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.

/pdf/econometric-analysis-of-cross-section-and-panel-data-3jzr8emmtf.pdf

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

We compare four different estimation methods for a coefficient of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum empirical likelihood (MEL) estimator and a generalized method of moments (GMM) (or the estimating equation) estimator. Tables and figures are given for enough values of the parameters to cover most of interest. We have found that the LIML estimator has good performance when the number of instruments is large, that is, the micro-econometric models with many instruments or many weak instruments in the terminology of recent econometric literatures. We give a new result on the asymptotic optimality of the LIML estimator when the number of instruments is large.

/pdf/a-new-light-from-old-wisdoms-alternative-estimation-methods-2coihy07up.pdf

A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations and Microeconometric Models

THE TEST OF OVERIDENTIFYING restrictions of one equation in a simultaneous system
proposed by Anderson and Rubin [1] and amplified by Koopmans and Hood [7] has been a
source of some confusion in the literature. For instance, Liu and Breen [8] claimed that "It
is ... clear that the test does not really test the null hypothesis (of zero restrictions on the
endogenous and exogenous variables)" because, they thought the restrictions on the
endogenous variables were included in the computation of the likelihood under the
alternative hypothesis. After Fisher and Kadane [3] gave a verbal argument showing that
the test is consistent over a wide class of alternatives, Liu and Breen [9] withdrew their
earlier view. Nonetheless there is a problem in that generally the null hypothesis is
expressed in terms of the structural form, while generally consistency is a matter of the
reduced form. Our purpose is to reexamine this problem, and prove two theorems showing
the equivalence of various conditions in the literature. We suggest that the null hypothesis
be extended.

A comment on the test of overidentifying restrictions

We compare four different estimation methods for a coefficient of a linear structural equation with instrumental variables As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum empirical likelihood (MEL) estimator and a generalized method of moments (GMM) (or the estimating equation) estimator Tables and figures are given for enough values of the parameters to cover most of interest We have found that the LIML estimator has good performance when the number of instruments is large, that is, the micro-econometric models with many instruments or many weak instruments in the terminology of recent econometric literatures We give a new result on the asymptotic optimality of the LIML estimator when the number of instruments is large

Trygve Haavelmo was awarded the 1989 Alfred Nobel Memorial Prize for Economic Science for his introduction of the probability approach to econometrics. This paper gives some background to Haavelmo's innovations and tells of the early development of econometric methods in simultaneous equation models. Emphasis is on the statistical inference involved and relations to other statistical problems and procedures.

