A factor analysis model is proposed for the case of a mixture of various types of discrete and continuous manifest variables. It is indicated that the likelihood of parameters can be described for a mixture of different types of distributions by assuming local independence. For estimation of the parameters of interest, the method of marginal maximum likelihood is used, where scores of latent factors are integrated out from the likelihood. A kind of the EM algorithm is utilized for optimization. As an example, the case of a mixture of normal, binomial and Poisson distributions is provided.
In the present paper the ORTHOMAX rotation problem is reconsidered. It is shown that its solution can be presented as a steepest ascent flow on the manifold of orthogonal matrices. A matrix formulation of the ORTHOMAX problem is given as an initial value problem for matrix differential equation of first order. The solution can be found by any available ODE numerical integrator. Thus the paper proposes a convergent method for direct matrix solution of the ORTHOMAX problem. The well-known first order necessary condition for the VARIMAX maximizer is reestablished for the ORTHOMAX case without using Lagrange multipliers. Additionally new second order optimality conditions are derived and as a consequence an explicit second order necessary condition for further classification of the ORTHOMAX maximizer is obtained.
This article investigates factors that influenced Japanese voters in the early 1996 in determining which political party to support. Proportional-odds model, a model which retains ordinal nature of political hues or ideologies of the Japanese political parties, is fitted to the data. Samples with answers “I do not know$rdquo; to the questions are treated as missing. The EM algorithm enables us to incorporate the samples with missingvalues. We found that determining which party to support is a purely political decision for Japanese voters based solely on their ideologies and attitude towards the current cabinet, not to be influenced by their geographical profiles nor financial situations. Missing-value problem were found not to be ignored in the sense that marginally significant or insignificant explanatory variables can easily turn otherwise when the same model is fitted only for the data with no missing-values.
The Biased Choice Model is often used in psychology to analyze asymmetric confusion matrices arising from stimulus identification experiments. In this paper, several mathematical properties of the Biased Choice Model as well as the conditions under which the Biased Choice Model completely fits a data matrix are investigated. Then a new parameter estimation procedure is proposed and an interpretation of the Biased Choice Model in terms of maximum entropy principle is presented. There are many sub-models that impose further structure on the Biased Choice Model. This paper clarifies the relationships among such models and the conditions under which these models fit the data.
In this paper, we propose fuzzy regression analysis based on a quadratic programming approach. In fuzzy regression analysis, a quadratic programming approach gives more diverse spread coefficients than a linear programming approach. Moreover, a quadratic programming approach can integrate the central tendency of least squares and the possibilistic properties of fuzzy regression. Due to the characteristic of the quadratic programming problem, the proposed approach can obtain the optimal regression model representing possibilistic properties with the central tendency. In this approach, we classify the given data into two groups, i.e., the center-located group and the remaining group. Then, the upper and the lower approximation models can be obtained based on the classification result. By changing the weight coefficients of the objective function in the quadratic programming problem, we can analyze the given data in various angles.