Yutaka Kano

Osaka University | Handai

The article On Averaging Variables in a Confirmatory Factor Analysis Model

Recently, it is becoming more active to apply appropriate statistical methods dealing with missing data in clinical trials. Under not missing at random missingness, MLE based on direct-likelihood, or observed likelihood, possibly has a serious bias. A solution to the bias problem is to add auxiliary variables such as surrogate endpoints to the mode...

In this paper, we consider a transition model on a response variable to describe repeated measurement data and we provide sufficient conditions to check model identifiability when analyzing data with nonignorable missing values. The sufficient conditions can give us intuitive model characteristics to achieve identifiability. In addition to the mode...

An approach to studying reciprocal-effects in a cross-sectional data is to apply nonrecursive structural equation models. This article takes a theoretical approach to study the identifiability problem of reciprocal-effect models. Identifiability conditions are presented under a variety of settings.

A path analysis method for causal systems based on generalized linear models is proposed by using entropy. A practical example is introduced, and a brief explanation of the entropy coefficient of determination is given. Direct and indirect effects of explanatory variables are discussed as log odds ratios, i.e., relative information, and a method fo...

In this paper, a new test for the equality of the mean vectors between a two groups with the same number of the observations in high-dimensional data. The existing tests for this problem require a strong condition on the population covariance matrix. The proposed test in this paper does not require such conditions for it. This test will be obtained...

When data are missing due to at most one cause from some time to next time, we can make sampling distribution inferences about the parameter of the data by modeling the missing-data mechanism correctly. Proverbially, in case its mechanism is missing at random (MAR), it can be ignored, but in case not missing at random (NMAR), it can not be. There a...

When a missing-data mechanism is NMAR or non-ignorable, missingness is itself vital information and it must be taken into the likelihood, which, however, needs to introduce additional parameters to be estimated. The incompleteness of the data and introduction of more parameters can cause the identification problem. When a response variable is binar...

This article discusses asymptotic theory for the maximum likelihood estimator based on incomplete data. Although much literature has implicitly assumed the basic properties of the estimator, such as consistency and asymptotic normality, it is hard to find their precise and comprehensive proofs. In this article, we first show that under MAR an estim...

The problem of hypothesis testing concerning the mean vector for high dimensional data has been investigated by many authors. They have proposed several test criteria and obtained their asymptotic distributions, under somewhat restrictive conditions, when both the sample size and the dimension tend to infinity. Indeed, the conditions used by these...

In this paper we propose a test for testing the equality of the mean vectors of two groups with unequal covariance matrices based on N"1 and N"2 independently distributed p-dimensional observation vectors. It will be assumed that N"1 observation vectors from the first group are normally distributed with mean vector @m"1 and covariance matrix @S"1....

In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data (Spirtes et al. 2000; Pearl 2000). Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to discover the co...

It is natural to assume that a missing-data mechanism depends on latent variables in the analysis of incomplete data in latent variate modeling because latent variables are error-free and represent key notions investigated by applied researchers. Unfortunately, the missing-data mechanism is then not missing at random (NMAR). In this article, a new...

A simple computational method for estimation of parameters via a type of EM algorithm is proposed in restricted latent class analysis, where equality and constant constraints are considered. These constraints create difficulty in estimation. In order to simply and stably estimate parameters in restricted latent class analysis, a simple computationa...

Structural equation modeling (SEM) typically utilizes first- and second-order moment structures. This limits its applicability since many unidentified models and many equivalent models that researchers would like to distinguish are created. In this paper, we relax this restriction and assume non-normal distributions on exogenous variables. We shall...

Test of independence for 2—2 contingency tables with nonignorable nonresponses is discussed. Dependency assumption between two observed outcomes is required to achieve identification in many models with nonignorable nonresponses in the analysis of 2—2 contingency tables (e.g., [Ma, W.-Q., Geng, Z., Li, X.-T., 2003. Identification of nonresponse mec...

A new Gaussian graphical modeling that is robustified against possible outliers is proposed. The likelihood function is weighted according to how the observation is deviated, where the deviation of the observation is measured based on its likelihood. Test statistics associated with the robustified estimators are developed. These include statistics...

The application of independent component analysis to discovery of a causal ordering between observed variables is studied. Path analysis is a widely-used method for causal analysis. It is of confirmatory nature and can provide statistical tests for assumed causal relations based on comparison of the implied covariance matrix with a sample covarianc...

Independent component analysis (ICA) has been extensively studied since it was originated in the field of signal processing. However, almost all the researches have focused on estimation and paid little at- tention to testing. In this paper, we discuss testing significance of mixing and demixing coefficients in ICA. We propose test statistics to ex...

