Asymptotic Expansions of the Information Matrix Test Statistic

Econometrica ◽  
1991 ◽  
Vol 59 (3) ◽  
pp. 787 ◽  
Author(s):  
Andrew Chesher ◽  
Richard Spady
Keyword(s):  
Asymptotic Expansions ◽  
Information Matrix ◽  
Test Statistic ◽  
Information Matrix Test

scholarly journals How Robust Standard Errors Expose Methodological Problems They Do Not Fix, and What to Do About It

2015 ◽  
Vol 23 (2) ◽  
pp. 159-179 ◽  
Author(s):  
Gary King ◽  
Margaret E. Roberts
Keyword(s):  
Model Misspecification ◽  
Information Matrix ◽  
Theory And Practice ◽  
Standard Errors ◽  
Test Statistic ◽  
Methodological Problems ◽  
Variance Estimates ◽  
Information Matrix Test ◽  
Published Research ◽  
Robust Standard Errors

“Robust standard errors” are used in a vast array of scholarship to correct standard errors for model misspecification. However, when misspecification is bad enough to make classical and robust standard errors diverge, assuming that it is nevertheless not so bad as to bias everything else requires considerable optimism. And even if the optimism is warranted, settling for a misspecified model, with or without robust standard errors, will still bias estimators of all but a few quantities of interest. The resulting cavernous gap between theory and practice suggests that considerable gains in applied statistics may be possible. We seek to help researchers realize these gains via a more productive way to understand and use robust standard errors; a new general and easier-to-use “generalized information matrix test” statistic that can formally assess misspecification (based on differences between robust and classical variance estimates); and practical illustrations via simulations and real examples from published research. How robust standard errors are used needs to change, but instead of jettisoning this popular tool we show how to use it to provide effective clues about model misspecification, likely biases, and a guide to considerably more reliable, and defensible, inferences. Accompanying this article is software that implements the methods we describe.

Assessing Person Fit With the Information Matrix Test

Methodology ◽  
2015 ◽  
Vol 11 (1) ◽  
pp. 3-12 ◽  
Author(s):  
Jochen Ranger ◽  
Jörg-Tobias Kuhn
Keyword(s):  
Simulation Study ◽  
Type I Error ◽  
Information Matrix ◽  
Small Samples ◽  
Type I ◽  
Person Fit ◽  
Power Of The Test ◽  
Order Expansion ◽  
Trait Stability ◽  
Information Matrix Test

In this manuscript, a new approach to the analysis of person fit is presented that is based on the information matrix test of White (1982) . This test can be interpreted as a test of trait stability during the measurement situation. The test follows approximately a χ2-distribution. In small samples, the approximation can be improved by a higher-order expansion. The performance of the test is explored in a simulation study. This simulation study suggests that the test adheres to the nominal Type-I error rate well, although it tends to be conservative in very short scales. The power of the test is compared to the power of four alternative tests of person fit. This comparison corroborates that the power of the information matrix test is similar to the power of the alternative tests. Advantages and areas of application of the information matrix test are discussed.

scholarly journals Testing for Consistency using Artificial Regressions

1989 ◽  
Vol 5 (3) ◽  
pp. 363-384 ◽  
Author(s):  
Russell Davidson ◽  
James G. MacKinnon
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Information Matrix ◽  
Binary Choice ◽  
Parameter Estimates ◽  
Linear Regression Models ◽  
Score Tests ◽  
Binary Choice Models ◽  
Lagrange Multiplier Tests ◽  
Information Matrix Test

We consider several issues related to Durbin-Wu-Hausman tests; that is, tests based on the comparison of two sets of parameter estimates. We first review a number of results about these tests in linear regression models, discuss what determines their power, and propose a simple way to improve power in certain cases. We then show how in a general nonlinear setting they may be computed as “score” tests by means of slightly modified versions of any artificial linear regression that can be used to calculate Lagrange multiplier tests, and explore some of the implications of this result. In particular, we show how to create a variant of the information matrix test that tests for parameter consistency. We examine the conventional information matrix test and our new version in the context of binary-choice models, and provide a simple way to compute both tests using artificial regressions.

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