scholarly journals Likelihood Ratio Testing under Measurement Errors

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 966 ◽  
Author(s):  
Michel Broniatowski ◽  
Jana Jurečková ◽  
Jan Kalina
Keyword(s):  
Likelihood Ratio ◽  
Measurement Errors ◽  
Type I Error ◽  
Alternative Hypothesis ◽  
Random Variable ◽  
Ratio Test ◽  
Type I ◽  
Likelihood Ratio Testing ◽  
And Performance ◽  
Unobservable Parameter

We consider the likelihood ratio test of a simple null hypothesis (with density f 0 ) against a simple alternative hypothesis (with density g 0 ) in the situation that observations X i are mismeasured due to the presence of measurement errors. Thus instead of X i for i = 1 , … , n , we observe Z i = X i + δ V i with unobservable parameter δ and unobservable random variable V i . When we ignore the presence of measurement errors and perform the original test, the probability of type I error becomes different from the nominal value, but the test is still the most powerful among all tests on the modified level. Further, we derive the minimax test of some families of misspecified hypotheses and alternatives. The test exploits the concept of pseudo-capacities elaborated by Huber and Strassen (1973) and Buja (1986). A numerical experiment illustrates the principles and performance of the novel test.

scholarly journals Anchor Selection Using the Wald Test Anchor-All-Test-All Procedure

2016 ◽  
Vol 41 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Mian Wang ◽  
Carol M. Woods
Keyword(s):  
Likelihood Ratio ◽  
Type I Error ◽  
Wald Test ◽  
Future Research ◽  
Ratio Test ◽  
Type I ◽  
Multiple Model ◽  
Selection Strategies ◽  
Item Functioning ◽  
Likelihood Ratio Testing

Methods for testing differential item functioning (DIF) require that the reference and focal groups are linked on a common scale using group-invariant anchor items. Several anchor-selection strategies have been introduced in an item response theory framework. However, popular strategies often utilize likelihood ratio testing with all-others-as-anchors that requires multiple model fittings. The current study explored alternative anchor-selection strategies based on a modified version of the Wald χ2 test that is implemented in flexMIRT and IRTPRO, and made comparisons with methods based on the popular likelihood ratio test. Accuracies of anchor identification of four different strategies (two testing methods combined with two selection criteria), along with the power and Type I error associated with respective follow-up DIF tests, will be presented. Implications for applied researchers and suggestions for future research will be discussed.

scholarly journals A Likelihood Ratio Test For The Homogeneity of Between-Study Variance in Network Meta-Analysis

2021 ◽  
Author(s):  
Dapeng Hu ◽  
Chong Wang ◽  
Annette O'Connor
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Random Effects ◽  
Type I Error ◽  
Meta Analysis ◽  
Indirect Evidence ◽  
Point Estimate ◽  
Ratio Test ◽  
Type I ◽  
Statistical Heterogeneity

Abstract Background: Network meta-analysis (NMA) is a statistical method used to combine results from several clinical trials and simultaneously compare multiple treatments using direct and indirect evidence. Statistical heterogeneity is a characteristic describing the variability in the intervention effects being evaluated in the different studies in network meta-analysis. One approach to dealing with statistical heterogeneity is to perform a random effects network meta-analysis that incorporates a between-study variance into the statistical model. A common assumption in the random effects model for network meta-analysis is the homogeneity of between-study variance across all interventions. However, there are applications of NMA where the single between-study assumption is potentially incorrect and instead the model should incorporate more than one between-study variances. Methods: In this paper, we develop an approach to testing the homogeneity of between-study variance assumption based on a likelihood ratio test. A simulation study was conducted to assess the type I error and power of the proposed test. This method is then applied to a network meta-analysis of antibiotic treatments for Bovine respiratory disease (BRD). Results: The type I error rate was well controlled in the Monte Carlo simulation. The homogeneous between-study variance assumption is unrealistic both statistically and practically in the network meta-analysis BRD. The point estimate and conffdence interval of relative effect sizes are strongly inuenced by this assumption. Conclusions: Since homogeneous between-study variance assumption is a strong assumption, it is crucial to test the validity of this assumption before conducting a network meta-analysis. Here we propose and validate a method for testing this single between-study variance assumption which is widely used for many NMA.

