Skew-normal factor analysis models with incomplete data

Traditional factor analysis (FA) rests on the assumption of multivariate normality. However, in some practical situations, the data do not meet this assumption; thus, the statistical inference made from such data may be misleading. This paper aims at providing some new tools for the skew-normal (SN) FA model when missing values occur in the data. In such a model, the latent factors are assumed to follow a restricted version of multivariate SN distribution with additional shape parameters for accommodating skewness. We develop an analytically feasible expectation conditional maximization algorithm for carrying out parameter estimation and imputation of missing values under missing at random mechanisms. The practical utility of the proposed methodology is illustrated with two real data examples and the results are compared with those obtained from the traditional FA counterparts.     

Dynamic factor analysis with non-linear temporal aggregation constraints

Summary.  The paper estimates an index of coincident economic indicators for the US economy by using time series with different frequencies of observation (monthly and quarterly, possibly with missing values). The model that is considered is the dynamic factor model that was proposed by Stock and Watson, specified in the logarithms of the original variables and at the monthly frequency, which poses a problem of temporal aggregation with a non-linear observational constraint when quarterly time series are included. Our main methodological contribution is to provide an exact solution to this problem that hinges on conditional mode estimation by iteration of the extended Kalman filtering and smoothing equations. On the empirical side the contribution of the paper is to provide monthly estimates of quarterly indicators, among which is the gross domestic product, that are consistent with the quarterly totals. Two applications are considered: the first dealing with the construction of a coincident index for the US economy, whereas the second does the same with reference to the euro area.     

一级统计学科建设若干问题探讨

一级统计学科建设若干问题探讨黄沂木一、经济体制改革促进了大统计学科的建立—两门统计学之争到此为止在很长的一段时间里,我国在高度集中的计划经济体制下,统计由原苏联“成套进口”。人们也遵从原苏联科学院、中央统计局、高等教育部于１９５４年联合召开的统计科学...     

Three-mode factor analysis with binary core and orthonormality constraints

Summary A constrained version of Three-mode Factor Analysis model is considered in order to make its interpretation easier. The constraints are obtained by fixing some elements of the core to zero and requiring orthonormal factor loadings. An algorithm to solve the related minimization problem and an example of core constraints with theoretically interesting features, are given.     

Influence in covariance structure analysis: with an application to confirmatory factor analysis

Influence functions are derived for the parameters in covariance structure analysis, where the parameters are estimated by minimizing a discrepancy function between the assumed covariance matrix and the sample covariance matrix. The case of confirmatory factor analysis is studied precisely with a numerical example. Comparing with a general procedure called one-step estimation, the proposed procedure has two advantages:1) computing cost is cheaper, 2) the property that arbitrary influence can be decomposed into a fi-nite number of components discussed by Tanaka and Castano-Tostado(1990) can be used for efficient computing and the characterization of a covariance structure model from the sensitivity perspective. A numerical comparison is made among the confirmatory factor analysis and some procedures of ex-ploratory factor analysis by using the decomposition mentioned above.     

Exploring the variability of DNA molecules via principal geodesic analysis on the shape space

Most of the linear statistics deal with data lying in a Euclidean space. However, there are many examples, such as DNA molecule topological structures, in which the initial or the transformed data lie in a non-Euclidean space. To get a measure of variability in these situations, the principal component analysis (PCA) is usually performed on a Euclidean tangent space as it cannot be directly implemented on a non-Euclidean space. Instead, principal geodesic analysis (PGA) is a new tool that provides a measure of variability for nonlinear statistics. In this paper, the performance of this new tool is compared with that of the PCA using a real data set representing a DNA molecular structure. It is shown that due to the nonlinearity of space, the PGA explains more variability of the data than the PCA.     

Independent exploratory factor analysis with application to atmospheric science data

The independent exploratory factor analysis method is introduced for recovering independent latent sources from their observed mixtures. The new model is viewed as a method of factor rotation in exploratory factor analysis (EFA). First, estimates for all EFA model parameters are obtained simultaneously. Then, an orthogonal rotation matrix is sought that minimizes the dependence between the common factors. The rotation of the scores is compensated by a rotation of the initial loading matrix. The proposed approach is applied to study winter monthly sea-level pressure anomalies over the Northern Hemisphere. The North Atlantic Oscillation, the North Pacific Oscillation, and the Scandinavian pattern are identified among the rotated spatial patterns with a physically interpretable structure.     

