Topic
Covariance
About: Covariance is a research topic. Over the lifetime, 27801 publications have been published within this topic receiving 980521 citations.
Papers published on a yearly basis
Papers
More filters
Book•
01 Dec 1969TL;DR: The concepts of power analysis are discussed in this paper, where Chi-square Tests for Goodness of Fit and Contingency Tables, t-Test for Means, and Sign Test are used.
Abstract: Contents: Prefaces. The Concepts of Power Analysis. The t-Test for Means. The Significance of a Product Moment rs (subscript s). Differences Between Correlation Coefficients. The Test That a Proportion is .50 and the Sign Test. Differences Between Proportions. Chi-Square Tests for Goodness of Fit and Contingency Tables. The Analysis of Variance and Covariance. Multiple Regression and Correlation Analysis. Set Correlation and Multivariate Methods. Some Issues in Power Analysis. Computational Procedures.
115,069 citations
TL;DR: In this article, a general null model based on modified independence among variables is proposed to provide an additional reference point for the statistical and scientific evaluation of covariance structure models, and the importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical models.
Abstract: Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for covariance structure models. Large-sample theory provides a chi-square goodness-of-fit test for comparing a model against a general alternative model based on correlated variables. This model comparison is insufficient for model evaluation: In large samples virtually any model tends to be rejected as inadequate, and in small samples various competing models, if evaluated, might be equally acceptable. A general null model based on modified independence among variables is proposed to provide an additional reference point for the statistical and scientific evaluation of covariance structure models. Use of the null model in the context of a procedure that sequentially evaluates the statistical necessity of various sets of parameters places statistical methods in covariance structure analysis into a more complete framework. The concepts of ideal models and pseudo chi-square tests are introduced, and their roles in hypothesis testing are developed. The importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical models is also emphasized. Normed and nonnormed fit indices are developed and illustrated.
16,420 citations
15 Oct 2005
TL;DR: Principal component analysis (PCA) as discussed by the authors replaces the p original variables by a smaller number, q, of derived variables, the principal components, which are linear combinations of the original variables.
Abstract: When large multivariate datasets are analyzed, it is often desirable to reduce their dimensionality. Principal component analysis is one technique for doing this. It replaces the p original variables by a smaller number, q, of derived variables, the principal components, which are linear combinations of the original variables. Often, it is possible to retain most of the variability in the original variables with q very much smaller than p. Despite its apparent simplicity, principal component analysis has a number of subtleties, and it has many uses and extensions. A number of choices associated with the technique are briefly discussed, namely, covariance or correlation, how many components, and different normalization constraints, as well as confusion with factor analysis. Various uses and extensions are outlined.
Keywords:
dimension reduction;
factor analysis;
multivariate analysis;
variance maximization
14,773 citations
Book•
14 Sep 1984
TL;DR: In this article, the distribution of the Mean Vector and the Covariance Matrix and the Generalized T2-Statistic is analyzed. But the distribution is not shown to be independent of sets of Variates.
Abstract: Preface to the Third Edition.Preface to the Second Edition.Preface to the First Edition.1. Introduction.2. The Multivariate Normal Distribution.3. Estimation of the Mean Vector and the Covariance Matrix.4. The Distributions and Uses of Sample Correlation Coefficients.5. The Generalized T2-Statistic.6. Classification of Observations.7. The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance.8. Testing the General Linear Hypothesis: Multivariate Analysis of Variance9. Testing Independence of Sets of Variates.10. Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices.11. Principal Components.12. Cononical Correlations and Cononical Variables.13. The Distributions of Characteristic Roots and Vectors.14. Factor Analysis.15. Pattern of Dependence Graphical Models.Appendix A: Matrix Theory.Appendix B: Tables.References.Index.
9,693 citations
Book•
01 Jan 2003TL;DR: In this paper, a framework for investigating change over time is presented, where the multilevel model for change is introduced and a framework is presented for investigating event occurrence over time.
Abstract: PART I 1. A framework for investigating change over time 2. Exploring Longitudinal Data on Change 3. Introducing the multilevel model for change 4. Doing data analysis with the multilevel mode for change 5. Treating TIME more flexibly 6. Modelling discontinuous and nonlinear change 7. Examining the multilevel model's error covariance structure 8. Modelling change using covariance structure analysis PART II 9. A Framework for Investigating Event Occurrence 10. Describing discrete-time event occurrence data 11. Fitting basic Discrete-Time Hazard Models 12. Extending the Discrete-Time Hazard Model 13. Describing Continuous-Time Event Occurrence Data 14. Fitting Cox Regression Models 15. Extending the Cox Regression Model
8,435 citations