scholarly journals A Note on the Sampling Distribution of the Likelihood Ratio Test in the Context of the Linear Logistic Test Model

2016 ◽  
Vol 38 (4) ◽  
Author(s):  
Rainer W. Alexandrowicz
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Type I Error ◽  
Sampling Distribution ◽  
Weight Matrix ◽  
Ratio Test ◽  
Type I ◽  
Test Model ◽  
Linear Logistic Test Model ◽  
Error Risk

One important tool for assessing whether a data set can be described equally well with a Rasch Model (RM) or a Linear Logistic Test Model (LLTM) is the Likelihood Ratio Test (LRT). In practical applications this test seems to overly reject the null hypothesis, even when the null hypothesis is true. Aside from obvious reasons like inadequate restrictiveness of linear restrictions formulated in the LLTM or the RM not being true, doubts have arisen whether the test holds the nominal type-I error risk, that is whether its theoretically derived sampling distribution applies. Therefore, the present contribution explores the sampling distribution of the likelihood ratio test comparing a Rasch model with a Linear Logistic Test Model. Particular attention is put on the issue of similar columns in the weight matrixW of the LLTM: Although full column rank of this matrix is a technical requirement, columns can differ in only a few entries, what in turn might have an impact on the sampling distribution of the test statistic. Therefore, a system of how to generate weight matrices with similar columns has been established and tested in a simulation study. The results were twofold: In general, the matricesconsidered in the study showed LRT results where the empirical alpha showed only spurious deviations from the nominal alpha. Hence the theoretically chosen alpha seems maintained up to random variation. Yet, one specific matrix clearly indicated a highly increased type-I error risk: The empirical alpha was at least twice the nominal alpha when using this weight matrix. This shows that we have to indeed consider the internal structure of the weight matrix when applying the LRT for testing the LLTM. Best practice would be to perform a simulation or bootstrap/re-sampling study for the weight matrix under consideration in order to rule out a misleadingly significant result due to reasons other than true model misfit.

The Effects of Purification and the Evaluation of Differential Item Functioning With the Likelihood Ratio Test

Methodology ◽  
2012 ◽  
Vol 8 (4) ◽  
pp. 134-145 ◽  
Author(s):  
Fabiola González-Betanzos ◽  
Francisco J. Abad
Keyword(s):  
Differential Item Functioning ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Type I Error ◽  
Error Rates ◽  
Ratio Test ◽  
Type I ◽  
Two Stage ◽  
Item Functioning ◽  
Size Type

The current research compares the effects of several strategies to establish the anchor subtest when detecting for differential item functioning (DIF) using the IRT likelihood ratio test in one- and two-stage procedures. Two one-stage strategies were examined: (1) “One item” and (2) “All other items” used as anchor. Additionally, two two-stage strategies were tested: (3) “One anchor item with posterior anchor test augmentation” and (4) “All other items with purification.” The strategies were compared in a simulation study, where sample sizes, DIF size, type of DIF, and software implementation (MULTILOG vs. IRTLRDIF) were manipulated. Results indicated that Procedure (1) was more efficient than (2). Purification was found to improve Type I error rates substantially with the “all other items” strategy, while “posterior anchor test augmentation” did not yield a significant improvement. In relation to the effect of the software used, we found that MULTILOG generally offers better results than IRTLRDIF.

ModL: exploring and restoring regularity when testing for positive selection

2018 ◽  
Vol 35 (15) ◽  
pp. 2545-2554 ◽  
Author(s):  
Joseph Mingrone ◽  
Edward Susko ◽  
Joseph P Bielawski
Keyword(s):  
Positive Selection ◽  
Likelihood Ratio ◽  
Type I Error ◽  
Error Rates ◽  
Ratio Test ◽  
Type I ◽  
Chi Square ◽  
Type I Error Rates ◽  
Modified Likelihood Ratio Test ◽  
Modified Likelihood