Robustness of bayesian factor analysis estimates

This paper presents the result of a study of the robustness of posterior estimators of the factor loading matrix, the factor scores, and the disturbance covariance matrix (the main model parameters) in a Bayesian factor analysis with respect to variations in the values of the parameters of their prior distributions (the hyperparameter). We adopt the ε - contamination model of Berger and Berliner(1986) to generate prior distributions whose hyper-paramters reflects small variations in the elements of the uncontaminated hyperparameters, and we use directional derivatives to examine the variation of the uncontaminated estimators with respect to changes in the values of the hyperparameters, in the directions of the main model parameters. Several matrix norms are used to measure the closeness of the resulting values. We illustrate the results with a numerical example.     

Bayesian analysis for confirmatory factor model with finite-dimensional Dirichlet prior mixing

Confirmatory factor analysis (CFA) model is a useful multivariate statistical tool for interpreting relationships between latent variables and manifest variables. Often statistical results based on a single CFA are seriously distorted when data set takes on heterogeneity. To address the heterogeneity resulting from the multivariate responses, we propose a Bayesian semiparametric modeling for CFA. The approach relies on using a prior over the space of mixing distributions with finite components. Blocked Gibbs sampler is implemented to cope with the posterior analysis. Results obtained from a simulation study and a real data set are presented to illustrate the methodology.     

企业绿色投入产出核算——基于电力企业的研究和分析

 企业投入产出核算作,最为加强企业全面核算的一种有效方法,自提出之日起就在企业尤其是大中型企业的管理实践中得以广泛应用。然而,由于经济外部性的存在,现实中企业生产活动同自然资源/环境之间存在着相互影响,相互作用的负反馈机制。任何一企业的生产活动的成本代价,不仅包括对各种生产要素的消耗,而且也包括由于其外部不经济而对自然所造成的损失。这就意味着任何企业生产成本不仅包括传统的生产成本（劳动力,燃料,固定资产等）,而且还包括企业生产过程中由于外部不经济所带来的外部成本。而传统的企业投入产出核算中则没有包括后者。 针对这种情况,本文特别以电力公司为背景,对企业绿色投入产出核算进行研究和分析,具体构造有关电力公司绿色投入产出核算表式及相应的投入产出模型,并利用绿色投入产出核算方法对电力公司的主要技术经济指标,产品的构成及生产规划和决策进行深入分析,最后对电产品的成本和电价的理论进行探讨。     

Bayesian correlated factor analysis of socio-demographic indicators

Recent changes in European family dynamics are often linked to common latent trends of economic and ideational change. Using Bayesian factor analysis, we extract three latent variables from eight socio-demographic indicators related to family formation, dissolution, and gender system and collected on 19 European countries within four periods (1970, 1980, 1990, 1998). The flexibility of the Bayesian approach allows us to introduce an innovative temporal factor model, adding the temporal dimension to the traditional factorial analysis. The underlying structure of the Bayesian factor model proposed reflects our idea of an autoregressive pattern in the latent variables relative to adjacent time periods. The results we obtain are consistent with current interpretations in European demographic trends.     

Robust confirmatory factor analysis based on the forward search algorithm

A key concept of the forward search algorithm in confirmatory factor analysis is ordering of the data on the basis of observational residuals. These residuals are computed under the proposed model and measure the discrepancy between the observed and predicted response for each unit of the sample. Regression-type factor scores are used to estimate model predictions. Informative forward plots are created for indexing influential observations and to show the dynamics of the estimates throughout the search. The detailed influence of each observation on the model parameters and fit indices is analyzed and a robust model inference is achieved. Real and simulated data sets with known contamination schemes are used to demonstrate the performance of the forward search algorithm.     

Measurement and analysis of demographic processes: the characteristics of generation

Since it would take too long (100 years) to ascertain all demographic data about a given age group, i.e., all those born in a given year, these data are determined hypothetically by measuring the various characteristics of persons of all ages in a given time period (1-2 years). Also needed is an indicator of the population as a whole; cumulative coefficients are used for this purpose. One of these is the overall coefficient of births, meaning the number of children a women would have over her whole period of fertility if she had the precise number of children at each period in her life as other women of that age. An analogous indicator is used for measuring mortality--the average life expectancy of a person at each stage in his life. The crude coefficient of population reproduction represents the number of girls to which each woman will give birth between the ages of 15 and 50. This has to be corrected by the number of those who will not live to reproductive age. The result is the corrected coefficient of reproduction of the female population. This coefficient is often thought to reflect the population's growth prospects; if less than unity, therefore, the population will not reproduce itself. This is an incorrect interpretation. The impact of immigration and emigration on the population must also be incorportated. In addition to the above hypothetical indicators, we must also develop real population indicators. Techniques must also be employed to evaluate the reliability of these demographic indicators.     

