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Statistical model

About: Statistical model is a(n) research topic. Over the lifetime, 19987 publication(s) have been published within this topic receiving 904164 citation(s). The topic is also known as: Models, Statistical & statistical model.
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Journal ArticleDOI
Abstract: The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.

42,619 citations

06 May 2013-
Abstract: I. FUNDAMENTAL CONCEPTS 1. Introduction 1.1. A Scientist in Training 1.2. Questions of Whether, If, How, and When 1.3. Conditional Process Analysis 1.4. Correlation, Causality, and Statistical Modeling 1.5. Statistical Software 1.6. Overview of this Book 1.7. Chapter Summary 2. Simple Linear Regression 2.1. Correlation and Prediction 2.2. The Simple Linear Regression Equation 2.3. Statistical Inference 2.4. Assumptions for Interpretation and Statistical Inference 2.5. Chapter Summary 3. Multiple Linear Regression 3.1. The Multiple Linear Regression Equation 3.2. Partial Association and Statistical Control 3.3. Statistical Inference in Multiple Regression 3.4. Statistical and Conceptual Diagrams 3.5. Chapter Summary II. MEDIATION ANALYSIS 4. The Simple Mediation Model 4.1. The Simple Mediation Model 4.2. Estimation of the Direct, Indirect, and Total Effects of X 4.3. Example with Dichotomous X: The Influence of Presumed Media Influence 4.4. Statistical Inference 4.5. An Example with Continuous X: Economic Stress among Small Business Owners 4.6. Chapter Summary 5. Multiple Mediator Models 5.1. The Parallel Multiple Mediator Model 5.2. Example Using the Presumed Media Influence Study 5.3. Statistical Inference 5.4. The Serial Multiple Mediator Model 5.5. Complementarity and Competition among Mediators 5.6. OLS Regression versus Structural Equation Modeling 5.7. Chapter Summary III. MODERATION ANALYSIS 6. Miscellaneous Topics in Mediation Analysis 6.1. What About Baron and Kenny? 6.2. Confounding and Causal Order 6.3. Effect Size 6.4. Multiple Xs or Ys: Analyze Separately or Simultaneously? 6.5. Reporting a Mediation Analysis 6.6. Chapter Summary 7. Fundamentals of Moderation Analysis 7.1. Conditional and Unconditional Effects 7.2. An Example: Sex Discrimination in the Workplace 7.3. Visualizing Moderation 7.4. Probing an Interaction 7.5. Chapter Summary 8. Extending Moderation Analysis Principles 8.1. Moderation Involving a Dichotomous Moderator 8.2. Interaction between Two Quantitative Variables 8.3. Hierarchical versus Simultaneous Variable Entry 8.4. The Equivalence between Moderated Regression Analysis and a 2 x 2 Factorial Analysis of Variance 8.5. Chapter Summary 9. Miscellaneous Topics in Moderation Analysis 9.1. Truths and Myths about Mean Centering 9.2. The Estimation and Interpretation of Standardized Regression Coefficients in a Moderation Analysis 9.3. Artificial Categorization and Subgroups Analysis 9.4. More Than One Moderator 9.5. Reporting a Moderation Analysis 9.6. Chapter Summary IV. CONDITIONAL PROCESS ANALYSIS 10. Conditional Process Analysis 10.1. Examples of Conditional Process Models in the Literature 10.2. Conditional Direct and Indirect Effects 10.3. Example: Hiding Your Feelings from Your Work Team 10.4. Statistical Inference 10.5. Conditional Process Analysis in PROCESS 10.6. Chapter Summary 11. Further Examples of Conditional Process Analysis 11.1. Revisiting the Sexual Discrimination Study 11.2. Moderation of the Direct and Indirect Effects in a Conditional Process Model 11.3. Visualizing the Direct and Indirect Effects 11.4. Mediated Moderation 11.5. Chapter Summary 12. Miscellaneous Topics in Conditional Process Analysis 12.1. A Strategy for Approaching Your Analysis 12.2. Can a Variable Simultaneously Mediate and Moderate Another Variable's Effect? 12.3. Comparing Conditional Indirect Effects and a Formal Test of Moderated Mediation 12.4. The Pitfalls of Subgroups Analysis 12.5. Writing about Conditional Process Modeling 12.6. Chapter Summary Appendix A. Using PROCESS Appendix B. Monte Carlo Confidence Intervals in SPSS and SAS

26,130 citations

01 Jan 1974-
Abstract: Applied Linear Statistical Models 5e is the long established leading authoritative text and reference on statistical modeling. The text includes brief introductory and review material, and then proceeds through regression and modeling for the first half, and through ANOVA and Experimental Design in the second half. All topics are presented in a precise and clear style supported with solved examples, numbered formulae, graphic illustrations, and "Notes" to provide depth and statistical accuracy and precision. The Fifth edition provides an increased use of computing and graphical analysis throughout, without sacrificing concepts or rigor. In general, the 5e uses larger data sets in examples and exercises, and where methods can be automated within software without loss of understanding, it is so done.

10,745 citations

Journal ArticleDOI
Abstract: + Abstract: Statistical parametric maps are spatially extended statistical processes that are used to test hypotheses about regionally specific effects in neuroimaging data. The most established sorts of statistical parametric maps (e.g., Friston et al. (1991): J Cereb Blood Flow Metab 11:690-699; Worsley et al. 119921: J Cereb Blood Flow Metab 12:YOO-918) are based on linear models, for example ANCOVA, correlation coefficients and t tests. In the sense that these examples are all special cases of the general linear model it should be possible to implement them (and many others) within a unified framework. We present here a general approach that accommodates most forms of experimental layout and ensuing analysis (designed experiments with fixed effects for factors, covariates and interaction of factors). This approach brings together two well established bodies of theory (the general linear model and the theory of Gaussian fields) to provide a complete and simple framework for the analysis of imaging data. The importance of this framework is twofold: (i) Conceptual and mathematical simplicity, in that the same small number of operational equations is used irrespective of the complexity of the experiment or nature of the statistical model and (ii) the generality of the framework provides for great latitude in experimental design and analysis.

9,254 citations

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Topic's top 5 most impactful authors

Christian Soize

21 papers, 663 citations

Christopher K. Wikle

19 papers, 1.2K citations

Noel A Cressie

19 papers, 1.1K citations

Christopher J. Taylor

16 papers, 7K citations

Aapo Hyvärinen

15 papers, 2.1K citations