ABSTRACT Meta-analysis methods based on individual patient data (IPD) have attracted attention in estimating a treatment-covariate interaction effect. An existing metaregression approach, based on aggregate data (AD) such as a treatment effect estimate and its standard error, is used only for the inference of between-trial interaction which indicates a relationship between the treatment effect estimates and mean covariate values; in contrast, the use of IPD can achieve estimation of not only the between-trial interaction but also within-trial interaction which indicates a relationship between individual outcomes and individual covariate values. However, most of the IPD metaanalyses are often difficult to implement because practitioners cannot always collect the IPD from all trials involved. We propose a new meta-analysis method for estimating both the between-trial and the within-trial interaction, in which we assume an IPD meta-analysis model for the missing IPD and then marginalize its density with respect to the missing IPD. The proposed method allows one to estimate the withintrial interaction even when only AD are available, and has potential benefits for another meta-analytic situation where some trials provide IPD and the others provide only AD.Through simulation studies, we demonstrate how close estimates of the between-trial and the within-trial interaction from the proposed method are to those from the IPD meta-analysis.

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ABSTRACT Since a latent trait can not be directly observed in item response theory models,it is difficult to specify an item response function (IRF). Many mathematical modelshave been proposed, among which the two-parameter logistic model (2PLM) is often included. In this article, we will propose a new parametric model, namely, a finite mixture of logistic models (MLM). The MLM has different mixing weights per item, and can model a plateau in the learning curve, which is a well-known phenomenon in education and psychology. It is also known that finite mixtures have some problems with estimating item parameters. Therefore, we develop a new useful estimation algorithm for item parameters and present simulation studies which show that this estimation algorithm works well. In fact, when the MLM was applied to analyze real data, we also found that the MLM makes it possible to distinguish whether or not a plateau appears in an IRF, whereas the 2PLM does not have this capability.

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ABSTRACT An algorithm for the constrained least squares problem is proposed in which the upper bound of the condition number of a parameter matrix is predetermined. Inthe algorithm, the parameter matrix to be obtained is reparameterized using its sin gular value decomposition, and the loss function is minimized alternately over the singular vector matrices and the singular values with condition number constraint. It was demonstrated that the algorithm recovered full rank matrices in simulated reverse component analysis, in which the matrices were estimated from their reduced rank counterparts. The proposed algorithm is useful for avoiding degenerate solutions in which parameter matrices become rank decient, which is illustrated in its application to generalized oblique Procrustes rotation and three-mode Parafac component analysis.

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ABSTRACT Overdispersion is a common phenomenon in discrete data analysis with generalized linear models which can never be ignored. In the literature on model selection with overdispersion, the main stream of the methods is to use the maximum likelihood method with a strong assumption of dening an entire distribution of the data to construct information criteria. For example, Fitzmaurice (1997) proposed model selection methods based on Efron's (1986) double-exponential families. However, the assumption of a parametric distribution of the data is sometimes too strong. In this paper,we propose a new model selection strategy based on the quasi-likelihood functions.First, we dene a statistical model with two moments in the form of mean and variance. Second, we dene the semiparametric information based on the semiparametric statistical models. Finally, we propose the semiparametric information criterion (SIC) based on quasi-likelihood estimators with weak assumptions on the rst two moments.Although the proposed semiparametric information criterion is inspired by data with overdispersion, it applies more generally to data no matter whether they are discrete or continuous. It may be useful for any models for which the quasi-likelihood methods are appropriate. We also demonstrate the use of SIC through simulation studies and data application of the well-known data on germination of Orobanche.

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ABSTRACT This paper analyzes whether procedures for multiple comparison derived in Hyodo et al. (2013) work for an unbalanced case and under non-normality. We focus onpairwise multiple comparisons and comparisons with a control among mean vectors, and show that the asymptotic properties of these procedures remain valid in an unbalanced high-dimensional setting. We also numerically justify that the derived procedures are robust under non-normality, i.e., the coverage probability of these procedures can be controlled with or without the assumption of normality of the data.

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