Analysis of means approach for random factor analysis

Analysis of means (ANOM) is a powerful tool for comparing means and variances in fixed-effects models. The graphical exhibit of ANOM is considered as a great advantage because of its interpretability and its ability to evaluate the practical significance of the mean effects. However, the presence of random factors may be problematic for the ANOM method. In this paper, we propose an ANOM approach that can be applied to test random effects in many different balanced statistical models including fixed-, random- and mixed-effects models. The proposed approach utilizes the range of the treatment averages for identifying the dispersions of the underlying populations. The power performance of the proposed procedure is compared to the analysis of variance (ANOVA) approach in a wide range of situations via a Monte Carlo simulation study. Illustrative examples are used to demonstrate the usefulness of the proposed approach and its graphical exhibits, provide meaningful interpretations, and discuss the statistical and practical significance of factor effects.     

Sensitivity measures of influence on the loading matrix in exploratory factor analysis

For the detection of influential observations on the loading matrix of the factor analysis model, we propose to use the infinitesimal version of two matrix coefficients, including Escoufier (1973)'s also discussed the application in factor analysis of some sensitivity measures used for similar purposes in principal component analysis.     

Full information maximum likelihood estimation in factor analysis with a large number of missing values

We consider the problem of full information maximum likelihood (FIML) estimation in factor analysis when a majority of the data values are missing. The expectation–maximization (EM) algorithm is often used to find the FIML estimates, in which the missing values on manifest variables are included in complete data. However, the ordinary EM algorithm has an extremely high computational cost. In this paper, we propose a new algorithm that is based on the EM algorithm but that efficiently computes the FIML estimates. A significant improvement in the computational speed is realized by not treating the missing values on manifest variables as a part of complete data. When there are many missing data values, it is not clear if the FIML procedure can achieve good estimation accuracy. In order to investigate this, we conduct Monte Carlo simulations under a wide variety of sample sizes.     

Variable selection via the weighted group lasso for factor analysis models

We consider the problem of selecting variables in factor analysis models. The $L_1$ regularization procedure is introduced to perform an automatic variable selection. In the factor analysis model, each variable is controlled by multiple factors when there are more than one underlying factor. We treat parameters corresponding to the multiple factors as grouped parameters, and then apply the group lasso. Furthermore, the weight of the group lasso penalty is modified to obtain appropriate estimates and improve the performance of variable selection. Crucial issues in this modeling procedure include the selection of the number of factors and a regularization parameter. Choosing these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for evaluating the factor analysis model via the weighted group lasso. Monte Carlo simulations are conducted to investigate the effectiveness of the proposed procedure. A real data example is also given to illustrate our procedure. The Canadian Journal of Statistics 40: 345–361; 2012 © 2012 Statistical Society of Canada     

Correspondence analysis of repair data: a case study for electric cable shovels

In mining operation, effective maintenance scheduling is very important because of its effect on the performance of equipment and production costs. Classifying equipment on the basis of repair durations is considered one of the essential works to schedule maintenance activities effectively. In this study, repair data of electric cable shovels used in the Western Coal Company, Turkey, has been analyzed using correspondence analysis to classify shovels in terms of repair durations. Correspondence analysis, particularly helpful in analysing cross-tabular data in the form of numerical frequencies, has provided a graphical display that permitted more rapid interpretation and understanding of the repair data. The results indicated that there are five groups of shovels according to their repair duration. Especially, shovels numbered 2, 3, 7, 10 and 11 required a repair duration of<1 h and maintained relatively good service condition when compared with others. Thus, priority might be given to repair them in maintenance job scheduling even if there is another failed shovel waiting to be serviced. This type of information will help mine managers to increase the number of available shovels in operation.     

Segmental dynamic factor analysis for time series of curves

A new approach is introduced in this article for describing and visualizing time series of curves, where each curve has the particularity of being subject to changes in regime. For this purpose, the curves are represented by a regression model including a latent segmentation, and their temporal evolution is modeled through a Gaussian random walk over low-dimensional factors of the regression coefficients. The resulting model is nothing else than a particular state-space model involving discrete and continuous latent variables, whose parameters are estimated across a sequence of curves through a dedicated variational Expectation-Maximization algorithm. The experimental study conducted on simulated data and real time series of curves has shown encouraging results in terms of visualization of their temporal evolution and forecasting.