In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We discuss the comparative advantages of this approach over a one-step approach. Considerations in specification, assessment of fit, and respecification of measurement models using confirmatory factor analysis are reviewed. As background to the two-step approach, the distinction between exploratory and confirmatory analysis, the distinction between complementary approaches for theory testing versus predictive application, and some developments in estimation methods also are discussed.

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Structural equation modeling in practice: a review and recommended two-step approach

Normed and nonnormed fit indexes are frequently used as adjuncts to chi-square statistics for evaluating the fit of a structural model A drawback of existing indexes is that they estimate no known population parameters A new coefficient is proposed to summarize the relative reduction in the noncentrality parameters of two nested models Two estimators of the coefficient yield new normed (CFI) and nonnormed (FI) fit indexes CFI avoids the underestimation of fit often noted in small samples for Bentler and Bonett's (1980) normed fit index (NFI) FI is a linear function of Bentler and Bonett's non-normed fit index (NNFI) that avoids the extreme underestimation and overestimation often found in NNFI Asymptotically, CFI, FI, NFI, and a new index developed by Bollen are equivalent measures of comparative fit, whereas NNFI measures relative fit by comparing noncentrality per degree of freedom All of the indexes are generalized to permit use of Wald and Lagrange multiplier statistics An example illustrates the behavior of these indexes under conditions of correct specification and misspecification The new fit indexes perform very well at all sample sizes

Comparative fit indexes in structural models

Feature selection techniques have become an apparent need in many bioinformatics applications. In addition to the large pool of techniques that have already been developed in the machine learning and data mining fields, specific applications in bioinformatics have led to a wealth of newly proposed techniques.

In this article, we make the interested reader aware of the possibilities of feature selection, providing a basic taxonomy of feature selection techniques, and discussing their use, variety and potential in a number of both common as well as upcoming bioinformatics applications.

Contact: yvan.saeys@psb.ugent.be

Supplementary information: http://bioinformatics.psb.ugent.be/supplementary_data/yvsae/fsreview

A review of feature selection techniques in bioinformatics

Feature selection has been the focus of interest for quite some time and much work has been done. With the creation of huge databases and the consequent requirements for good machine learning techniques, new problems arise and novel approaches to feature selection are in demand. This survey is a comprehensive overview of many existing methods from the 1970's to the present. It identifies four steps of a typical feature selection method, and categorizes the different existing methods in terms of generation procedures and evaluation functions, and reveals hitherto unattempted combinations of generation procedures and evaluation functions. Representative methods are chosen from each category for detailed explanation and discussion via example. Benchmark datasets with different characteristics are used for comparative study. The strengths and weaknesses of different methods are explained. Guidelines for applying feature selection methods are given based on data types and domain characteristics. This survey identifies the future research areas in feature selection, introduces newcomers to this field, and paves the way for practitioners who search for suitable methods for solving domain-specific real-world applications.

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Feature Selection for Classification

We briefly outline the information-theoretic (I-T) approaches to valid inference including a review of some simple methods for making formal inference from all the hypotheses in the model set (multimodel inference). The I-T approaches can replace the usual t tests and ANOVA tables that are so inferentially limited, but still commonly used. The I-T methods are easy to compute and understand and provide formal measures of the strength of evidence for both the null and alternative hypotheses, given the data. We give an example to highlight the importance of deriving alternative hypotheses and representing these as probability models. Fifteen technical issues are addressed to clarify various points that have appeared incorrectly in the recent literature. We offer several remarks regarding the future of empirical science and data analysis under an I-T framework.

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AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons

Applications of Statistics

Discriminant Analysis for Time Series (R.H. Shumway). Optimum Rules for Classification into Two Multivariate Normal Populations with the Same Covariance Matrix (S. D. Gupta). Large Sample Approximations and Asymptotic Expansions of Classification Statistics (M. Siotani). Bayesian Discrimination (S. Geisser). Classification of Growth Curves (J.C. Lee). Nonparametric Classification (J.D. Broffitt). Logistic Discrimination (J.A. Anderson). Nearest Neighbor Methods in Discrimination (L. Devroye, T.J. Wagner). The Classification and Mixture Maximum Likelihood Approaches to Cluster Analysis (G.J. McLachlan). Graphical Techniques for Multivariate Data and for Clustering (J.M. Chambers, B. Kleiner). Cluster Analysis Software (R.K. Blashfield, M.S. Aldenderfer, L.C. Morey). Single-link Clustering Algorithms (F.J. Rohlf). Theory of Multidimensional Scaling (J. de Leeuw, W. Heiser). Multidimensional Scaling and its Applications (M. Wish, J.D. Carroll). Intrinsic Dimensionality Extraction (K. Fukunaga). Structural Methods in Image Analysis and Recognition (L.N. Kanal, B.A. Lambird, D. Lavine). Image Models (N. Ahuja, A. Rosenfeld). Image Texture Survey (R.M. Haralick). Applications of Stochastic Languages (K.S. Fu). A Unifying Viewpoint on Pattern Recognition (J.C. Simon, E. Backer, J. Sallentin). Logical Functions in the Problems of Empirical Prediction (G.S. Lbov). Inference and Data Tables with Missing Values (N.G. Zagoruiko, V.N. Yolkina). Recognition of Electrocardiographic Patterns (J.H. van Bemmel). Waveform Parsing Systems (C.G. Stockman). Continuous Speech Recognition: Statistical Methods (F. Jelinek, R.L. Mercer, L.R. Bahl). Applications of Pattern Recognition in Radar (A. Grometstein, W.H. Schoendorf). White Blood Cell Recognition (E.S. Gelsema, G.H. Landeweerd). Pattern Recognition Techniques for Remote Sensing Applications (P.H. Swain). Optical Character Recognition - Theory and Practice (G. Nagy). Computer and Statistical Considerations for Oil Spill Identification (Y.T. Chien, T.J. Killeen). Pattern Recognition in Chemistry (B.R. Kowalski, S. Wold). Covariance Matrix Representation and Object-Predicate Symmetry (T. Kaminuma, S. Tomita, S. Watanabe). Multivariate Morphometrics (P.A. Reyment). Multivariate Analysis with Latent Variables (P.M. Bentler, D.G. Weeks). Use of Distance Measures, Information Measures and Error Bounds in Feature Evaluation (M. Ben-Bassat). Topics in Measurement Selection (J.M. Van Campenhout). Selection of Variables under Univariate Regression Models (P.R. Krishnaiah). On the Selection of Variables under Regression Models using Krishnaiah's Finite Intersection Tests (J.L. Schmidhammer). Dimensionality and Sample Size Considerations in Pattern Recognition Practice (A.K. Jain, B. Chandrasekaran). Selecting Variables in Discriminant Analysis for Improving upon Classical Procedures (W. Schaafsma). Selection of Variables in Discriminant Analysis (P.R. Krishnaiah). Index.

Paruchuri R. Krishnaiah

Papers

Applications of Statistics

Classification, pattern recognition, and reduction of dimensionality

Statistics and probability : essays in honor of C.R. Rao

Multivariate Analysis Vi

Multivariate Analysis V.