Causal discovery is the task of nding,plausible causal re- lationships from statistical data [1, 2]. Such methods rely on various assumptions about the data generating process to identify it from un- controlled observations. We have recently proposed a causal discovery method based on independent component analysis (ICA) called LiNGAM [3], showing...

In structural equation modeling, one often introduces fixed parameters to achieve identification of the model under consideration. For example, one path coefficient from a latent variable to an observed one is fixed to be one to determine the scale of the latent variable in a measurement model. It is also useful to make a constraint among parameter...

Independent component analysis (ICA) is a statistical method of identifying independent latent factors. Many procedures for the estimation problem have been developed. Most of them identify most non-normal factors, instead of independent factors. Intuitively speaking, this is because the central limit theory tells that the sum of more independent v...

It is first pointed out that most often used reliability coefficient α and one-factor model based reliability ρ are seriously biased when unique factors are covariated. In the case, the α is no longer a lower bound of the true reliability. Use of Bollen's formula (Bollen 1980) on reliability is highly recommended. A web-based program termed "STERA"...

Similarities and distinctions have been pointed out be- tween ICA and traditional multivariate methods such as factor analysis, principal component analysis and projection pursuit. In this paper, a new important con- nection between ICA and traditional factor analysis is made. The key of the connection is "factor rotation."

Theory of variable selection for structural models that do not have clear dependent variables is developed. Theory is derived within the framework of the curved exponential family of distributions for observed variables. The idea of Rao's score test was taken to construct a test statistic for variable selection, and its statistical properties are e...

It is very important to choose appropriate variables to be analyzed in multivariate analysis when there are many observed variables such as those in a questionnaire. What is actually done in scale construction with factor analysis is nothing but variable selection. In this paper, we take several goodness-of-fit statistics as measures of variable se...

Let Xn be a sequence of random ρ-vectors such that , where and Z is a continuously distributed random ρ-vector. Let f(·) be a measurable mapping from a domain of Rp to Rq, where the domain may not include b, i.e., f(b) may not be defined Under this setup, we study the asymptotic distribution of f(XRn). Two theorems are developed to obtain thu asymp...

Any exploratory factor analysis model requires at least three indicators (observed variables) for each common factor to ensure model identifiability. If one makes exploratory factor analysis for a data set in which one of common factors would have only two indicators in its population, one would encounter difficulties such as improper solutions and...

Based on concentration probability of estimators about a true parameter, third-order asymptotic efficiency of the first-order bias-adjusted MLE within the class of first-order bias-adjusted estimators has been well established in a variety of probability models. In this paper we consider the class of second-order bias-adjusted Fisher consistent est...

There are many causes of occurrence of improper solutions in factor analysis. Identifying potential causes of the improper solutions gives very useful information on suitability of the model considered for a data set. This paper studies possible causes of improper solutions in exploratory factor analysis, focusing upon (A) sampling fluctuations, (B...

The normal theory maximum likelihood and asymptotically distribution free methods are commonly used in covariance structure practice. When the number of observed variables is too large, neither method may give reliable inference due to bad condition numbers or unstable solutions. The main existing solution to the problem of high dimension is to bui...

Fifth-order (asymptotic) efficiency of the second-order bias-corrected MLE, minimizing the n -3 term of an expansion of the quadratic risk of Fisher-consistent estimators bias-corrected similarly, is established in a general curved exponential family with a structural parameter vector. A characterization theorem of the MLE in terms of its higher-or...

Identifiability of full factor analysis model for x = (x1, x2T)T is discussed, when the marginal model for x2 and/or the conditional model for x2 given x1 conform to factor analysis models. Two numerical examples are given for illustrative purposes.

When some of observed variates do not conform to the model under consideration, they will have a serious effect on the results of statistical analysis. In factor analysis the model with inconsistent variates may result in improper solutions. In this article a useful method for identifying a variate as inconsistent is proposed in factor analysis. Th...

Recently, robust extensions of normal theory statistics have been proposed to permit modeling under a wider class of distributions (e.g., Taylor, 1992). Let X be a p × 1 random vector, μ a p × 1 location parameter, and V a p × p scatter matrix. Kano et al. (1993) studied inference in the elliptical class of distributions and gave a criterion for th...

We develop statistical inference based on the maximum likelihood method in elliptical populations with an unknown density function. The method assuming the multivariate normal distribution, using the sample mean and the sample covariance matrix, is basically correct even for elliptical populations under a certain kurtosis adjustment, but is not sta...

