Consumer Research, 44(6), 1274-1306.
Izogo, Emest Emeka and Chanaka Jayawardhena (2018), Online Shopping Experience in An Emerging
e-retailing market: Towards a Conceptual Model, Journal of Consumer Behavior, 17(4), 379-392.
Khan, Imran and Zillur Rahman (2016), Retail Brand Experience: Scale Development and Validation,
Journal of Product & Brand Management, 25(5), 435-451.
Kingma, Diederik P. and Jimmy Lei Ba (2015), ADAM: A Method for Stochastic Optimization,
arXiv:1412.6980v8, 1-15.
Klaus, Philipp 'Phil' and Stan Maklan (2012), EXQ: A Multiple-item Scale for Assessing Service
Experience, Journal of Service Management, 23(1), 5-33.
Klaus, Philipp 'Phil' and Stan Maklan (2013), Towards A Better Measure of Customer Experience,
International Journal of Market Research, 55(2), 5-33.
Klemelä, Jussi Sakari (2014), Multivariate Nonparametric Regression and Visualization: With R andApplications to Finance, Wiley.
28

Kostyra, Daniel S., Jochen Reiner, Martin Natter, and Daniel Klapper (2016), Decomposing the Effectsof Online Customer Reviews on Brand, Price, and Product Attributes, International Journal of
Research in Marketing, 33(1), 11-26.
Kozinets, Robert V. (2002), The Field Behind the Screen: Using Netnography for Marketing Researchin Online Communities, Journal of Marketing Research, 39(1), 61-72.
Kozinets, Robert V., Kristine de Valck, Andrea C. Wojnicki, and Sarah J.S. Wilner (2010), Networked
Narratives: Understanding Word-of-Mouth Marketing in Online Communities, Journal ofMarketing, 74(2), 71-89.
Krein, Roger A., Ambuj Jain, and Daniel J. Howard (1992), Store Shopping Experience and Consumer
Price-Quality-Value Perceptions, Journal of Retailing, 68(4), 376-398
Larasati, Aisyah, Camille DeYong, and Lisa Slevitch (2011), Comparing Neural Network and Ordinal
Logistic Regression to Analyze Attitude Responses, Service Science, 3(4), 304-312.
Lee, Joehoon, Yasaman Bahri, Romman Novak, Samuel S. Schoenholz, Jeffery Pennington, and Jascha
Sohl-Dickstein (2018), Deep Neural Networks as Gaussian Processes, arXiv:1711.00165, 1-17.
Lemon, Katherine N. and Peter C. Verthoef (2016), Understanding Customer Experience Throughout
the Customer Journey, Journal of Marketing, 80(6), 69-96.
Lin, Shu–Ping, Chen-Lung Yang, Ya–hui Chan, and Chwen Sheu (2010), Refining Kano's ‘Quality
Attributes–Satisfaction’ Model: A moderated regression approach, International Journal of
Product Economics, 126(2), 255-263.
Ma, Liye, Baohong Sun, and Sunder Kekre (2015), The Squeaky Wheel Gets the Grease- An Empirical
Analysis of Customer Voice and Firm Intervention on Twitter, Marketing Science, 43(5), 627-645.
Marchand, André, Thorsten Hernnig–Thurau, and Caroline Wiertz (2017), Not all Digital Word of
Mouth is Created Equal: Understanding the Respective Impact of Consumer Reviews andMicroblogs on New Product Success, International Journal of Research in Marketing, 34(2), 336354.

