The analysis of paired comparison experiments with frequency data such as win-loss records is usually dealt with using the Bradley-Terry model, wherein the number of wins is supposed to have a binomial distribution. This assumption of probability distribution is inappropriate and inconvenient in quantitative analysis with continuous variables such as preference tests of consumers in biology. In this paper, a practical method is proposed to apply the Bradley-Terry model to the repeated pair-comparison experiments with quantitative data. It is obtained by the nonlinear least squares method under the assumption of the additive normal error structure. Some simple methods for the estimation of precision and for the hypothesis testing are also given. An application to the food preference test of a captive northern fur seal suggests the validity and advantage of the method.
With the maturity of the consumers' life, its importance is growingly recognized to examine the variability of the preference among consumers as well as the average preference. In this paper, we propose a Bayesian hierarchical model to estimate the distribution of preference from a paired comparison experiment of multiple objects. In the likelihood function of Thurstone's model, each individual has his/her own preference scores of the objects. The distribution of the preference is regarded as a prior for the parameters, and has hyper parameters. We formulate the prior distribution in terms of a self-consistency index, mean preference directions of objects, and preference variability indices of objects. The posterior distribution of the parameters and the hyper parameters are estimated by Markov chain Monte Carlo algorithm. With an experiment of twenty varieties of violet, we show that the most preferred varieties in the experiment can be different from those with high purchasing probabilities.
The estimation problem of a fish growth curve by a tag-recapture experiment with both of the measurement and the process errors is considered. In this model, the true values of lengths of fishes at release are unknown nuisance parameters, and the number of the nuisance parameters goes to infinity as the sample size increases. In such a model, the maximum likelihood method has the potential drawback of inconsistency. In this paper, the conditional score method is applied to eliminate the nuisance parameters. An objective function corresponding to the conditional score method is given. The properties and performance of this method are evaluated through asymptotic efficiency and simulation.
In recent years, a variety of mixed linear models have been proposed for QTL interval mapping and marker-assisted prediction of QTL-and polygene-effects in outbred populations of livestock species. For a model containing the effects of a cluster of linked QTLs or a chromosomal segment marked, a computing procedure is proposed herein for constructing the gametic relationship matrix whose elements are the expected values of the identity-by-descent (IBD) proportions between gametes for individuals. It is shown that the IBD set for two gametes given can be systematically partitioned into some sub-sets that have lower dimensional components according to the related gametogenesis processes. Noticing such property of the IBD set and using the joint gametogenesis process at the marker locus, a recursive method is developed to systematically calculate the required IBD sets and the elements of the gametic relationship matrix. It is expected that the proposed method is efficient compared to the path counting-like method, especially for complex pedigrees of many animals. Further investigation is needed to develop a computing strategy for directly making up the inverse of the gametic relationship matrix.
The viewpoints to private gardens in Japan were compared between Japanese and British students. Sample of garden landscapes was collected through area sampling. From the rate of familiarity of British students to garden landscapes, gardens were divided into ‘unfamiliar’ and‘familiar’ gardens. Comparison was made by correspondence analysis to the data gathered in psychological experiments using questionnaires. When two groups' characters are compared by correspondence analysis, the meaning of components revealed by correspondence analysis differs between the two groups. To see this in detail, two components of British's with the highest similarity to the first two components of Japanese's were extracted using correlation between Japanese and British eigen vectors and orthogonal transformation. This procedure revealed the following results. 1) The viewpoints to garden landscapes were similar between Japanese's and British's to a certain degree. 2) There were also some differences in viewpoints between the two, including ‘natural’, ‘manmade’, ‘modern’, ‘spacious’ and so on. 3) Some ‘unfamiliar’ garden landscapes gave quite different impression between the two groups. 4) The configuration of ‘familiar’ garden landscapes was quite similar between the two groups.