Bulletin of the Computational Statistics of Japan

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　In this study, we propose a test procedure for testing sequentially whether the response can be expressed by a linear trend with increasing dose levels in a dose response experiment. For realizing our sequential test procedure, we apply group sequential procedure to test sequentially the hypotheses of orthogonal contrasts among the population means to express a linear trend of the response. If we can first detect a linear trend at an early stage in the sequential test, it is possible to terminate the procedure with a few data up to the stage. Thus, the procedure is useful from an economical point of view when high costs are involved for obtaining the data.
　In the procedure, we give an integral formula to determine the clitical limits for satisfying a predefined type I familywise error rate. Furthermore, we show how to decide a required sample size at each dose with guaranteeing the power of the test. In our simulation studies, we compare the superiority among the test procedures based on three α spending functions for various configurations of population means in terms of the power of the test and the required sample size.

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　In exploratory factor analyses (EFA), factor rotation techniques are needed to interpret the result of EFA, and thus, many factor rotation methods have been developed. This paper overviews the factor rotation problem and rotation methods for the problem. Although factor rotation problem is very traditional one, there are some recent works including a rotation method using component loss functions, which has been investigated theoretically. Various factor rotation criteria are introduced and optimization algorithms for the criteria are explained. Furthermore, the use of rotation techniques in structural equation modeling and regularized approach are described.

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　Factor analysis model and structural equation modeling have been widely used to investigate the causality of manifest and latent variables. In recent years, the application of L₁ regularization to these models has attracted attention. In this paper, we report on the latest research about factor analysis and structural equation modeling via L₁ regularization, and discuss their future perspective.

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　In the classic formulation of factor analysis (FA), common and unique factors are regarded as latent random variables. A very different formulation of FA has recently been presented, in which common and unique factors are treated as parameters and all model parts are expressed with parameter matrices. The FA procedure with this new formulation can be referred to as matrix decomposition factor analysis (MDFA). The studies on MDFA and its developments are reviewed in this paper. Following the introduction, properties of the MDFA solution are discussed. Then, the residual analysis and factor score identification procedures in MDFA are described with a sparse MDFA procedure. A feature of MDFA is that its solution can be mathematically compared with the principal component analysis (PCA) solution, and some inequalities have been presented that contrast MDFA and PCA solutions. Those facts and the related empirical results are reviewed. Finally, we discuss the constrained uniqueness FA, which is a constrained variant of MDFA and can be reduced to minimum rank FA.

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