Abstract Motivation Likelihood ratio tests are commonly used to test for positive selection acting on proteins. They are usually applied with thresholds for declaring a protein under positive selection determined from a chi-square or mixture of chi-square distributions. Although it is known that such distributions are not strictly justified due to the statistical irregularity of the problem, the hope has been that the resulting tests are conservative and do not lose much power in comparison with the same test using the unknown, correct threshold. We show that commonly used thresholds need not yield conservative tests, but instead give larger than expected Type I error rates. Statistical regularity can be restored by using a modified likelihood ratio test. Results We give theoretical results to prove that, if the number of sites is not too small, the modified likelihood ratio test gives approximately correct Type I error probabilities regardless of the parameter settings of the underlying null hypothesis. Simulations show that modification gives Type I error rates closer to those stated without a loss of power. The simulations also show that parameter estimation for mixture models of codon evolution can be challenging in certain data-generation settings with very different mixing distributions giving nearly identical site pattern distributions unless the number of taxa and tree length are large. Because mixture models are widely used for a variety of problems in molecular evolution, the challenges and general approaches to solving them presented here are applicable in a broader context. Availability and implementation https://github.com/jehops/codeml_modl Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Which Statistic Should Be Used to Detect Item Preknowledge When the Set of Compromised Items Is Known?

2017 ◽  
Vol 41 (6) ◽  
pp. 403-421 ◽  
Author(s):  
Sandip Sinharay
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Type I Error ◽  
Null Distribution ◽  
Real Data ◽  
Major Type ◽  
Ratio Test ◽  
Type I ◽  
Posterior Shift ◽  
Item Preknowledge

Benefiting from item preknowledge is a major type of fraudulent behavior during educational assessments. Belov suggested the posterior shift statistic for detection of item preknowledge and showed its performance to be better on average than that of seven other statistics for detection of item preknowledge for a known set of compromised items. Sinharay suggested a statistic based on the likelihood ratio test for detection of item preknowledge; the advantage of the statistic is that its null distribution is known. Results from simulated and real data and adaptive and nonadaptive tests are used to demonstrate that the Type I error rate and power of the statistic based on the likelihood ratio test are very similar to those of the posterior shift statistic. Thus, the statistic based on the likelihood ratio test appears promising in detecting item preknowledge when the set of compromised items is known.

scholarly journals A likelihood ratio test for the homogeneity of between-study variance in network meta-analysis

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Dapeng Hu ◽  
Chong Wang ◽  
Annette M. O’Connor
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Random Effects ◽  
Type I Error ◽  
Meta Analysis ◽  
Indirect Evidence ◽  
Point Estimate ◽  
Ratio Test ◽  
Type I ◽  
Statistical Heterogeneity

Abstract Background Network meta-analysis (NMA) is a statistical method used to combine results from several clinical trials and simultaneously compare multiple treatments using direct and indirect evidence. Statistical heterogeneity is a characteristic describing the variability in the intervention effects being evaluated in the different studies in network meta-analysis. One approach to dealing with statistical heterogeneity is to perform a random effects network meta-analysis that incorporates a between-study variance into the statistical model. A common assumption in the random effects model for network meta-analysis is the homogeneity of between-study variance across all interventions. However, there are applications of NMA where the single between-study assumption is potentially incorrect and instead the model should incorporate more than one between-study variances. Methods In this paper, we develop an approach to testing the homogeneity of between-study variance assumption based on a likelihood ratio test. A simulation study was conducted to assess the type I error and power of the proposed test. This method is then applied to a network meta-analysis of antibiotic treatments for Bovine respiratory disease (BRD). Results The type I error rate was well controlled in the Monte Carlo simulation. We found statistical evidence (p value = 0.052) against the homogeneous between-study variance assumption in the network meta-analysis BRD. The point estimate and confidence interval of relative effect sizes are strongly influenced by this assumption. Conclusions Since homogeneous between-study variance assumption is a strong assumption, it is crucial to test the validity of this assumption before conducting a network meta-analysis. Here we propose and validate a method for testing this single between-study variance assumption which is widely used for many NMA.

scholarly journals Likelihood ratio test between two groups of castor oil plant traits

2016 ◽  
Vol 46 (7) ◽  
pp. 1158-1164
Author(s):  
Betania Brum ◽  
Sidinei José Lopes ◽  
Daniel Furtado Ferreira ◽  
Lindolfo Storck ◽  
Alberto Cargnelutti Filho
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Type I Error ◽  
Plant Traits ◽  
Small Sample ◽  
Ratio Test ◽  
Type I ◽  
Sample Sizes ◽  
Oil Plant ◽  
Small Sample Sizes