29

Matzler, Kurt, Franz Bailom, Hans H. Hinterhuber, Birgit Renzl, and Johann Pichler (2004), The
Asymmetric Relationship Between Attribute-Level Performance and Overall Customer
Satisfaction: A reconsideration of the importance–performance analysis, Industrial Marketing
Management, 33(4), 271-277.
Mittal, Vikas, Wagner A. Kamakura (2001), Satisfaction, Repurchase Intent, and Repurchase Behavior:
Investigating the Moderating Effect of Customer Characteristics, Journal of Marketing Research,
38(1), 131-142.
Mittal, Vikas, William T. Ross, Jr., and Patrick M. Baldasare (1998), The Asymmetric Impact ofNegative and Positive Attribute-Level Performance on Overall Satisfaction and Repurchase
Intentions, Journal of Marketing, 62(1), 33-47.
Nikhashemi, S. R., Charles Jebrarhakirthy, and Khaldoon Nusair (2019), Uncovering the Roles of Retail
Brand Experience and Brand Love in the Apparel Industry: Non-linear Structural Equation
Modelling Approach, Journal of Retailing and Consumer Services, 48, 122-135.
Novak, Thomas P., Danna L. Hoffman, and Yiu–Fai Yung (2000), Measuring the Customer Experiencein Online Environments: A Structural Modeling Approach, Marketing Science, 19(1), 22-42.
Parasuraman, A., Valarie A. Zeithaml, and Leonard L. Berry (1985), A Conceptual Model of Service
Quality and Its Implications for Future Research, Journal of Marketing, 49(4), 41-50.
Parasuraman, A., Valarie A. Zeithaml, and Leonard L. Berry (1988), SERVQUAL: A Multiple-Item
Scale for Measuring Consumer Perceptions of Service Quality, Journal of Retailing, 64(1), 12-40.
Parasuraman, A., Valarie A. Zeithaml, and Leonard L. Berry (1994), Reassessment of Expectations as a
Comparison Standard in Measuring Service Quality: Imprications for Further Research, Journal ofMarketing, 58(1), 111-124.
Pelletier, Mark J. and Joel E. Collier (2018), Experiential Purchase Quality: Exploring the Dimensions
and Outcomes of Highly Memorable Experiential Purchases, Journal of Service Research, 21(4),456-473.

30

Proserpio, Davide and Georgios Zervas (2017), Online reputation Management: Estimating the Impactof Management Response on Consumer Reviews, Marketing Science, 36(5), 645-665.
Rakuten, Inc. (2016), Rakuten Travel data, Informatics Research Data Repository, National Institute of
informatics. (dataset). https://doi.org/10.32130/idr.2.2.
Robinson, P. M. (1988), Root-N-Consistent Semiparametric Regression, Econometrica, 56(4), 931-954.
Sato, Toshikuni (2019), Construct Validation for a Nonlinear Measurement Model in Marketing andConsumer Behavior Research, Data Science and Service Research Discussion Paper (Tohoku
University), No.101, 1-39.
Schmitt, Brend (1999), Experiential Marketing, Journal of Marketing Management, 15(1), 53-67.
Sridhar, Shrihari and Rajin Srinivasan (2012), Social Influence Effects in Online Product Ratings,
Journal of Marketing, 76(5), 70-88.
Srivastava, Nitish, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov (2014),
Dropout: A Simple Way to Prevent Neural Networks from Overfitting, Journal of Machine
Learning Research, 15(1), 1929-1958.
Teixeira, Jorge, Lia Patrício, Nuno J. Nunes. Leonel Nóbrega, Raymond P. Fisk, and Larry Constantine(2012), Customer Experience Modeling: From Customer Experience to Service Design, Journal ofService Management, 23(3), 362-276.
Tirunillai, Seshadri and Gerard J. Tellis (2014), Mining Marketing Meaning from Online Chatter:
Strategic Brand Analysis of Big Data Using Latent Dirichlet Allocation, Journal of Marketing
Research, 51(4), 463-479.
Toubia, Olivier, Garud Iyengar, Renée Bunnell, and Alain Lemaire (2019), Extracting Feature ofEntertainment Products: A Guided Latent Dirichlet Allocation Approach Informed by thePsychology of Media Consumption, Journal of Marketing Research, 56(1), 18-36.
Trusov, Michael, Randolph E. Bunklin, and Koen Pauwels (2009), Effects of Word-of-Mouth versus
Traditional Marketing; Findings from an Internet Social Networking Site, Journal of Marketing,73(5), 90-102.
31

Velten, Kai (2009), Mathematical Modeling and Simulation: Introduction for Scientists and Engineers,
Wiley.
Venables, W. N. and B. D. Ripley (2002), Modern Applied Statistics with S, Springer.
Verhoef, Peter C., Katherine N. Lemon, A. Parasuraman, Anne Roggeveen, Michael Tsiros, and Leonard
A. Schlesinger (2009), Customer Experience Creation: Determinants, Dynamics and Management
Strategies, Journal of Retailing, 85(1), 31-41.
Wang, Yang and Alexander Chaudhry (2018), When and How Managers' Responses to Online Reviews
Affect Subsequent Reviews, Journal of Marketing Research, 55(2), 163-177.

