This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the maximum likelihood (ML)‐based standardized root mean squared residual (SRMR) and supplementing it with either Tucker‐Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, McDonald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff criteria for the ML‐based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true‐population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and G...

Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives

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.

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A new look at the statistical model identification

The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.

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Econometric Analysis of Cross Section and Panel Data

This paper presents specification tests that are applicable after estimating a dynamic model from panel data by the generalized method of moments (GMM), and studies the practical performance of these procedures using both generated and real data. Our GMM estimator optimally exploits all the linear moment restrictions that follow from the assumption of no serial correlation in the errors, in an equation which contains individual effects, lagged dependent variables and no strictly exogenous variables. We propose a test of serial correlation based on the GMM residuals and compare this with Sargan tests of over-identifying restrictions and Hausman specification tests.

http://people.stern.nyu.edu/wgreene/Econometrics/Arellano-Bond.pdf

Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations.

CHAPTER 1: Introduction to Design CHAPTER 2: Principles of Estimation and Inference: Means and Variance CHAPTER 3: Design and Analysis of Single-Factor Experiments: Completely Randomized Design CHAPTER 4: Single-Factor Experiments Having Repeated Measures on the Same Element CHAPTER 5: Design and Analysis of Factorial Experiments: Completely-Randomized Design CHAPTER 6: Factorial Experiments: Computational Procedures and Numerical Example CHAPTER 7: Multifactor Experiments Having Repeated Measures on the Same Element CHAPTER 8: Factorial Experiments in which Some of the Interactions are Confounded CHAPTER 9: Latin Squares and Related Designs CHAPTER 10: Analysis of Covariance

Statistical Principles in Experimental Design

Pao-Lu Hsu was bom in Peking in 1909 and obtained his B.Sc. degree from Tsing Hua University in 1933. He spent the years 1936-1940 at University College, London where he received a Ph.D. in 1938 and an D.Sc. in 1940. From London he returned to China to accept a professorship in the Department of Mathematics at Peking University.

Pao-Lu Hsu 1909-1970

/pdf/the-statistical-analysis-of-data-general-statistics-a-primer-2jjq6g08rg.pdf

The Statistical Analysis of Data.@@@General Statistics.@@@A Primer in Data Reduction: An Introductory Statistics Textbook.@@@A First Course in Statistics.@@@Introductory Statistics for the Behavioral Sciences.

https://statweb.stanford.edu/~ckirby/ted/papers/2007_MultipleDiscoveries.pdf

Multiple discoveries: Distribution of roots of determinantal equations

The performance of a production process is characterized by the quantity and quality of the output; it is affected by factors of production, such as conditions of the process and quantities of inputs. In experimentation where the factors are controlled, we assume a bivariate linear regression model with quantity and quality of output as dependent variates. In operation where quality of output is controlled by adjusting one of the factors, another regression model is used in which quantity of output and the one factor are dependent variates. The second model is derived from the first. It is shown how to use experimental data to estimate the coefficients of the regression of quantity of output in the second model; this regression function is desired for predicting performance in operation. Confidence regions and tests of hypotheses are treated. The exposition is in the form of an analysis of a particular problem met by a chemical engineering firm.

Some Statistical Problems in Relating Experimental Data to Predicting Performance of a Production Process

In Chapter 2 we start with the statistical information as it is obtained by the investigator; this information might be an instructor’s list of students and their grades, a record of the tax rates of counties in Florida, or the prices of Grade A large eggs in each of ten Chicago grocery stores averaged over the past 36 months. We refer to such statistical information as data, the recorded results of observation. After the collection of data, the next step in a statistical study is to organize the information in meaningful ways, often in the form of tables and graphs or charts. These displays or summaries are descriptions which help the investigator, as well as the eventual reader of the study, to understand the implications of the collected information. In later chapters we shall develop numerical descriptions that are more succinct than these tables and charts.

T. W. Anderson

Papers

Pao-Lu Hsu 1909-1970

The Statistical Analysis of Data.@@@General Statistics.@@@A Primer in Data Reduction: An Introductory Statistics Textbook.@@@A First Course in Statistics.@@@Introductory Statistics for the Behavioral Sciences.

Multiple discoveries: Distribution of roots of determinantal equations

Some Statistical Problems in Relating Experimental Data to Predicting Performance of a Production Process

Organization of Data