The study proposes and empirically tests a new model for delineating product markets—MARKDEF. In MARKDEF product market definitions are analytically obtained using consumer perceptions. MARKDEF provides important diagnostic capability. It not only enables one to gain insight into the overall similarity/dissimilarity of products but also the attributes which account for these. In particular, MARKDEF gives a measure called the overall index of deviation which reflects the overall degree to which two products differ from each other. In addition, MARKDEF provides a measure of deviation on each attribute for the products under consideration, which aids in understanding the attributes responsible for differentiating the products. MARKDEF is supported in the product class investigated, namely candy bars. Attempts are made to validate the methodology by comparing the results obtained from MARKDEF with those of other standard procedures like multidimensional scaling and cluster analysis, and it is demonstrated that MARKDEF has good overall validity.
This paper examines a Bayesian study of estimating the heritability by comparing intraclass correlation coefficients between standard scores (SS) of MZ (monozygotic) twins as opposed to DZ (dizygotic) twins. For that purpose, we derive the marginal posterior distribution of ρ and obtain its approximate distribution. A numerical example shows that IQ standard score is possibly constrained by genetic factors.
A new multidimensional unfolding method is developed. The most important advantage of the proposed method is that the goodness of fit criterion is constructed on the basis of the response model of ranking behavior so that the analysis never fails to arrive at a solution space where data and distances correspond in their rank order as much as possible. This implies that the method guarantees elimination of such degeneracies as caused by minimizing the so-called stress measure at the expense of order correspondences between the data and the model as is often the case with the conventional nonmetric unfolding approach. The method is applied to two sets of real data for illustrative purposes.
As artificial data sets for correspondence analysis, a torus data and a solid torus data are presented. The former has two circular traits and the latter two circular traits and one linear trait representing the radius. The eigenvalue problem for each data is shown to be solvable analytically by dealing with the two parameters each describing the circular trait as free parameters. The solution shows a competition of eigenvalues of the traits involved, so-called Guttman effect.
An alternative sufficient condition for checking identifiability of the simultaneous equation model is proposed using the notation of the RAM (Reticular Action Model; McArdle & McDonald, 1984). The new rule can be more widely applied for checking identifiability of the simultaneous equation model compared with other rules. Using the notation of the RAM, an estimation procedure for the simultaneous equation model based on GLS (generalized least squares) is also proposed. When there are fixed parameters and linearly constrained parameters in the model, the estimates which contain the covariances between observable endogenous variables and residual variables can be obtained from explicit formulas of matrix. The consistency and the asymptotic covariance of this estimator are shown. By using the data from Kluegel, Singleton & Starnes (1989), the procedure is empirically compared to ML (maximum likelihood) and GLS (Browne, 1974).