온라인리뷰 평점에 대한 다항분포적 접근: 비제한 최우추정법

In this study, we propose a multinomial distribution approach to estimate the mean and variance(or standard deviation) of online review rate. Because consumer’s online review rates have the tendency to be concentrated at the boundary values​​(upper or lower bounds) of a limited integer range, arithmetic mean and standard deviation of the online review rate may have the limitations to be biased or to distort the effects of the mean and variance(or standard deviation) of online review rate. First, we introduce the concept of latent online review rate, which lays under the observed online review rate. While the actual online review rate is observed in the limited integer range, the latent online review rate is assumed to exist in unbounded range. Then, we combine the distributional characteristics of the latent online review rate to estimate an unbounded MLE for the mean and variance(or standard deviation) of online review rate. We derive the likelihood function for the review counts of each integer in the limited integer range, that can follow the multinomial distribution with interval-wise probabilities that apply the distribution of latent online review rate. The unbounded MLE for the mean and variance(or standard deviation) of online review rate can be evaluated as overcoming the limits of using the arithmetic mean and arithmetic variance (or arithmetic standard deviation). The unbounded MLE for the mean is more aligned with the center of the observed distribution of the online review rate than the arithmetic mean, and the unbounded MLEs for the mean and standard deviation show a relatively less correlation compared to the arithmetic mean and arithmetic standard deviation(which show a high negative correlation). With an empirical analysis of an FE regression model to weekly movie panel data, we also found that the unbounded MLE for the mean and standard deviation of online review rate provided statistically more valid results than applying the arithmetic mean and standard deviation, in terms of the magnitude of the effect of the rating mean and the influence of the rating standard deviation.