Factor Score Estimates Research Articles

被験者母数を用いた構造方程式モデリング―ＩＲＴにおいて項目母数が推定されている場合の分析―

One of the problems with structural equation modeling (SEM) is that the estimation of measurement equation is not separated from the estimation of structural equation. The main aim of this study was to propose a new method to overcome that problem by using ability parameters estimated by item response theory (IRT) as data. According to IRT, the error variance of measurement equation can be easily computed as the reciprocal of the information function. By using the estimates of the error variance, we can fix all parameters in measurement equation and can separate the estimation of structural equation from that of measurement equation. This method also allows us to estimate relations among factor scores with improved precision, because the errors of estimating factor scores are taken into account. The article concludes with a simulation result for verifying the efficacy of this method and an actual numerical.

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.

Analysis of structural equation model with ignorable missing continuous and polytomous data

The main purpose of this article is to develop a Bayesian approach for structural equation models with ignorable missing continuous and polytomous data. Joint Bayesian estimates of thresholds, structural parameters and latent factor scores are obtained simultaneously. The idea of data augmentation is used to solve the computational difficulties involved. In the posterior analysis, in addition to the real missing data, latent variables and latent continuous measurements underlying the polytomous data are treated as hypothetical missing data. An algorithm that embeds the Metropolis-Hastings algorithm within the Gibbs sampler is implemented to produce the Bayesian estimates. A goodness-of-fit statistic for testing the posited model is presented. It is shown that the proposed approach is not sensitive to prior distributions and can handle situations with a large number of missing patterns whose underlying sample sizes may be small. Computational efficiency of the proposed procedure is illustrated by simulation studies and a real example.

狩野論文へのコメント

Although the regression analysis among estimated factor scores may be criticized due to the attenuation of the estimated regression coefficients, this classical procedure can well separate the inferences of structural models from some propagation of information from the measurement model by approximately applying the conditionality principle. The author justifies and modifies the traditional approach by deriving the structural model with additional paths from measurement errors of the indicator variables to the response variables whose formal inference is nearly equivalent to the classical approaches by factor scores.

Bayesian Selection on the Number of Factors in a Factor Analysis Model

This paper considers a Bayesian approach for selecting the number of factors in a factor analysis model with continuous and polvtomous variables. A procedure for computing the important statistic in model selection, namely the Bayes factor, is developed via path sampling. The main computation effort is on simulating observations from the appropriate posterior distribution. This task is done by a hybrid algorithm which combines the Gibbs sampler and the Metropolis-Hastings algorithm. Bayesian estimates of thresholds, factor loadings, unique variances, and latent factor scores as well as their standard errors can be produced as by-products. The empirical performance of the proposed procedure is illustrated by means of a simulation study and a real example.

Estimation for Polynomial Structural Equation Models

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.

Statistical analysis of nonlinear factor analysis models

This paper presents a Bayesian analysis of a general nonlinear factor analysis model. Both the non‐informative and conjugate prior distributions are considered. A hybrid algorithm that combines the Metropolis‐Hastings algorithm and the Gibbs sampler is implemented to produce direct estimates of the latent factor scores and the structural parameters. Standard errors estimates as well as a goodness‐of‐fit statistic for assessing the posited model are presented. To illustrate the methodology, results from a simulation study and a real example are reported.

Robust principal component and factor analysis in the geostatistical treatment of environmental data

In this paper we show the usage of robust multivariate statistical methods in geostatistics. A usual procedure to estimate the values of variables (e.g. geochemical variables) measured at certain points of a region is to apply geostatistical methods like Krige estimation (based on the estimation of variograms). Here we emphasize robust principal component and factor analysis for the preliminary investigation of the data to reduce the dimension. Geostatistical methods are applied afterwards to the estimated factor scores. The final results show the influence of certain combinations of variables in the considered region. Moreover, the estimated factor scores with the robust procedure indicate outlying observations in a much better way. Copyright © 1999 John Wiley & Sons, Ltd.