Covariance structure analysis uses chi 2 goodness-of-fit test statistics whose adequacy is not known. Scientific conclusions based on models may be distorted when researchers violate sample size, variate independence, and distributional assumptions. The behavior of 6 test statistics is evaluated with a Monte Carlo confirmatory factor analysis study...

Recent research of asymptotic robustness shows that the likelihood ratio (LR) test statistic for test-of-independence based on normal theory remains valid for a general case where only independence is assumed. In contrast, under elliptical populations the LR statistic is correct if a kurtosis adjustment is made. Thus, the LR statistic itself is ava...

Covariance structure analysis uses χ–2 goodness-of-fit test statistics whose adequacy is not known. Scientific conclusions based on models may be distorted when researchers violate sample size, variate independence, and distributional assumptions. The behavior of 6 test statistics was evaluated with a Monte Carlo confirmatory factor analysis study....

It is shown that the maximum likelihood and generalized least-squares estimators of unique variances in the conditional model are asymptotically equivalent to those in the marginal model in factor analysis. The asymptotic covariance matrices of the estimators are expressed in matrix form.

A model for the relation between multivariate Fourth-order central moments of a set of variables and the marginal kurtoses and covariances among these variables is used to produce an estimator for covariance structure analysis that is asymptotically efficient and yields an asymptotic X 2 goodness of fit test of the covariance structure while substa...

This paper presents the asymptotic distribution of Ihara and Kano's noniterative estimator of the uniqueness in exploratory factor analysis. When the number of factors is overestimated, the estimator is not a continuous function of the sample covariance matrix and its asymptotic distribution is not normal, but the consistency holds. It is also show...

This paper discusses the analysis of covariance structures in a wide class of multivariate distributions whose marginal distributions may have heterogeneous kurtosis parameters. Elliptical distributions often used as a generalization of the normal theory are members of this class. It is shown that a simple adjustment of the weight matrix of normal...

Based on the usual factor analysis model, this paper investigates the relationship between improper solutions and the number of factors, and discusses the properties of the noniterative estimation method of Ihara and Kano in exploratory factor analysis. The consistency of the Ihara and Kano estimator is shown to hold even for an overestimated numbe...

In a factor analysis model, the asymptotic variance of the non-iterative estimator of Ihara and Kano (1986) is first provided, and five kinds of estimators, based on Ihara and Kano's method are constructed by using the asymptotic result. These estimators and that based on the maximum likelihoodare compared both theoretically and experimentally. In...

This paper is concerned with the consistency of estimators in a single common factor analysis model when the dimension of the observed vector is not fixed. In the model several conditions on the sample sizen and the dimensionp are established for the least squares estimator (L.S.E.) to be consistent. Under some assumptions,p/n→0 is a necessary and...

A closed form estimator of the uniqueness (unique variance) in factor analysis is proposed. It has analytically desirable properties—consistency, asymptotic normality and scale invariance. The estimation procedure is given through the application to the two sets of Emmett's data and Holzinger and Swineford's data. The new estimator is shown to lead...

This paper presents a condition that estimators in a covariance structure model are weakly (strongly) consistent, which is equivalent to Shapiro’s condition [A. Shapiro, S. Afr. Stat. J. 17, 33-81 (1983; Zbl 0517.62025)]. The condition is composed of three parts, each of which is simpler and is checked more easily. This result is applied to a proof...

It is shown that if a random p-vector x conforms to an r-common factor model and an external variable Z is given, then there exists a family of linear combinations X of x and Z such that [x': X]' conforms to an r-common factor model

Structural equation modeling (SEM) is a statistical approach that integrates factor analysis and path analysis (e.g. Bollen, 1989). SEM has been successfully applied to experimental and observational studies in social sciences. SEM is built on normal assumption and the assumption limits its applicability. It should be noted that observed variables...

Independent component analysis (ICA, see, e.g., Hyvarinen, et al., 2001) is a technique of multivariate analysis that has been developed to separate a multivariate observational sensor vector x consisting of unobserved source signals s mixed linearly by an unknown mixed matrix A. The noisy ICA model is a variant of ICA models created by adding an e...

The typical independent component analysis (ICA) model for an observed m-vector x is expressed as x = As + e ,w heres denotes an n × 1 latent vector whose com- ponents are independent and nonnormal, A is an m × n mixing matrix and e is an m×1 noise vector. In many cases, the error vector e are assumed to be normally dis- tributed. The equation abov...

This paper investigates the effect of additional information upon parameter estimation in multivariate structural models. It is shown that the asymptotic covariances of estimators based on a model with additional variables are smaller than those based on a model with no additional variables, where the estimation methods employed are the methods of...