ABSTRACT: The likelihood ratio test (LRT), to the independence between two sets of variables, allows to identify whether there is a dependency relationship between them. The aim of this study was to calculate the type I error and power of the LRT for determining independence between two sets of variables under multivariate normal distributions in scenarios consisting of combinations of 16 sample sizes; 40 combinations of the number of variables of the two groups; and nine degrees of correlation between the variables (for the power). The rate of type I error and power were calculate at 640 and 5,760 scenarios, respectively. A performance evaluation of the LRT was conducted by computer simulation by the Monte Carlo method, using 2,000 simulations in each scenario. When the number of variables was large (24), the TRV controlled the rate of type I errors and showed high power in sizes greater than 100 samples. For small sample sizes (25, 30 and 50), the test showed good performance because the number of variables did not exceed 12.

scholarly journals Likelihood-Ratio-Test Methods for Drug Safety Signal Detection from Multiple Clinical Datasets

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Lan Huang ◽  
Jyoti Zalkikar ◽  
Ram Tiwari
Keyword(s):  
Signal Detection ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Drug Safety ◽  
Drug Exposure ◽  
Type I Error ◽  
Test Methods ◽  
Ratio Test ◽  
Type I ◽  
Safety Signal

Pre- and postmarket drug safety evaluations usually include an integrated summary of results obtained using data from multiple studies related to a drug of interest. This paper proposes three approaches based on the likelihood ratio test (LRT), called the LRT methods, for drug safety signal detection from large observational databases with multiple studies, with focus on identifying signals of adverse events (AEs) from many AEs associated with a particular drug or inversely for signals of drugs associated with a particular AE. The methods discussed include simple pooled LRT method and its variations such as the weighted LRT that incorporates the total drug exposure information by study. The power and type-I error of the LRT methods are evaluated in a simulation study with varying heterogeneity across studies. For illustration purpose, these methods are applied to Proton Pump Inhibitors (PPIs) data with 6 studies for the effect of concomitant use of PPIs in treating patients with osteoporosis and to Lipiodol (a contrast agent) data with 13 studies for evaluating that drug’s safety profiles.

On estimating and testing associations between random coefficients from multivariate generalized linear mixed models of longitudinal outcomes

2015 ◽  
Vol 26 (3) ◽  
pp. 1130-1145 ◽  
Author(s):  
Susan K Mikulich-Gilbertson ◽  
Brandie D Wagner ◽  
Paula D Riggs ◽  
Gary O Zerbe
Keyword(s):  
Likelihood Ratio ◽  
Mixed Models ◽  
Generalized Linear Mixed Models ◽  
Mathematical Proof ◽  
Linear Mixed Models ◽  
Delta Method ◽  
Standard Errors ◽  
Ratio Test ◽  
Type I ◽  
Time Lags

Different types of outcomes (e.g. binary, count, continuous) can be simultaneously modeled with multivariate generalized linear mixed models by assuming: (1) same or different link functions, (2) same or different conditional distributions, and (3) conditional independence given random subject effects. Others have used this approach for determining simple associations between subject-specific parameters (e.g. correlations between slopes). We demonstrate how more complex associations (e.g. partial regression coefficients between slopes adjusting for intercepts, time lags of maximum correlation) can be estimated. Reparameterizing the model to directly estimate coefficients allows us to compare standard errors based on the inverse of the Hessian matrix with more usual standard errors approximated by the delta method; a mathematical proof demonstrates their equivalence when the gradient vector approaches zero. Reparameterization also allows us to evaluate significance of coefficients with likelihood ratio tests and to compare this approach with more usual Wald-type t-tests and Fisher’s z transformations. Simulations indicate that the delta method and inverse Hessian standard errors are nearly equivalent and consistently overestimate the true standard error. Only the likelihood ratio test based on the reparameterized model has an acceptable type I error rate and is therefore recommended for testing associations between stochastic parameters. Online supplementary materials include our medical data example, annotated code, and simulation details.

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