https://www.jstor.org/stable/pdfplus/4616185.pdf

Trygve Haavelmo and simultaneous equation models

I: Introduction.- 1 The Nature of SPSS.- 1.1 Getting Started with SPSS for Windows.- 1.2 Managing Data and Files.- 1.3 Transforming Variables and Data Files.- 1.4 Examining and Printing Output.- 1.5 Missing Values.- Exercises.- II: Descriptive Statistics.- 2 Organization of Data.- 2.2 Organization of Categorical Data.- 2.3 Organization of Numerical Data.- Exercises.- Appendix II: SPSS Syntax for Organization of Data.- 3 Measures of Location.- 3.1 The Mode.- 3.2 The Median and Other Percentiles.- 3.3 The Mean.- Exercises.- Appendix III: SPSS Syntax for Measures of Location.- 4 Measures of Variability.- 4.1 Ranges.- 4.2 The Mean Deviation.- 4.3 The Standard Deviation.- 4.5 Some Uses of Location and Dispersion Measures Together.- Exercises.- Appendix IV: SPSS Syntax for Measures of Variability.- 5 Summarizing Multivariate Data: Association Between Numerical Variables.- 5.1 Association of Two Numerical Variables.- 5.2 More than Two Variables.- Exercises.- Appendix V: SPSS Syntax for Summarizing Multivariate Data: Association Between Numerical Variables.- 6 Summarizing Multivariate Data: Association Between Categorical Variables.- 6.1 Two-by-Two Frequency Tables.- 6.2 Larger Two-Way Frequency Tables.- 6.3 Three Categorical Variables.- 6.4 Effects of a Third Variable.- Exercises.- Appendix VI: SPSS Syntax for Summarizing Multivariate Data: Association Between Categorical Variables.- III: Probability.- 7 Basic Ideas of Probability.- 7.3 Probability in Terms of Equally Likely Cases.- 7.8 Random Sampling Random Numbers.- Exercises.- Appendix VII: SPSS Syntax for Basic Ideas of Probability.- 8 Probability Distributions.- 8.5 Family of Standard Normal Distributions.- Exercises.- Appendix VIII: SPSS Syntax for Probability Distributions.- 9 Sampling Distributions.- 9.1 Sampling from a Population.- 9.2 Sampling Distribution of a Sum and of a Mean.- 9.5 The Normal Distribution of Sample Means.- Exercises.- IV: Statistical Inference.- 10 Using a Sample to Estimate Characteristics of One Population.- 10.1 Estimation of a Mean by a Single Number.- 10.2 Estimation of Variance and Standard Deviation.- 10.3 An Interval of Plausible Values for a Mean.- 10.4 Estimation of a Proportion.- 10.5 Estimation of a Median.- 10.6 Paired Measurements.- Exercises.- Appendix X: SPSS Syntax for Using a Sample to Estimate Characteristics of One Population.- 11 Answering Questions About Population Characteristics.- 11.1 Testing a Hypothesis About a Mean.- 11.3 Testing Hypotheses About a Mean when the Standard Deviation is Unknown.- 11.4 P Values: Another Way to Report Tests of Significance.- 11.5 Testing Hypotheses About a Proportion.- 11.6 Testing Hypotheses About a Median: The Sign Test.- 11.7 Paired Measurements.- Exercises.- Appendix XI: SPSS Syntax for Answering Questions About Population Characteristics.- 12 Differences Between Two Populations.- 12.1 Comparison of Two Independent Sample Means when the Population Standard Deviations are Known.- 12.2 Comparison of Two Independent Sample Means when the Population Standard Deviations are Unknown but Treated as Equal.- 12.3 Comparison of Two Independent Sample Means when the Population Standard Deviations are Unknown and not Treated as Equal.- 12.4 Comparison of Two Independent Sample Proportions.- 12.5 The Sign Test for a Difference in Locations.- Exercises.- Appendix XII: SPSS Syntax for Differences Between Two Populations.- 13 Variability in One Population and in Two Populations.- 13.1 Variability in One Population.- 13.2 Variability in Two Populations.- Exercises.- Appendix XIII: SPSS Syntax for Variability in One Population and in Two Populations.- V: Statistical Methods for Other Problems.- 14 Inference on Categorical Data.- 14.1 Tests of Goodness of Fit.- 14.2 Chi-Square Tests of Independence.- 14.3 Measures of Association.- Exercises.- Appendix XIV: SPSS Syntax for Inference on Categorical Data.- 15 Simple Regression Analysis.- 15.1 The Scatter Plot and Correlation Coefficient.- 15.2 SPSS for Simple Regression Analysis.- 15.3 Another Example: Inverse Association of x and y.- Exercises.- Appendix XV: SPSS Syntax for Simple Regression Analysis.- 16 Comparisons of Several Populations.- 16.1 One-Way Analysis of Variance.- 16.2 Which Groups Differ from Which, and by How Much?.- 16.3 Analysis of Variance of Ranks.- Exercises.- Appendix XVI: SPSS Syntax for Comparisons of Several Populations.- Appendix Data Files.

T. W. Anderson

Papers

A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations and Microeconometric Models

A comment on the test of overidentifying restrictions

A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations and Microeconometric Models

Trygve Haavelmo and simultaneous equation models

The SPSS Guide to the New Statistical Analysis of Data