Figure 1.
Examples of boxplots for some of the stores from the chain of restaurants
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October 2016, 1(4): 299-308.
doi: 10.3934/bdia.2016012
Modeling daily guest count prediction
Department of Computer Science and Engineering York University 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada |
We present a novel method for analyzing data with temporal variations. In particular, the problem of modeling daily guest count forecast for a restaurant with more than 60 chain stores is presented. We study the transaction data collected from each store, perform data preprocessing and feature constructions for the data. We then discuss different forecasting techniques based on data mining and machine learning techniques. A new modeling algorithm SW-LAR-LASSO is proposed. We compare multiple regression model, poisson regression model, and the proposed SW-LAR-LASSO model for prediction. Experimental results show that the approach of combining sliding windows and LAR-LASSO produces the best results with the highest precision. This approach can also be applied to other areas where temporal variations exist in the data.
Mathematics Subject Classification:
Primary: 58F15, 58F17; Secondary: 53C3.
Citation:
Fok Ricky, Lasek Agnieszka, Li Jiye, An Aijun. Modeling daily guest count prediction. Big Data & Information Analytics,
2016, 1
(4)
: 299-308.
doi: 10.3934/bdia.2016012
![]()
References:
| [1] |
S. Coxe, S. West and L. S. Aiken,
The analysis of count data: A gentle introduction to
poisson regression and its alternatives, J. Pers. Assess, 91 (2009), 121-136.
doi: 10.1080/00223890802634175. |
| [2] |
B. Efron, T. Hastie, I. Johnstone and R. Tibshirani,
Tibshirani, Least angle regression, The Annals of Statistics, 32 (2004), 407-499.
doi: 10.1214/009053604000000067. |
| [3] |
F. G. Forst,
Forecasting restaurant sales using multiple regression and box-jenkins analysis, J. Appl. Bus. Res, 382 (1992), 2157-8834.
doi: 10.19030/jabr.v8i2.6157. |
| [4] |
T. Hastie, R. Tibshirani and J. Friedman,
The Elements of Statistical Learning, Data Mining,
Inference, and Prediction, Springer Series in Statistics, Springer, New York, (2009).
doi: 10.1007/978-0-387-84858-7. |
| [5] |
S. E. Kimes, R. B. Chase, S. Choi, P. Y. Lee and E. N. Ngonzi,
Restaurant revenue management applying yield management to the restaurant industry, Cornell Hospitality Q, 39 (1998), 32-39.
doi: 10.1177/001088049803900308. |
| [6] |
A. Lasek, N. Cercone and J. Saunders,
Restaurant sales and customer demand forecasting:
Literature survey and categorization of methods, Smart City 360, 166 (2016), 479-491.
doi: 10.1007/978-3-319-33681-7_40. |
| [7] |
M. S. Morgan and P. K. Chintagunta,
Forecasting restaurant sales using self-selectivity models, J. Retail. Consum. Serv, 4 (1997), 117-128.
doi: 10.1016/S0969-6989(96)00035-5. |
| [8] |
D. Reynolds, I. Rahman and W. Balinbin, Econometric modeling of the U.S. restaurant industry International, J. Hospitality Manage, 34 (2013), 317-323. |
| [9] |
K. Ryu and A. Sanchez,
The evaluation of forecasting methods at an institutional foodservice
dining facility, J. Hospitality Financ. Manage, (2013), 27-45.
doi: 10.1080/10913211.2003.10653769. |
| [10] |
K. F. Sellers and G. Shmueli, Predicting censored count data with COM-Poisson regression, Working Paper, Indian School of Business, Hyderabad, 2010. |
| [11] |
J. T. Wulu Jr, K. P. Singh, F. Famoye, T. N. Thomas and G. McGwin, Regression analysis of count data, J. Ind. Soc. Ag. Statistics, 55 (2002), 220-230. |
show all references
References:
| [1] |
S. Coxe, S. West and L. S. Aiken,
The analysis of count data: A gentle introduction to
poisson regression and its alternatives, J. Pers. Assess, 91 (2009), 121-136.
doi: 10.1080/00223890802634175. |
| [2] |
B. Efron, T. Hastie, I. Johnstone and R. Tibshirani,
Tibshirani, Least angle regression, The Annals of Statistics, 32 (2004), 407-499.
