scholarly journals A comparison of empirical BLUP with different considerations of residual error variance for genotype evaluation of multi-location trials

2019 ◽  
Vol 17 (1) ◽  
pp. e0701
Author(s):  
Renhe Zhang ◽  
Xiyuan Hu
Keyword(s):  
Mixed Model ◽  
Type I Error ◽  
Block Design ◽  
Model Fitting ◽  
Covariance Structure ◽  
Error Variance ◽  
Error Rates ◽  
Residual Error ◽  
Type I ◽  
The North

AbstractThe empirical best linear unbiased prediction (eBLUP) is usually based on the assumption that the residual error variance (REV) is homogenous. This may be unrealistic, and therefore limits the accuracy of genotype evaluations for multi-location trials, where the REV often varies across locations. The objective of this contribution was to investigate the direct implications of the eBLUP with different considerations about REV based on the mixed model for evaluation of genotype simple effects (i.e. genotype effects at individual locations). A series of 14 multi-location trials from a rape-breeding program in the north of China were simultaneously analyzed from 2012 to 2014 using a randomized complete block design at each location. The results showed that the model with heterogeneous REV was more appropriate than the one with homogeneous REV in all of the trials according to model fitting statistics. Whether the REV differences across locations were accounted for in the analysis procedure influenced the variance estimate of related random effects and testing of the variance of genotype-location (G-L) interactions. Ignoring REV differences by use of the eBLUP could result not only in an inflation or deflation of statistical Type I error rates for pair-wise testing but also in an inaccurate ranking of genotype simple effects for these trials. Therefore, it is suggested that in application of the eBLUP for evaluation of genotype simple effects in multi-location trials, the heterogeneity of REV should be accounted for based on mixed model approaches with appropriate variance-covariance structure.

A Practical Method for Analyzing Factorial Designs with Heteroscedastic Data

2008 ◽  
Vol 102 (3) ◽  
pp. 643-656
Author(s):  
Guiillermo Vallejo ◽  
M. Paula Fernández ◽  
Manuel Ato ◽  
Pablo E. Livacic-Rojas
Keyword(s):  
Mixed Model ◽  
Type I Error ◽  
Practical Method ◽  
Error Rates ◽  
Type I ◽  
Factorial Designs ◽  
Symmetric Distributions ◽  
Higher Power ◽  
Asymmetric Distributions ◽  
Heteroscedastic Data

The Type I error rates and powers of three recent tests for analyzing nonorthogonal factorial designs under departures from the assumptions of homogeneity and normality were evaluated using Monte Carlo simulation. Specifically, this work compared the performance of the modified Brown-Forsythe procedure, the generalization of Box's method proposed by Brunner, Dette, and Munk, and the mixed-model procedure adjusted by the Kenward-Roger solution available in the SAS statistical package. With regard to robustness, the three approaches adequately controlled Type I error when the data were generated from symmetric distributions; however, this study's results indicate that, when the data were extracted from asymmetric distributions, the modified Brown-Forsythe approach controlled the Type I error slightly better than the other procedures. With regard to sensitivity, the higher power rates were obtained when the analyses were done with the MIXED procedure of the SAS program. Furthermore, results also identified that, when the data were generated from symmetric distributions, little power was sacrificed by using the generalization of Box's method in place of the modified Brown-Forsythe procedure.

scholarly journals PSII-7 Type I error rates of two strategies to analyze a randomized complete block design within multiple sites

2019 ◽  
Vol 97 (Supplement_2) ◽  
pp. 235-236
Author(s):  
Hilda Calderon Cartagena ◽  
Christopher I Vahl ◽  
Steve S Dritz
Keyword(s):  
Degrees Of Freedom ◽  
Type I Error ◽  
Block Design ◽  
Error Rates ◽  
Type I ◽  
Block Designs ◽  
Significant Treatment ◽  
Type I Error Rates ◽  
Treatment Interaction ◽  
To Come

