Yasuo Amemiya

Instrumental variable estimator for the nonlinear errors-in-variables model

Abstract Estimation for the nonlinear errors-in-variables model is considered. It isassumed that additional information is available in the form of observations on instrumental variables. An estimation procedure is presented for the parameters of the model. Asymptotic properties of the estimator are investigated.

Estimation for Polynomial Structural Equation Models

Abstract Structural equation analysis is one of the most widely used statistical methods in social and behavioral science research and has become a popular tool in marketing. Subject matter needs for considering nonlinear structural models have been well documented. But current fitting procedures are available only for a limited class of models. In this article a systematic statistical approach is developed for the general polynomial structural equation model. The new procedure applies a method of moments procedure similar to the one used in errors-in-variables regression to the factor score estimates from the measurement model fit. The asymptotic properties of the estimator are derived, and a modified estimator with better small-sample properties is introduced. Simulation studies are reported to show the usefulness of the procedure and to compare its performance to other methods. An example from a substance abuse prevention study is also discussed.

What Should be Done When an Estimated between-Group Covariance Matrix is not Nonnegative Definite?

Abstract Estimation of covariance components in the multivariate random-effect model with nested covariance structure is discussed. There are two covariance matrices to be estimated, namely, the between-group and the within-group covariance matrices. These two covariance matrices are most often estimated by forming a multivariate analysis of variance and equating mean square matrices to their expectations. Such a procedure involves taking the difference between the between-group mean square and the within-group mean square matrices, and often produces an estimated between-group covariance matrix that is not nonnegative definite. We present estimators of the two covariance matrices that are always proper covariance matrices. The estimators are the restricted maximum likelihood estimators if the random effects are normally distributed. The estimation procedure is extended to more complicated models, including the twofold nested and the mixed-effect models. A numerical example is presented to illustrate the ...

Generalized Appended Product Indicator Procedure for Nonlinear Structural Equation Analysis

Interest in considering nonlinear structural equation models is well documented in the behavioral and social sciences as well as in the education and marketing literature. This article considers estimation of polynomial structural models. An existing method is shown to have a limitation that the produced estimator is inconsistent for most practical situations. A new procedure is introduced and defined for a general model using products of observed indicators. The resulting estimator is consistent without assuming any distributional form for the underlying factors or errors. Identification assessment and standard error estimation are discussed. A simulation study addresses statistical issues including comparisons of discrepancy functions and the choice of appended product indicators. Application of the new procedure in a substance abuse prevention study is also reported.

Uncovering energy-efficiency opportunities in data centers

The combination of rapidly increasing energy use of data centers (DCs), which is triggered by dramatic increases in IT (information technology) demands, and increases in energy costs and limited energy supplies has made the energy efficiency of DCs a central concern from both a cost and a sustainability perspective. This paper describes three important technology components that address the energy consumption in DCs. First, we present a mobile measurement technology (MMT) for optimizing the space and energy efficiency of DCs. The technology encompasses the interworking of an advanced metrology technique for rapid data collection at high spatial resolution and measurement-driven modeling techniques, enabling optimal adjustments of a DC environment within a target thermal envelope. Specific example data demonstrating the effectiveness of MMT is shown. Second, the static MMT measurements obtained at high spatial resolution are complemented by and integrated with a real-time sensor network. The requirements and suitable architectures for wired and wireless sensor solutions are discussed. Third, an energy and thermal model analysis for a DC is presented that exploits both the high-spatial-resolution (but static) MMT data and the high-timeresolved (but sparse) sensor data. The combination of these two data types (static and dynamic), in conjunction with innovative modeling techniques, provides the basis for extending the MMT concept toward an interactive energy management solution.

Latent Variable Analysis of Multivariate Spatial Data

Multivariate spatial or geo-referenced data arise naturally in such disciplines as ecology, agriculture, geology, and atmospheric sciences. In practice, interest often lies in modeling underlying structure and representing interrelationships in terms of a smaller number of variables. For such situations, statistical analysis using a latent variable model is proposed. We present a general model that incorporates spatial correlation and potential lagged or shifted dependencies and that can represent subject matter theory or serve as a practical exploratory model. Procedures for model fitting, parameter estimation, inferences, and latent variable prediction are developed without restrictive assumptions on distribution and covariance function forms. The properties and usefulness of the proposed approaches are assessed by asymptotic theory and an extensive simulation study. An example from precision agriculture is also presented.

A method of moments technique for fitting interaction effects in structural equation models

The desire to fit structural equation models containing an interaction term has received much methodological attention in the social science literature. This paper presents a technique for the cross-product structural model that utilizes factor score estimates and results in closed-form moments-type estimators. The technique, which does not require normality for the underlying factors, was originally introduced in a very general form by Wall and Amemiya (2000) for any polynomial structural model. In this paper, the practical implementation of this method, including standard error estimation, is presented specifically for the cross-product model. The procedure is applied to an example from social/behavioural epidemiology where the flexibility of the cross-product model provides a useful description of the underlying theory. A simulation study is also presented comparing the method of moments for the cross-product model with three other procedures.

Two-stage instrumental variables estimators for the nonlinear errors-in-variables model

Abstract Estimation for the nonlinear functional errors-in-variables model is considered under the assumption that instrumental variables are available. The approximate bias in the ordinary instrumental variable estimator due to the nonlinearity of the relationship is derived. Utilizing the nonlinearity of the relationship, an estimator of the error covariance matrix is introduced. Using the error covariance matrix estimator, two types of two-stage instrumental variable estimators are proposed. The two two-stage estimators do not have the asymptotic bias due to the nonlinearity. A Monte Carlo experiment also shows the superiority of the two-stage estimators over the ordinary estimator.

The asymptotic distributions of some estimators for a factor analysis model

Under the errors-in-variables parameterization, the limiting behavior of the estimators of the parameters of the factor analysis model is investigated. An explicit expression is given for the covariance matrix of the limiting distribution of the estimators. It is demonstrated that the limiting distribution of the vector containing the estimated error variances and the estimated coefficients holds for a wide range of assumptions about the true factors.

Mixture Factor Analysis for Approximating a Nonnormally Distributed Continuous Latent Factor with Continuous and Dichotomous Observed Variables.

Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus dichotomous outcomes. For dichotomous outcomes, normal ML path estimates have bias that worsens as latent factor skew/kurtosis increases and does not diminish as sample size increases, whereas the mixture factor analysis model produces nearly unbiased estimators as sample sizes increase (500 and greater) and offers near nominal coverage probability. For continuous outcome variables, both methods produce factor loading estimates with minimal bias regardless of latent factor skew, but the mixture factor analysis is more efficient. The method is demonstrated using data motivated by a study on youth with cystic fibrosis examining predictors of treatment adherence. In summary, mixture factor analysis provides improvements over normal ML estimation in the presence of skewed/kurtotic latent factors, but due to variability in the estimator relating the latent factor to dichotomous outcomes and computational issues, the improvements were only fully realized, in this study, at larger sample sizes (500 and greater).