scholarly journals Approximations of the power functions for Wald, likelihood ratio, and score tests and their applications to linear and logistic regressions

2020 ◽  
Vol 15 (4) ◽  
pp. 335-349
Author(s):  
Eugene Demidenko
Keyword(s):  
Linear Regression ◽  
Likelihood Ratio ◽  
Statistical Power ◽  
Score Test ◽  
Power Functions ◽  
Score Tests ◽  
Local Alternative ◽  
Asymptotic Tests ◽  
Local Properties ◽  
Logistic Regressions

Traditionally, asymptotic tests are studied and applied under local alternative. There exists a widespread opinion that the Wald, likelihood ratio, and score tests are asymptotically equivalent. We dispel this myth by showing that These tests have different statistical power in the presence of nuisance parameters. The local properties of the tests are described in terms of the first and second derivative evaluated at the null hypothesis. The comparison of the tests are illustrated with two popular regression models: linear regression with random predictor and logistic regression with binary covariate. We study the aberrant behavior of the tests when the distance between the null and alternative does not vanish with the sample size. We demonstrate that these tests have different asymptotic power. In particular, the score test is generally asymptotically biased but slightly superior for linear regression in a close neighborhood of the null. The power approximations are confirmed through simulations.

SEMIPARAMETRIC INDEPENDENCE TESTING FOR TIME SERIES OF COUNTS AND THE ROLE OF THE SUPPORT

2018 ◽  
Vol 35 (6) ◽  
pp. 1111-1145 ◽  
Author(s):  
David Harris ◽  
Brendan McCabe
Keyword(s):  
Time Series ◽  
Likelihood Ratio ◽  
Negative Binomial ◽  
Score Test ◽  
Finite Sample ◽  
Natural Numbers ◽  
Score Tests ◽  
First Order ◽  
Semiparametric Likelihood ◽  
Asymptotically Efficient

This article considers testing for independence in a time series of small counts within an Integer Autoregressive (INAR) model, taking a semiparametric approach that avoids any distributional assumption on the arrivals process of the model. The nature of the testing problem is shown to differ depending on whether or not the support of the arrivals distribution is the full set of natural numbers (as would be the case for Poisson or Negative Binomial distributions for example) or some strict subset of the natural numbers (such as for a Binomial or Uniform distribution). The theory for these two cases is studied separately.For the case where the arrivals have support on the natural numbers, a new asymptotically efficient semiparametric test, the effective score (Neyman-Rao) test, is derived. The semiparametric Likelihood-Ratio, Wald and score tests are shown to be asymptotically equivalent to the effective score test, and hence also asymptotically efficient. Asymptotic relative efficiency calculations demonstrate that the semiparametric effective score test can provide substantial power advantages over the first order autocorrelation coefficient, which is most commonly applied in practice.For the case where the arrivals have support that is a strict subset of the natural numbers, the theory is considerably altered because the support of the observations becomes different under the null and alternative hypotheses. The semiparametric Likelihood-Ratio, Wald and score tests become asymptotically degenerate in this case, while the effective score test remains valid. Remarkably, in this case the effective score test is also found to have power against local alternatives that shrink to the null at the rate T−1. In rare cases where the arrival support is partly or totally known, additional tests exploiting this information are considered.Finite sample properties of the tests in these various cases demonstrate the semiparametric effective score test can provide substantial power advantages over the first order autocorrelation test implied by a parametric Poisson specification. The simulations also reveal situations in which the first order autocorrelation is preferable in finite samples, so a hybrid of the effective score and autocorrelation tests is proposed to capture most of the benefits of each test.

scholarly journals A powerful and efficient two-stage method for detecting gene-to-gene interactions in GWAS

Biostatistics ◽  
2017 ◽  
Vol 18 (3) ◽  
pp. 477-494 ◽  
Author(s):  
Jakub Pecanka ◽  
Marianne A. Jonker ◽  
Zoltan Bochdanovits ◽  
Aad W. Van Der Vaart ◽  
Keyword(s):  
Complex Traits ◽  
Multiple Testing ◽  
Statistical Power ◽  
Genome Wide Association Study ◽  
Score Test ◽  
Interaction Model ◽  
Type I ◽  
Two Stage ◽  
Genome Wide ◽  
Strong Control

Summary For over a decade functional gene-to-gene interaction (epistasis) has been suspected to be a determinant in the “missing heritability” of complex traits. However, searching for epistasis on the genome-wide scale has been challenging due to the prohibitively large number of tests which result in a serious loss of statistical power as well as computational challenges. In this article, we propose a two-stage method applicable to existing case-control data sets, which aims to lessen both of these problems by pre-assessing whether a candidate pair of genetic loci is involved in epistasis before it is actually tested for interaction with respect to a complex phenotype. The pre-assessment is based on a two-locus genotype independence test performed in the sample of cases. Only the pairs of loci that exhibit non-equilibrium frequencies are analyzed via a logistic regression score test, thereby reducing the multiple testing burden. Since only the computationally simple independence tests are performed for all pairs of loci while the more demanding score tests are restricted to the most promising pairs, genome-wide association study (GWAS) for epistasis becomes feasible. By design our method provides strong control of the type I error. Its favourable power properties especially under the practically relevant misspecification of the interaction model are illustrated. Ready-to-use software is available. Using the method we analyzed Parkinson’s disease in four cohorts and identified possible interactions within several SNP pairs in multiple cohorts.

Corrected likelihood ratio and score tests for the beta distribution

2003 ◽  
Vol 73 (8) ◽  
pp. 585-596 ◽  
Author(s):  
André Luis Santiago Maia ◽  
Antô Nio Carlos Braga Junior ◽  
Gauss Cordeiro
Keyword(s):  
Likelihood Ratio ◽  
Beta Distribution ◽  
Score Tests

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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