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 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 Exact Tests of Zero Variance Component in Presence of Multiple Variance Components with Application to Longitudinal Microbiome Study

2018 ◽  
Author(s):  
Jing Zhai ◽  
Kenneth Knox ◽  
Homer L. Twigg ◽  
Hua Zhou ◽  
Jin J. Zhou
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Variance Components ◽  
Null Hypothesis ◽  
Variance Component ◽  
Ratio Test ◽  
Type I ◽  
Exact Tests ◽  
Sample Sizes ◽  
Microbiome Composition

SummaryIn the metagenomics studies, testing the association of microbiome composition and clinical conditions translates to testing the nullity of variance components. Computationally efficient score tests have been the major tools. But they can only apply to the null hypothesis with a single variance component and when sample sizes are large. Therefore, they are not applicable to longitudinal microbiome studies. In this paper, we propose exact tests (score test, likelihood ratio test, and restricted likelihood ratio test) to solve the problems of (1) testing the association of the overall microbiome composition in a longitudinal design and (2) detecting the association of one specific microbiome cluster while adjusting for the effects from related clusters. Our approach combines the exact tests for null hypothesis with a single variance component with a strategy of reducing multiple variance components to a single one. Simulation studies demonstrate that our method has correct type I error rate and superior power compared to existing methods at small sample sizes and weak signals. Finally, we apply our method to a longitudinal pulmonary microbiome study of human immunodeficiency virus (HIV) infected patients and reveal two interesting genera Prevotella and Veillonella associated with forced vital capacity. Our findings shed lights on the impact of lung microbiome to HIV complexities. The method is implemented in the open source, high-performance computing language Julia and is freely available at https://github.com/JingZhai63/VCmicrobiome.

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.

A Monte Carlo Comparison of Seven ε-Adjustment Procedures in Repeated Measures Designs With Small Sample Sizes

1994 ◽  
Vol 19 (1) ◽  
pp. 57-71 ◽  
Author(s):  
Stephen M. Quintana ◽  
Scott E. Maxwell
Keyword(s):  
Repeated Measures ◽  
Type I Error ◽  
Error Rates ◽  
Small Sample ◽  
Small Samples ◽  
Type I ◽  
Sample Sizes ◽  
Type I Error Rates ◽  
Repeated Measures Designs ◽  
Small Sample Sizes

The purpose of this study was to evaluate seven univariate procedures for testing omnibus null hypotheses for data gathered from repeated measures designs. Five alternate approaches are compared to the two more traditional adjustment procedures (Geisser and Greenhouse’s ε̂ and Huynh and Feldt’s ε̃), neither of which may be entirely adequate when sample sizes are small and the number of levels of the repeated factors is large. Empirical Type I error rates and power levels were obtained by simulation for conditions where small samples occur in combination with many levels of the repeated factor. Results suggested that alternate univariate approaches were improvements to the traditional approaches. One alternate approach in particular was found to be most effective in controlling Type I error rates without unduly sacrificing power.

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.

Comparing Alternative Corrections for Bias in the Bias-Corrected Bootstrap Test of Mediation

2021 ◽  
pp. 016327872110243
Author(s):  
Donna Chen ◽  
Matthew S. Fritz
Keyword(s):  
Effect Size ◽  
Statistical Power ◽  
Type I Error ◽  
Small Sample ◽  
Medium Effect ◽  
Type I ◽  
Sample Sizes ◽  
Bootstrap Test ◽  
Small Effect Size ◽  
Small Sample Sizes

Although the bias-corrected (BC) bootstrap is an often-recommended method for testing mediation due to its higher statistical power relative to other tests, it has also been found to have elevated Type I error rates with small sample sizes. Under limitations for participant recruitment, obtaining a larger sample size is not always feasible. Thus, this study examines whether using alternative corrections for bias in the BC bootstrap test of mediation for small sample sizes can achieve equal levels of statistical power without the associated increase in Type I error. A simulation study was conducted to compare Efron and Tibshirani’s original correction for bias, z 0, to six alternative corrections for bias: (a) mean, (b–e) Winsorized mean with 10%, 20%, 30%, and 40% trimming in each tail, and (f) medcouple (robust skewness measure). Most variation in Type I error (given a medium effect size of one regression slope and zero for the other slope) and power (small effect size in both regression slopes) was found with small sample sizes. Recommendations for applied researchers are made based on the results. An empirical example using data from the ATLAS drug prevention intervention study is presented to illustrate these results. Limitations and future directions are discussed.

scholarly journals Permutation-based methods for mediation analysis in studies with small sample sizes

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e8246
Author(s):  
Miranda E. Kroehl ◽  
Sharon Lutz ◽  
Brandie D. Wagner
Keyword(s):  
Indirect Effect ◽  
Mediation Analysis ◽  
Type I Error ◽  
Permutation Test ◽  
Error Rates ◽  
Small Sample ◽  
Type I ◽  
Permutation Testing ◽  
Sample Sizes ◽  
Small Sample Sizes

Background Mediation analysis can be used to evaluate the effect of an exposure on an outcome acting through an intermediate variable or mediator. For studies with small sample sizes, permutation testing may be useful in evaluating the indirect effect (i.e., the effect of exposure on the outcome through the mediator) while maintaining the appropriate type I error rate. For mediation analysis in studies with small sample sizes, existing permutation testing methods permute the residuals under the full or alternative model, but have not been evaluated under situations where covariates are included. In this article, we consider and evaluate two additional permutation approaches for testing the indirect effect in mediation analysis based on permutating the residuals under the reduced or null model which allows for the inclusion of covariates. Methods Simulation studies were used to empirically evaluate the behavior of these two additional approaches: (1) the permutation test of the Indirect Effect under Reduced Models (IERM) and (2) the Permutation Supremum test under Reduced Models (PSRM). The performance of these methods was compared to the standard permutation approach for mediation analysis, the permutation test of the Indirect Effect under Full Models (IEFM). We evaluated the type 1 error rates and power of these methods in the presence of covariates since mediation analysis assumes no unmeasured confounders of the exposure–mediator–outcome relationships. Results The proposed PSRM approach maintained type I error rates below nominal levels under all conditions, while the proposed IERM approach exhibited grossly inflated type I rates in many conditions and the standard IEFM exhibited inflated type I error rates under a small number of conditions. Power did not differ substantially between the proposed PSRM approach and the standard IEFM approach. Conclusions The proposed PSRM approach is recommended over the existing IEFM approach for mediation analysis in studies with small sample sizes.

Sign in / Sign up

Export Citation Format

Share Document