doi: 10.1214/009053604000000067. |
| [3] |
F. G. Forst,
Forecasting restaurant sales using multiple regression and box-jenkins analysis, J. Appl. Bus. Res, 382 (1992), 2157-8834.
doi: 10.19030/jabr.v8i2.6157. |
| [4] |
T. Hastie, R. Tibshirani and J. Friedman,
The Elements of Statistical Learning, Data Mining,
Inference, and Prediction, Springer Series in Statistics, Springer, New York, (2009).
doi: 10.1007/978-0-387-84858-7. |
| [5] |
S. E. Kimes, R. B. Chase, S. Choi, P. Y. Lee and E. N. Ngonzi,
Restaurant revenue management applying yield management to the restaurant industry, Cornell Hospitality Q, 39 (1998), 32-39.
doi: 10.1177/001088049803900308. |
| [6] |
A. Lasek, N. Cercone and J. Saunders,
Restaurant sales and customer demand forecasting:
Literature survey and categorization of methods, Smart City 360, 166 (2016), 479-491.
doi: 10.1007/978-3-319-33681-7_40. |
| [7] |
M. S. Morgan and P. K. Chintagunta,
Forecasting restaurant sales using self-selectivity models, J. Retail. Consum. Serv, 4 (1997), 117-128.
doi: 10.1016/S0969-6989(96)00035-5. |
| [8] |
D. Reynolds, I. Rahman and W. Balinbin, Econometric modeling of the U.S. restaurant industry International, J. Hospitality Manage, 34 (2013), 317-323. |
| [9] |
K. Ryu and A. Sanchez,
The evaluation of forecasting methods at an institutional foodservice
dining facility, J. Hospitality Financ. Manage, (2013), 27-45.
doi: 10.1080/10913211.2003.10653769. |
| [10] |
K. F. Sellers and G. Shmueli, Predicting censored count data with COM-Poisson regression, Working Paper, Indian School of Business, Hyderabad, 2010. |
| [11] |
J. T. Wulu Jr, K. P. Singh, F. Famoye, T. N. Thomas and G. McGwin, Regression analysis of count data, J. Ind. Soc. Ag. Statistics, 55 (2002), 220-230. |
Figure 2.
Three iterations of the sliding window are shown. Each line interval denotes a week. The shaded boxes denote the sliding windows for the training data over eight weeks and the empty boxes denote the weeks where the guest counts are predicted
Figure 3.
Experimental process for guest count predictions
Table 1.
Table of results from chosen stores. The bolded results denote the lowest predictive error among the three algorithms tested
| Benchmark Stores | Multiple regression | Poisson regression | SW-LAR-LASSO | localization |
| Store_1 | 7.88 | 8.28 | 8.40 | Canada stores |
| Store_2 | 15.56 | 16.71 | 15.00 | |
| Store_3 | 10.20 | 10.86 | 10.25 | |
| Store_4 | 13.15 | 14.51 | 12.86 | |
| Store_5 | 10.50 | 11.44 | 10.25 | |
| Store_6 | 16.04 | 17.66 | 14.19 | US Stores |
| Store_7 | 18.62 | 24.37 | 15.60 | |
| Store_8 | 16.02 | 15.69 | 12.89 | |
| Store_9 | -- | -- | 22.57 | |
| Store_10 | -- | -- | 14.68 |
| Benchmark Stores | Multiple regression | Poisson regression | SW-LAR-LASSO | localization |
| Store_1 | 7.88 | 8.28 | 8.40 | Canada stores |
| Store_2 | 15.56 | 16.71 | 15.00 | |
| Store_3 | 10.20 | 10.86 | 10.25 | |
| Store_4 | 13.15 | 14.51 | 12.86 | |
| Store_5 | 10.50 | 11.44 | 10.25 | |
| Store_6 | 16.04 | 17.66 | 14.19 | US Stores |
| Store_7 | 18.62 | 24.37 | 15.60 | |
| Store_8 | 16.02 | 15.69 | 12.89 | |
| Store_9 | -- | -- | 22.57 | |
| Store_10 | -- | -- | 14.68 |
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