Predicting Customer Buying Behavior Using the BG/NBD Model to Support Business Sustainability in a Self-Service Context

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This is a rather interesting paper that uses the BG/NBD model to explore consumer purchasing issues, demonstrating both theoretical novelty and practical relevance. However, the paper has the following issues that need to be addressed:

The introduction is too diffuse and fails to focus on the practical background of the paper. Could the authors provide industry research reports or data to demonstrate the urgency of the research topic?

Following up on the previous point, the introduction should briefly review the existing literature before moving on to the paper's contributions. It is recommended that the authors restructure the introduction to follow this logical flow.

In the literature review section, the authors have divided their analysis into four subsections. However, the rationale for choosing these four specific areas is not explained. The paper should briefly justify this structure before presenting the detailed literature review.

The core assumptions of the BG/NBD model include that customer transaction behavior follows a Poisson process, the transaction rate λ follows a Gamma distribution, and the customer dropout probability p follows a Beta distribution. However, the paper does not validate the applicability of these assumptions to the self-service car wash industry. It is recommended to add the relevant validation tests.

The study relies on transaction data from a single car wash company in Sibiu, Romania, from 2019-2020, which is a limited sample (N=10,759 in 2019). The paper does not discuss whether this sample size meets the minimum requirements for the BG/NBD model, nor does it compare the data with that of similar industries or regions (e.g., as seen in references [71-82]), which limits the generalizability of the findings. Given that the self-service car wash industry is highly localized, this sample may not be representative of the global market—a limitation that should be explicitly addressed in the discussion section.

COVID-19 represents a major confounding variable, as government restrictions likely influenced purchasing behavior. However, it was not integrated into the model as a covariate (e.g., through time-series adjustments or a stratified analysis) and was merely described as background context (Section 4). This makes it impossible to distinguish between the effects of the pandemic and the model's inherent prediction error.

Author Response

We are grateful for your thoughtful feedback and insightful suggestions, which have helped us improve both the clarity and quality of the manuscript.

 

This is a rather interesting paper that uses the BG/NBD model to explore consumer purchasing issues, demonstrating both theoretical novelty and practical relevance.

However, the paper has the following issues that need to be addressed:

The introduction is too diffuse and fails to focus on the practical background of the paper. Could the authors provide industry research reports or data to demonstrate the urgency of the research topic?

R: To focus on the practical background and demonstrate the urgency of the research topic relevant industry research reports (e.g., Antavo’s Global Customer Loyalty Report, 2024), as well as academic sources 9e.g., Jin [5], Belas [6]) have been incorporated into the Introduction – in a new and consistent paragraph.

Following up on the previous point, the introduction should briefly review the existing literature before moving on to the paper's contributions. It is recommended that the authors restructure the introduction to follow this logical flow.

R: The newly (above-mentioned) added paragraph also provides a brief review of the existing literature, ensuring the research context is clearly established.

In the literature review section, the authors have divided their analysis into four subsections. However, the rationale for choosing these four specific areas is not explained. The paper should briefly justify this structure before presenting the detailed literature review.

R: The Literature Review section has been reorganized and restructured to better align with the paper’s purpose. The rationale for choosing the - redesigned - subsections (as well as the overall logic of the approach) has been detailed in a dedicated (new) paragraph at the beginning of the Literature Review section.

 

The core assumptions of the BG/NBD model include that customer transaction behavior follows a Poisson process, the transaction rate λ follows a Gamma distribution, and the customer dropout probability p follows a Beta distribution. However, the paper does not validate the applicability of these assumptions to the self-service car wash industry. It is recommended to add the relevant validation tests.

To the best of our knowledge, the assumptions underlying the BG/NBD model were adopted as specified in the original article and used in the construction of the log-likelihood function. Following the maximization of this function, estimates of the model’s parameters were obtained (r and α representing the heterogeneity in transaction rates and a and b capturing the heterogeneity in dropout rates). These (estimated) parameters were subsequently used to predict the repeated transactions for the entire customer base, as well as for the loyal customers, for the year 2020. The predictive accuracy of these estimates was statistically tested by applying t-tests and chi-square tests.

The study relies on transaction data from a single car wash company in Sibiu, Romania, from 2019-2020, which is a limited sample (N=10,759 in 2019). The paper does not discuss whether this sample size meets the minimum requirements for the BG/NBD model, nor does it compare the data with that of similar industries or regions (e.g., as seen in references [71-82]), which limits the generalizability of the findings. Given that the self-service car wash industry is highly localized, this sample may not be representative of the global market—a limitation that should be explicitly addressed in the discussion section.

R: We have added a paragraph to discuss the sample size related issues – considering both the specifics of our study and comparisons with previous studies – while stressing that “the findings of the present study should be interpreted as company-specific, while their generalization to other companies within the same industry or to other industries at regional or global level should be approached with caution”.

