In the present research, we investigated the changes and individual differences of physical traits among the old people through physical function data and BMI (Body Mass Index) data of Japanese longitudinal study by using latent curve models. We first estimated the mean change patterns of physical traits, showing that in physical function moderate decrease was observed on average while female showed more rapid decrease. In BMI, female averagely indicated larger values than male but showed almost the similar change pattern to male. Individual differences of these changes were shown to be related to demographic variables, psychological variables, life-style variables such as smoking habits and other physical traits including eyesight. Additionally, longitudinal relationship was investigated between physical function and BMI, indicating the possibility that physical function may control rapid decreases of BMI in the old people. Finally, we attempted to extract multiple change patterns hidden in the whole data. As a result, two main classes were extracted whose change patterns were different in its intercepts and slopes. All analyses were conducted by Bayes estimation based on MCMC (Markov Chain Monte Carlo) method, and we showed the all program codes of WinBUGS in the Appendix.
This paper proposes a new model that measures customer loyalty from the days taken to repurchase in a shop. This model is based on IRT (Item Response Theory) and geometric distribution. It enables us not only to estimate customer loyalty as latent trait variables of each customer, but also to quantify the ability to pull in customers of shops. Moreover these shops could be any selling segment, for example, brand stores, manufacturers, or articles. In order to check the validity of this model, it is applied to actual ID-POS (point-of-sale with identification) data. In addition, another model using exponential distribution is proposed as an alternative model.
In this study, we assessed the effect of local dependence on itemparameter estimation based on comparable item parameters, using MarkovChain Monte Carlo method. The results showed that if we estimate item parameters ignoring local dependence, item parameter estimation will be more inaccurate than taking local dependence into account. Furthermore, it was supposed that the result of previous works, which were not based on comparable item parameters, was distorted.
In marketing, measurement of customers’ price sensitivity is regarded as important. If analysts can measure the price sensitivity of each customer, that data can be used as a base for determining how to approach customers. In this paper, a new model is proposed for measuring the individual price sensitivity of customers based on item response theory, which is a mathematical theory for developing and evaluating a test; using item response theory makes it possible to measure price sensitivity on a uniform scale. Parameters were estimated by using Markov chain monte carlo methods, and we show examples of applications of the proposed model to ID-POS data.
The purpose of this paper is to propose an extension model of the existing group analytic hierarchy process (AHP) model. In the existing AHP method, we need to obtain complete paired comparisons of criteria and alternatives. In practical applications, however, each evaluator carries out different paired comparison and incomplete paired comparisons are obtained. The proposed model can be applied to the situation where we get incomplete paired comparisons. By using this model, we evaluate the weights and dispersions of several criteria and alternatives, and then overall evaluation can be estimated by these weights. Furthermore we obtain the information about characteristics of evaluators by estimating the factor scores. In order to estimate the parameters, we use the Markov Chain Monte Carlo (MCMC) method. This proposed model is applied to brand evaluation by students.
In this article, the encounter probability, possibility to find unknown words in free descriptions was proposed. When a researcher thinks the amount of data was sufficient and decides to stop collecting data, this index gives us useful information. By the encounter probability, we can know how often we get unknown words. Free description data from two companies was analyzed by some Pareto distributions to decide most suitable model to explain frequency of words. Parameters of these distributions were estimated by using Markov chain monte carlo mehod. Consequently it was shown that these free descriptions were sufficient amount of information by calculating encounter probability.