32

Appendix I: Other Figures and Tables
Table 11: Details of each network

Model

FCNet

0th

1st

Words (684)
Attribute ratings (6)Dummy
Variables (21)8

Words (684)3Layer (unit or dimension)
2nd

3rd

4th

5th

9

9

4

Output (1)78Attribute Ratings (6)Dummy
Variables (21)Output (1)8
9th Degree Polynomial
for Each Attribute Rating
(54)
Dummy
Variables (21)Output (1)PLNet

Words (684)37P-PLNetWords (684)3

I-AMNet7
7th Degree Polynomial
Location (7)7th Degree Polynomial
Room (7)7th Degree Polynomial
Meal (7)7th Degree Polynomial
Bathroom (7)7th Degree Polynomial
Service (7)7th Degree Polynomial
F & A (7)

8
7
7
7
7

Output (1)

7
7
Dummy
Variables (21)attribute ratings (6)

70

100

30

40
Output (1)Dummy
Variables (21)attribute ratings (6)Words (684)
80

3
80

7
50

8
8
Output (1)Dummy
Variables (21)G-ANnet0

G-AMNet33

Figure 6: Partial dependence plots and marginal effect of each attribute rating on overall rating

34

35

Figure 7: Partial dependence plots and marginal effect of each word on overall rating

Figure 8: Different kinds of 2-dimensional partial dependence plot example

36

Table 12: Descriptive statistics for each variable

Location
Room
Meal
BathroomService
F&A

mean
4.084 (4.076)
4.193 (4.202)
3.937 (3.935)
4.002 (3.933)
3.952 (3.937)
3.970 (3.966)
3.945 (3.934)

Business
LeisureAlone
FamilyColleague
FriendCoupleno_Mealno_Bathroom
no_F & A
J_room
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct

freqency
22781(4779)
52905 (11140)
38330(8081)
30257(6385)
2892
(595)
4060
(828)
3790
(726)
23288
(4835)
3707
(738)
665
(138)
15646
(3373)
5800(1210)
4880
(967)
5449
(1127)
4865(1052)
7857(1670)
7374(1553)
7792(1634)
10960(2339)
9565(1946)
8061(1701)Overallvariance
0.889 (0.894)
0.720 (0.714)
1.007 (1.016)
0.948 (0.961)
0.989 (0.997)
0.987 (0.981)
0.992 (1.005)

37

min
1 (1)
1 (1)
1 (1)
1 (1)
1 (1)
1 (1)
1 (1)

1st.q
4 (4)
4 (4)
3 (3)
4 (3)
3 (3)
3 (3)
3 (3)

median
4 (4)
4 (4)
4 (4)
4 (4)
4 (4)
4 (4)
4 (4)

3rd.q
5 (5)
5 (5)
5 (5)
5 (5)
5 (5)
5 (5)
5 (5)

max
5 (5)
5 (5)
5 (5)
5 (5)
5 (5)
5 (5)
5 (5)

Appendix II: Details of ADAM
Back propagation with ADAM (Kingma & Ba, 2015; Goodfellow et al., 2016)
Require: L, Network depth
Require: 𝐁(𝑙) , 𝑙 ∈ {1,2, … , 𝐿}, The weight matrices, vectors, or scalars of the model.
Require: 𝒄(𝒍) , 𝑙 ∈ {1,2, … , 𝐿}, The bias (constant) parameters of the model.
Require: 𝐱, Input variables.
Require: 𝒚, Output variables.
Require: 𝑛 ∈ {1,2, … , 𝑁𝑑 }, Mini-batch size.
Require: 𝛼, Step size (𝛼 = 0.001).
Require: 𝜖, Small constant (𝜖 = 10−8) used for numerical stabilization.
Require: 𝜌1 , 𝜌2 ∈ [0,1), Exponential decay rates for moment estimates (𝜌1 =0.9, 𝜌2 =0.999).
Initialization：𝑡 ← 0 (Initialize time step)for 𝑙 = {1,2, … , 𝐿} do
(𝑙)

(𝑙)

𝐁0 , 𝒄0 ← 𝑁(0,1) (Initialize weight and bias parameters applied elementwise.),
(𝑙)

(𝑙)

(𝑙)

𝜽0 = {𝐁0 , 𝒄0 } (Combine weight and bias parameters as one matrix orvector.),(𝑙)

𝒈0 ← 𝟎 (Initialize 1st moment corresponding to the weight and bias
parameters),

38

(𝑙)

𝒉0 ← 𝟎 (Initialize 2st moment corresponding to the weight and bias
parameters).
end forStart Optimization：
(1)

(2)