COVID-19 represents a major confounding variable, as government restrictions likely influenced purchasing behavior. However, it was not integrated into the model as a covariate (e.g., through time-series adjustments or a stratified analysis) and was merely described as background context (Section 4). This makes it impossible to distinguish between the effects of the pandemic and the model's inherent prediction error.

R: We acknowledged the limitation that “for our dataset, it can only be deduced that the Covid-19 effects on the consumers’ behavior are embedded in the loyalty construct defined as repeated buying behavior (despite external negative influence factors). Accordingly, the model’s applicability during the Covid-19 period remains valid under this interpretation” – and suggest “including the Covid-19 pandemic as a covariate in the BG/NBD model” in future research.

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

I evaluated your paper. I find the topic very interesting, but there are some parts and points to be improved:

• technical:
  • please use uniform wording - in this text you use client, consumer, customer... choose one and stick to it throughout the text
  • there is confusion in referencing - for example p.2, l.59: if only two sources are mentioned they should be divided by comma, not dash; p.2, l.59: reference 17 should be 16 and yours (16, 18) should be 17, 18 and this has to be changes in the reference list
  • there are some language issues: instead of "unique" there should be "individual (p.8, l.326, p.9, l.357). In Figure 3 there should be "past" instead of "passed", in p.2 l.76 and p.8 l.338 there shoud be "loyal ones" instead of "one"
• conceptual issues:
  • I am not sure you can call a loyal customer in self-washing car service a person who repeated the transaction once?? Can you elaborate on this?
  • I don't quite understand why your theoretical part (Literature review) is on digital marketing, database marketing and sustainability, while you paper deals with loyalty and its predictions: I think this needs significant improvement.
  • I don't understand your point in the last sentence p.8. Please elaborate.
  • the second research limitation you identify makes not much sense in terms of the industry you look into.
  • Future research proposals are usually base on study limitations, which is not the case here.
• Structural issues:
  • the large part of  Discussion section looks more like conclusion (which is missing), particularly  research limitations and proposals for future research.

Comments on the Quality of English Language

Minor changes should be made, as mentioned above

Author Response

We are grateful for your thoughtful feedback and insightful suggestions, which have helped us improve both the clarity and quality of the manuscript.

 

I evaluated your paper. I find the topic very interesting, but there are some parts and points to be improved:

• technical:
• please use uniform wording - in this text you use client, consumer, customer... choose one and stick to it throughout the text

R: The entire text has been carefully checked for uniform wording, and the term “customer” has been used consistently throughout.

• there is confusion in referencing - for example p.2, l.59: if only two sources are mentioned they should be divided by comma, not dash; p.2, l.59: reference 17 should be 16 and yours (16, 18) should be 17, 18 and this has to be changes in the reference list

R: We have reviewed the manuscript and ensured that whenever only two sources are mentioned, they are now separated by a comma instead of a dash (e.g., former 10-11 and 12-13 citations). We have also reviewed the references and in light of the additional sources added, all references have been thoroughly checked.

• there are some language issues: instead of "unique" there should be "individual (p.8, l.326, p.9, l.357). In Figure 3 there should be "past" instead of "passed", in p.2 l.76 and p.8 l.338 there shoud be "loyal ones" instead of "one"

R: A comprehensive language and grammar review has been conducted (incl. “passed” replaced with “past” in Figure 3, “one” replaced with "ones"). We have used the term “unique customers” to mirror the concept of unique IDs (client card), noting that these IDs are not personalized.

• conceptual issues:
• I am not sure you can call a loyal customer in self-washing car service a person who repeated the transaction once?? Can you elaborate on this?

R:  We conceptualized and operationalized customer loyalty solely from the behavioral (also referred to as “cold”) perspective, whereby a customer is considered loyal if he/she repeatedly buys from the same company in a period (and added “For the analyzed period (2019 – 2020), customer loyalty is approached from the behavioral perspective and measured as repeated service usage”). This repeated behavior may entail one or multiple repeated transactions. In this study, the reason why we considered only one repeated transaction is data-related in the sense that considering more than one repeated transaction would reduce the database and thus, information would be lost. Nonetheless, we acknowledge that increasing the threshold of repeated transactions aligns with the behavioral loyalty theory and reapplying the prediction under the new assumptions may yield valuable results. The upper mentioned thoughts are included as research limitations and future research recommendations (“Operationalizing a loyal customer as one that has used the company’s services at least once in both years may constitute a fourth research limitation in the sense that one repeated transaction may not reflect the intended loyalty - although this assumption aligns with the behavioral loyalty perspective” (…) “increasing the threshold for repeated transactions and reapplying the model under this condition could yield valuable results”).

