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1 c intensity Cox Cox Cox 1. one-to-one intensity Cox Hughes 1994 RFM Recency Frequency and Monetary value ; konishi@ier.hit-u.ac.jp

one-to-one 2004 2000 intensity Cox Hughes 1994

2 Jonker et al Tsai and Chiu Cox km 5km

3 Korgaonkar et al Akaah et al km 15 km 30 km Sheather and Jones : : :

4 km Wedel and Kamakura homogeneity KM T T S(t)=Pr{T t i} S(t) KM S(t)KM =1 S(t)KM t i <t t i+1 S(t) KM (2.1) S(t) KM = S(t i) KM 1 Ri n i. S(t i) KM t>t i 1 R i t i n i t i 3 0

5 KM

6 Cox Kalbfleisch and Prentice Cox Cox 1972 Cox intensity T S(t) λ(t) S(t) t t + (3.1) λ i(t x)=λ 0(t)exp(β 1x 1i + β 2x 2i + + β mx mi), (i =1,...,k). (3.2) S i(t x) Cox = S 0(t) exp(β 1x 1i +β 2 x 2i + +β mx mi ). β =(β 1,...,β m) x =(x 1,...,x m) λ 0(t) S 0(t) 3.1 λ 0(t) exp(β 1x 1i + β 2x 2i + + β mx mi) 3.3 R t 1,...,t i,...,t R K(t i)={j : t j t i} t i t j = t i + (3.3) L(β)= R i=1 exp(β x i) Èj K(t i ) exp(β x. j) Newton-Raphson ˆβ

β =(β 1,...,β m) x =(x 1,...,x m) λ 0(t) S 0(t) 3.1 λ 0(t) exp(β 1x 1i + β 2x 2i + + β mx mi) 3.3 R t 1,...,t i,.

7 (3.4) LL(β)= R β x i R log ¾ i=1 i=1 j K(t i ) exp(β x j). 3.3 Breslow Cox AIC 2 3 a 5 b

8 Cox Cox exp( )/exp( ) = intensity km km 3km =0 =1 1cm =0 =

6 10 6.1 intensity 10 19.7 1 1000 3.8 0.

9 Cox n 4 3. Cox n 5

10 Cox Hughes 1994 RFM Recency Frequency, and Monetary value R F M 3 RFM Fader et al F M R S i(t x) Cox 2.1 KM Cox KM t i <t t i+1 t i 1 R i t>ti n i S i(t x) Cox S 0(t) 1 R i R n i 1 i (1/R i ) n R i i t i R i =exp(β x i) n i n i = È K k = È exp(β x k ) t i S 0(t)= S 0(t i) 1 ˆR i (1/ ˆR i ) 3.2 ˆn i (4.1) ¼ ½ β S i(t x) Cox = S exp( β x i ) 0(t) = S 0(t i) 1 ˆR (1/ i ˆR i ) exp( x i ). ˆn i 40 l t> S(t) S(t) SE(t) 95 (4.2) (4.3) E{1 {Ti t i }} = P {1 {Ti t i }} =1 S i(t x) Cox. = 1 l l i=1 1 S 0(t i) exp( β x i ).

1 KM Cox KM t i <t t i+1 t i 1 R i t>ti n i S i(t x) Cox S 0(t) 1 R i R n i 1 i (1/R i ) n R i i t i R i =exp(β x i) n i n i = È K k = È exp(β x k ) t

11 455 (4.4) = SE(t) 1 l 1 S 0(t i) exp( β x i ) S 0(t i) exp( β x i ). 4 Cox KM KM t> È 1/2 R S(t j) i i n i (n i Ri) Cox Cox KM KM 4 KM Cox S 0(t) KM Cox 2.1 S 0(t) Cox S 0(t) 4.1 KM exp( β x i) mm cm

12 KM Cox : S 0 (t) PWP Prentice et al., 1981 Cox KM

13 Cox Cox KM Cox International Conference on Recent Development of Statistical Modeling in Marketing Latent Variable and Latent Structure Approach