Monitoring pupil development by means of the kalman filter and smoother based upon SEM state space modeling

If test scores are collected from an individual pupil at different points in time and a state-space model is available for describing latent ability development over time, the Kalman filter and smoother turn out to be the optimal procedures for estimating the pupil's latent curves. The Kalman filter is implemented in the Nijmegen Pupil Monitoring System, LISKAL. The essentials of Kalman filtering and smoothing in comparison to traditional cross-sectional factor score estimators are explained, stressing unbiasedness considerations and the initialization problem. The state-space model is represented as an SEM (structural equation model) and estimated by means of an SEM program. The value of the Kalman filter and smoother in pupil monitoring is enhanced by specifying a “structured means” instead of the traditional “zero means” SEM model and by introducing random subject effects.

Nasopharyngeal carcinoma in Malaysian Chinese: salted fish and other dietary exposures.

We interviewed 282 histologically confirmed cases of nasopharyngeal carcinoma (NPC) in Chinese residents of Selangor and the Federal Territory, Malaysia, and an equal number of Chinese age-, sex-, and length-of-residence-matched controls sampled from the general population. Consumption of 55 dietary items during childhood, and 5 years pre-diagnosis of NPC, was analyzed by univariate and multivariate methods. Four salted preserved foods (fish, leafy vegetables, egg and root), fresh pork/beef organ meats and beer and liquor consumption exhibited strong positive associations, and 4 vegetable/fruit combinations strong negative associations with NPC. Factor analysis and multivariable modeling using estimated factor scores strongly supported separate effects on NPC of vegetables/fruits, salted preserved foods, pork/beef organ meats and beer/liquor consumption. Multivariable modeling associated NPC most clearly with high consumption of salted fish, salted eggs, pork/beef liver and beer and low consumption of Chinese flowering cabbage, oranges/tangerines and shrimp. A strong residual association of social class with NPC remained after adjustment for diet, which is consistent with a substantial role for non-dietary environmental factors.

Monitoring pupil development by means of the Kalman filter and smoother based upon sem state space modeling

If test scores are collected from an individual pupil at different points in time and a state space model is available for describing latent ability development over time, the Kalman filter and smoother turn out to be the optimal procedures for estimating the pupil's latent curves. The Kalman filter is implemented in the Nijmegen Pupil Monitoring System LISKAL. The essentials of Kalman filtering and smoothing in comparison to traditional cross-sectional factor score estimators are explained, stressing unbiasedness considerations and the initialization problem. The state space model is represented as a SEM model and estimated by means of a SEM program. The value of the Kalman filter and smoother in pupil monitoring is enhanced by specifying a “structured means” instead of the traditional “zero means” SEM model and by introducing random subject effects.

人間の視覚・聴覚情報 単色刺激における色彩感性値の推定と解析

In this paper, we examine the construction factors of color Kansei information which are perceived from single colors. To examine the construction factors, we perform a subjective evaluation experiment based on the Semantic Differential method which uses 201 monochromatic colors and 12 adjective pairs. Three factors were detected by using the factor analysis. This paper also investigates the ability of the potential interpolation method to estimate factor scores of arbitrary color stimulus. We carried out the potential interpolation for several uniform color spaces. The performance of the interpolation of the CIE L*a*b* was good. Finally, the average of the estimation error was within the individual dispersion of the subjective experiment.

Factor Structure of the Halstead-Reitan Neuropsychological Test Battery for Older Children

The underlying dimensions of the Halstead-Reitan Neuropsychological Test Battery for Older Children (HRNB-C) were examined for a large sample of school-referred children. First, a principal components analysis (PCA) of 17 HRNB-C subtests produced a seven-factor solution that accounted for 76% of the original variance. In the second phase, analysis of 31 scores from the HRNB-C, Wechsler Intelligence Scale for Children (WISC-R & WISC-III), and achievement tests produced a nine-factor solution accounting for 67% of the variance. Principal factor analyses (PFA) of these data were performed to permit comparison with the PCA solutions. The PFA and PCA solutions were similar and conclusions about factor structure were comparable. It is suggested that the use of factor/index scores may provide an additional approach to interpretation of the HRNB-C and guidelines for estimating factor scores are provided. Initial attempts at establishing construct validity are described, along with estimates of reliability for selected factors.