• I don't quite understand why your theoretical part (Literature review) is on digital marketing, database marketing and sustainability, while you paper deals with loyalty and its predictions: I think this needs significant improvement.

R: The Literature Review section has been reorganized and restructured to better align with the paper’s purpose. The rationale for choosing the - redesigned - subsections (as well as the overall logic of the approach) has been detailed in a dedicated (new) paragraph at the beginning of the Literature Review section.

• I don't understand your point in the last sentence p.8. Please elaborate.

R: After rereading the sentence, we found it very confusing and decided to delete it.

• the second research limitation you identify makes not much sense in terms of the industry you look into.

R: Totally agree, it does not make any sense considering the analyzed industry. We have deleted it.  

• Future research proposals are usually base on study limitations, which is not the case here.

R: We aligned the future research proposal with the study’s (enriched) limitations.

• Structural issues:
• the large part of  Discussion section looks more like conclusion (which is missing), particularly  research limitations and proposals for future research.
  
  R: In developing the Discussion section, we tried to respect the journal’s guidelines for this section (https://www.mdpi.com/journal/sustainability/instructions#preparation), as follows: 

Discussion: Authors should discuss the results and how they can be interpreted in perspective of previous studies and of the working hypotheses. The findings and their implications should be discussed in the broadest context possible and limitations of the work highlighted. Future research directions may also be mentioned. This section may be combined with Results.

 

Reviewer 3 Report

Comments and Suggestions for Authors

• The literature review needs to be improvised. There is a good use of references but more recent ones and strong scholarly work is required. Also, please provide a strong justification for 2019 - 2020 data usage in today's time. Is there any comparison how it is impacted the customer loyalty in regards to loyalty 2023 - 2024. 
• Improvise the methodology section as well to comprehend methods and time line.
• Discussion section also needs to improve. You can use clear headings for theoretical and practical implications. 
• As you mentioned some limitations, then why they were not part of the current study. Please provide reasoning. 

Author Response

We are grateful for your thoughtful feedback and insightful suggestions, which have helped us improve both the clarity and quality of the manuscript.

 

• The literature review needs to be improvised. There is a good use of references but more recent ones and strong scholarly work is required.

R: The Literature Review section has been improved. Both recent and strong scholarly work have been added.

• Also, please provide a strong justification for 2019 - 2020 data usage in today's time. Is there any comparison how it is impacted the customer loyalty in regards to loyalty 2023 - 2024. 

R: The (main) reason for using 2019-2020 data is related to data privacy. Since the database used in this research contains real business data from a company, a reasonable period of time needed to pass before these data could be accessed and used for research purposes. We agree that it would be highly valuable to compare these results with a period unaffected by the COVID-19 pandemic, therefore conducting a study covering 2023–2024 would represent an excellent direction for future research.

   

• Improvise the methodology section as well to comprehend methods and time line.

R: We have added a paragraph within the Materials and methods section regarding the used sample size.

• Discussion section also needs to improve. You can use clear headings for theoretical and practical implications. 

R: In developing the Discussion section, we tried to respect the journal’s guidelines for this section (https://www.mdpi.com/journal/sustainability/instructions#preparation), as follows: 

Discussion: Authors should discuss the results and how they can be interpreted in perspective of previous studies and of the working hypotheses. The findings and their implications should be discussed in the broadest context possible and limitations of the work highlighted. Future research directions may also be mentioned. This section may be combined with Results.

We have added more research limitations and based on them proposed future research directions.

 

• As you mentioned some limitations, then why they were not part of the current study. Please provide reasoning. 

R: For the first research limitations, including seasonality into the used prediction model was beyond the scope of the present paper. In the future, we will consider this modelling.

The second limitation can be hardly excluded as we cannot control who uses the client card.

For the third limitation, we can only deduce that the Covid-19 effects on the consumers’ behavior are embedded in the loyalty construct defined as repeated buying behavior (despite external negative influence factors). Accordingly, the model’s applicability during the Covid-19 period remains valid under this interpretation. Nonetheless, this deduction could be empirically tested by including the Covid-19 pandemic as a covariate in the BG/NBD model (suggested as future research direction).

The last limitation can be considered a theoretical one. In this regard, we have respected the behavioral loyalty perspective according to which a customer is considered a loyal one if it rebuys at least once in a given period. Clearly, we can increase the number of repeated transactions in the given period and reapply the prediction model in the future (suggested as future research direction).

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This version is better！

Reviewer 2 Report

Comments and Suggestions for Authors

Most of my comments were successfully addressed. The paper is ready to be published in this new form.

Reviewer 3 Report

Comments and Suggestions for Authors

The comments have been incorporated. It has improved a lot. Good Luck