14 Akaah, I. P., Korgaonkar, P. K. and Lund, D Direct marketing attitudes, Journal of Business Research, 34, Breslow, N Covariance analysis of censored survival data, Biometrics, 30, Cox, D. R Regression models and life tables with discussion Journal of the Royal Statistical Society Series B, 34, Fader, P. S., Hardie, Bruce G. S. and Lee, K. L RFM and CLV: Using Iso-value curves for customer base analysis, Journal of Marketing Research, XLII, Hughes, A. M Strategic Database Marketing: The Master Plan for Starting and Managinga Profitable, Customer-Based Marketing Program, Probus Pub Co., Chicago. Jonker, J. J., Piersma, N. and Van den Poel, D Joint optimization of customer segmentation and marketing policy to maximize long-term profitability, Expert Systems with Applications, 27, Kalbfleisch, J. D. and Prentice, R. L The Statistical Analysis of Failure Time Data, John Wiley and Sons, New York. Korgaonkar, P. K., Lund, D. and Price, B A structural equations approach toward examination of store attitude and store patronage behavior, Journal of Retailing, 61, index.html perm. or. jp/txt/index. html. Prentice, R. L., Williams, B. J. and Peterson, A. V On the regression analysis of multivariate failure time data, Biometrika, 68, Sheather, S. J. and Jones, M. C A reliable data-based bandwidth selection method for kernel density estimation, Journal of the Royal Statistical Society Series B, 53, Tsai,C.Y.andChiu,C.C A purchase-based market segmentation methodology, Expert Systems with Applications, 27, Wedel, M. and Kamakura, W. A Market Segmentation: Conceptual and Methodological Foundations, Kluwer Academic Publishers, Boston, Dordrecht, London bit

Fader, P. S., Hardie, Bruce G. S. and Lee, K. L. 2005. RFM and CLV: Using Iso-value curves for customer base analysis, Journal of Marketing Research, XLII, 415 430. Hughes, A. M. 1994.

15 Proceedings of the Institute of Statistical Mathematics Vol. 54, No. 2, (2006) 459 A Duration Analysis of Hair Salon Consumers Behavior and Prediction of Revisit Rates Yoko Konishi Institute of Economic Research, Hitotsubashi University In this study, we apply duration analysis to specify a model of hair salon customers behavior regarding their visits and then predict their next revisit rates. We estimate the intensity function by adopting the Cox model for the hair salon data to examine which demographic, geographic, and/or behavioral variables influence each customer s attitude. Our target customers use three hair services; haircut, color, and permanent wave. These customers were divided into non-loyal and loyal customers using the RFM method. Estimation results showed that the intensity functions of three items have been specified by different models, and we found differences in intensity between non-loyal and loyal customers. As a next step, we apply the Cox model estimation results to calculate the revisit rates for each customer within 100 days since the last visit from the interval prediction of his/her next revisit at 95 confidence interval level. We then compare the predicted rates with the actual rates of the customers revisits. For haircut, loyal and non-loyal customers actual revisit rates were within the predicted confidence interval based on the Cox model s results. However, hair color and permanent wave results based on the Cox model cannot predict the revisit rates well, but the predicted results based on the Kaplan-Meier estimation, which do not consider differences among individuals, yielded actual revisit rates within the prescribe confidence intervals. The prediction of revisit rates tell us when and how many customers will visit a salon and which services they will receive. The use of this information can help achieve an effective direct mailing strategy. Key words: Duration analysis, Cox model, hair salon.

duration analysis to specify a model of hair salon customers behavior regarding their visits and then predict their next revisit rates.

Japanese Journal of Applied Psychology

Japanese Journal of Applied Psychology 2014, Vol. 40, No. 2, 71 81 1) * Donations and Money-Beliefs, Empathy, and Normative Attitudes About Helping after Great East Japan Earthquake Nobuko WATANABE* Relationships