Estimation of factor scores with polytomous data by the EM algorithm

The main objective of this paper is to investigate the application of the EM algorithm for obtaining a Bayesian estimate of the factor score in a factor analysis model with polytomous data. The posterior distribution of the latent factor score given the manifest continuous or polytomous observations is derived, and then the EM algorithm is utilized to find the posterior mode estimate of the distribution. It is shown that both the E‐step and the M‐step of the algorithm are very simple. An expression for the covariance matrix of the posterior distribution is derived. Results of a simulation study are presented to illustrate some properties of the estimate and the EM algorithm.

New Procedure for Extension Analysis in Exploratory Factor Analysis

Exploratory common factors have been correlated with variables external to the factor analysis by either extension analysis estimates or by correlating the external variables with estimated factor scores. In item analysis, a set of such correlations with possible scales is often computed for final item selection. The purposes of the present article are to document a problem common to both methods of estimating such correlations and to propose a new method of extension analysis that avoids this problem with less restriction assumptions. Solutions for a common data set by all three methods of extension analysis are presented that show the expected difficulties and improvements in the results. Because the new extension procedure gives the correlations without using estimated factor scores, use of this extension procedure eliminates factor indeterminacy from the multiple ways to estimate common factor scores. This method of evaluating possible scales was shown to have advantages over item-remainder correlational analysis.

Computation of Wechsler Adult Intelligence Scale—Revised factor scores: Equal and differential weights.

Standard procedures for estimating factor scores for the Wechsler Adult Intelligence Scale-Revised (WAIS-R ; D. Wechsler, 1981) involve equally weighted sums of the subtests that load most highly on the factor being estimated. We argue that factor scores derived in this manner lack discriminant validity ; they are strongly biased toward g (the first unrotated factor) and away from the other 2 unrotated factors. If regression-like weights are applied to all of the WAIS-R subtests and the products are summed, the resulting differentially weighted factors give results that show similar convergent validity and much greater discriminant validity with respect to the original factors.

Estimation of Factor Scores Via FASCOR

The potential value of using factor scores as latent variables is discussed, and the mathematical procedure for estimating factor scores is reviewed. A computer program is described that estimates factor scores for a data set given the factor pattern matrix, the factor correlation matrix, and the variable correlation matrix. Sample input and output are presented.

Estimation of factor scores in a two-level confirmatory factor analysis model

In this paper, two approaches for estimating the between-group and the within-group factor scores in a two-level confirmatory factor analysis model will be investigated. In each approach, the regression method and the generalized least-squares method are studied. These methods will be compared with each other theoretically and empirically with a simulation study.

Estimation of Individual Factor Scores Based on Entrance Examination Data

Estimation of Individual Factor Scores Based on Entrance Examination Data

Estimation of individual genetic and environmental profiles in longitudinal designs

Parameter estimates obtained in the genetic analysis of longitudinal data can be used to construct individual genetic and environmental profiles across time. Such individual profiles enable the attribution of individual phenotypic change to changes in the underlying genetic or environmental processes and may lead to practical applications in genetic counseling and epidemiology. Simulations show that individual estimates of factor scores can be reliably obtained. Decomposition of univariate, and to a lesser extent of bivariate, phenotypic time series may yield estimates of independent individual G(t) and E(t), however, that are intercorrelated. The magnitude of these correlations depends somewhat on the autocorrelation structure of the underlying series, but to obtain completely independent estimates of genetic and environmental individual profiles, at least three measured indicators are needed at each point in time.