(𝐿)

while 𝜽𝑡 , 𝜽𝑡 , …, 𝜽𝑡

not converged do𝑡 ← 𝑡 + 1 (Iteration number).
Forward computation：𝐙(0) ← 𝐱 (Set input variables).
for 𝑙 = {1,2, … , 𝐿} do
(𝑙)

(𝑙)

𝐔 (𝑙) = 𝐁𝑡−1 𝐙(𝑙−1) + 𝒄𝑡−1 1𝑁 ,(A.1)

𝐙(𝑙) = g (𝑙) {𝐔 (𝑙) },

(A.2)

(𝑙)

(𝑙)

(𝑙)

𝜽𝑡−1 = {𝐁𝑡−1 , 𝒄𝑡−1 } (Combine weight and bias parameters as one matrix orvector.).
end for̂ = 𝐙(𝑙) (Compute Predicted Outputs),𝒚̂, 𝒚) (Compute Total Loss).
𝐽 = 𝐿(𝒚Backward computation：
(𝐿)

(A.3)

̂, 𝒚) = 𝒚
̂ − 𝒚.
∆𝑡 ← 𝛻𝒚̂ 𝐿(𝒚for 𝑙 = {𝐿 − 1, 𝐿 − 2, … ,1} do

39

(𝑙)

(𝑙+1) (𝑙+1)∆𝑡 ← 𝑓 ′(𝑙) {𝐔(𝑙) }⨀ {𝐁𝑡−1 ∆𝑡(𝑙−1) 𝑇
1 (𝑙) 𝐙(𝑙)𝜕𝜽𝑡 = 𝑁 ∆ [
]
1𝑁 𝑑
𝑑

(A.4)

},

(Compute gradients on weights and biases),

(𝑙)

(𝑙)

(𝑙)

(𝑙)

(𝑙)

(𝑙)

𝒈𝑡 ← 𝜌1 𝒈𝑡−1 + (1 − 𝜌1 )𝜕𝜽𝑡

(Update biased first moment estimate),(𝑙)𝒉𝑡 ← 𝜌2 𝒉𝑡−1 + (1 − 𝜌1 )𝜕𝜽𝑡 ⨀𝜕𝜽𝑡(Update biased second raw moment

estimate),
(𝑙)

(𝑙)

̂ 𝑡 ← 𝒈𝑡 ⁄(1 − 𝜌1𝑡 ) (Compute bias-corrected first moment estimate),𝒈̂ (𝑙) ← 𝒉(𝑙) ⁄(1 − 𝜌2𝑡 )𝒉𝑡𝑡(Computebias-corrected

secondraw

momentestimate),
(𝑙)
(𝑙)
(𝑙)
̂ (𝑙) + 𝜖) (Update weights and biases applied̂ 𝑡 ⁄(√𝒉𝜽𝑡 ← 𝜽𝑡−1 − 𝛼 𝒈𝑡element-wise),
(𝑙)

(𝑙)

(𝑙)

{𝐁𝑡 , 𝒄𝑡 } = 𝜽𝑡(Obtain updated weights and biases).

end while
(1)

(2)

(𝐿)

return 𝜽𝑡 , 𝜽𝑡 , …, 𝜽𝑡(Resulting parameters).

40

For equations (A.1) and (A.2), let 𝑝 be a number of unit in the 𝑙 th layer, and let 𝑞 be a number ofunit in 𝑙 − 1st layer, 𝐔 (𝑙) , defined as:llUl   U1  ,...,U N d  ,

(22)

where

U nl   Bl  znl 1  c l  b1 ,1u1l   l  l   b2 ,1u2  l  l  u3    b3 ,1  l   l 
u p 
  n bp ,1lb1 ,2lb1 ,3b2 ,2lb2 ,3b3 ,2lb3 ,3bp ,2bp ,3lb1 , q   z1l 1  c   l 1  l 1 l b2 , q   z2 c2   l 1 lb3 ,q   z3   c3  ,    l 1  
 l    zq c p 
bp ,q  
n

l

l

l

l

l

(23)

and

 z1l   g l   u1   l   l 
 z2 
 g  u2   l   l 
 z3    g  u3   ,  l   l g  u p 
zp 

n
 n (24)

for n = 1,…, N𝑑 . g (𝑙) is an activation function.
In Eq. (A.3) & (A.4), for the top layer (𝑙 = 𝐿), let 𝐸𝑛 == 1⁄2 (𝑦̂𝑛 − 𝑦𝑛 )2 be a loss function for
(𝐿)

(𝐿)

(𝐿)

sample 𝑛, and put 𝑦̂𝑛 = 𝑧𝑛 = 𝑢𝑛

1,Ln (𝐿)for a regression setting. Because 𝑑 (𝑢𝑛 − 𝑦𝑛 )⁄𝑑𝑢𝑛 = 1,

En
 L

un

 un L   yn  zn L   yn  yˆ n  yn .

(25)

Hence,

  L   1 ,1 , 1 ,2 ,..., 1 , Nd  .
L

L

L

(26)

For the other layers (𝑙 = 𝐿 − 1, 𝐿 − 2, … ,1), let 𝑟 be a unit number in the 𝑙 + 1st layer. Then, pl ,n 

En
l 

u p

   rl,n1 brpl 1 g   u pl ,n  .
r

41

(27)

Hence, 1l,1 l
  2 ,1
l 
 

 l   p ,1

1l,21l, N 

l 

l 

 2 ,2
 pl ,2d

 2 ,N .
 pl ,Nd d(28)

For PLNet and AMNet, consider adding some units or inputs independently in Eq. (A.1), divide
𝑝 = 𝑝̅ + 𝑝̃, and 𝑞 = 𝑞̅ + 𝑞̃, and define Eq. (A.1’) as follows:

U nl   Bl  znl 1  c l 
U1l,n  B l  0   z1nl 1  cn l   l     l     l 1    l  U n   0 B   zn  cn  b1,1l  u1 l  






 l 
 u l  b p    p ,1
l


 0
u 

 p 1  l  u p  p  n  0b1,q
l

0

l 

l 
  z1 l 1  c1 








  l 1
 cp 
0   zq 

 
 .
 l 1 l c p 1 bp 1 ,q  q zq 1









  l 1 l cbp  p ,q  q   zq  q  n  p  p 0

bp , q00

bp 1 ,q 10bp  p ,q 1

l

l

(29)

Hence, the above equation can be regarded as a restricted equation with fixed parameters, and thealgorithm will not be changed while keeping the fixed parameters as 0.

42

Appendix III: Simulation Result for AMNet
We generated 500 (and 100 for test) samples from the following settings and estimated two-layer(input layer + one hidden layer + output layer) AMNet model 100 times.

yi  0.5  0.485* x1,i  0.550* x2,i  sin 1.643* x3,i   cos  2.735* x4,i    i ,xi

i.i.d .MVN  0, I 4  ,ii.i.d .N  0,1 .

(30)

Activation function is defined as a sigmoid (logistic) function:g  x 

1.
1  e x(31)

For each optimization, we set epochs = 200 and batch sizes = 50, meaning each epoch uses 50 samples
randomly. The probabilistic optimization repeats an optimization until the sum of mini-batches achieves
the same number as the sample size, such that it needs 500/50 = 10 times. This repeats 200 times forconvergence of optimization. Before simulation, we generate data from Eq. (29) once and jointly search
the degree of the polynomial and the units in the hidden layer. Figure 9 shows the learning history of theMSE. Table 13 indicates the 7th degree, and its unit is the best for testing data. However, the 9th degree
unit is better for training data. According to test MSE, we adapt the two-layer AMNet with seven units
and use the inputs transformed by the 7th-degree polynomial (Figure 10).

Table 13: MSE of training and test data

degree & unit

2

3

4

5

6

7

8

train

1.29381.08581.07010.98051.02950.9701

1.0484

test

1.3497

1.09751.14881.0995

1.15291.0311

1.1533degree & unit

9

10

11

12

13

14

15

train

0.96730.99790.99711.05601.00950.98311.0007test

1.06081.0863

1.14261.1106

1.13971.11101.130843

Figure 9: Learning history of AMNet

Figure 10: AMNet for simulation study

Table 14 summarizes the result of this simulation study and shows bias and RMSE for betas 1 and 2.
A.RMS and A.Corr in Table 14 indicates the average RMS and the correlation coefficient between trueand estimated functions. The results indicate that betas 1 and 2 are estimated unbiased, and the sin andcos functions are also estimated closely by each network. We visualize those results in Figure 11.

44

Table 14: Results of simulation study

beta1

beta2

True

0.485

0.550

Bias

-0.0090.004

RMSE (

0.042) ( 0.045

)

sin

cos

A.RMS 0.528

0.569

A.Corr

0.939

0.951

Figure 11: Histograms of estimated betas 1 and 2 (upper side), the plots of true functions, and theaverage of estimated functions (bottom side)45