Abstract It is not unusual to come across randomized complete block designs (RCBD) replicated over a small number of sites in swine nutrition trials. For example, pens could be blocked by location or by initial body weight within three rooms or barns. One possibility is to analyze this design with the assumption of no treatment by site interaction which implies treatment differences are similar across all sites. This assumption might not always seem reasonable and site by treatment interaction could be included in the analysis to account for these differences should they exist. However, the site by treatment mean square becomes the error term for evaluating treatment. The objective of this study was to provide a recommendation of a practical strategy based on Type I error rates estimated from a simulation study. Scenarios with and without site by treatment interaction were considered with three sites and equal means across four treatments. The variance component for the error was set to 1 and the rest were either selected to be equal (σ2s = σ2b = σ2s*t =1) or one of them was set to 10. For the scenarios with no site by treatment interaction, σ2s*t = 0, for a total of 7 scenarios. Each scenario was simulated 10,000 times. For each simulation, both strategies were applied. The Kenward-Rodger approximation (KR) to the denominator degrees of freedom was also considered. Type I errors were estimated as the proportion of simulations with a significant treatment effect with α = 0.05. Overall, there was no evidence Type I error rates were inflated when the site by treatment interaction was omitted, even when σ2s*t = 10. The KR had no effect. In contrast, including the interaction term leads to a highly conservative Type I error rate far below the 5% level which results in a reduction of power; however, using KR mitigated the conservativeness.

scholarly journals Efficient mixed model approach for large-scale genome-wide association studies of ordinal categorical phenotypes

2020 ◽  
Author(s):  
Wenjian Bi ◽  
Wei Zhou ◽  
Rounak Dey ◽  
Bhramar Mukherjee ◽  
Joshua N Sampson ◽  
...  
Keyword(s):  
Mixed Model ◽  
Type I Error ◽  
Association Studies ◽  
Error Rates ◽  
Genome Wide Association ◽  
Alternative Methods ◽  
Type I ◽  
Genome Wide Association Studies ◽  
Type I Error Rates ◽  
Genome Wide

AbstractIn genome-wide association studies (GWAS), ordinal categorical phenotypes are widely used to measure human behaviors, satisfaction, and preferences. However, due to the lack of analysis tools, methods designed for binary and quantitative traits have often been used inappropriately to analyze categorical phenotypes, which produces inflated type I error rates or is less powerful. To accurately model the dependence of an ordinal categorical phenotype on covariates, we propose an efficient mixed model association test, Proportional Odds Logistic Mixed Model (POLMM). POLMM is demonstrated to be computationally efficient to analyze large datasets with hundreds of thousands of genetic related samples, can control type I error rates at a stringent significance level regardless of the phenotypic distribution, and is more powerful than other alternative methods. We applied POLMM to 258 ordinal categorical phenotypes on array-genotypes and imputed samples from 408,961 individuals in UK Biobank. In total, we identified 5,885 genome-wide significant variants, of which 424 variants (7.2%) are rare variants with MAF < 0.01.

Covariance Structure Selection and Type I Error Rates in Split-Plot Designs

Methodology ◽  
2013 ◽  
Vol 9 (4) ◽  
pp. 129-136 ◽  
Author(s):  
Pablo Livacic-Rojas ◽  
Guillermo Vallejo ◽  
Paula Fernández ◽  
Ellián Tuero-Herrero
Keyword(s):  
Type I Error ◽  
Covariance Structure ◽  
Error Rates ◽  
Information Criteria ◽  
Covariance Structures ◽  
Future Research ◽  
Dispersion Matrix ◽  
Type I ◽  
Type I Error Rates ◽  
Split Plot

We examined the selection of covariance structures and the Type I error rates of the Criterion Selector Akaike’s (Akaike’s Information Criteria, AIC) and the Correctly Identified Model (CIM). Data were analyzed with a split-plot design through the Monte Carlo simulation method and SAS 9.1 statistical software. We manipulated the following variables: sample size, relation between group size and dispersion matrix size, type of dispersion matrix, and form of the distribution. Our findings suggest that AIC selects heterogeneous covariance structure more frequently than original covariance structure. Specifically, AIC mostly selected heterogeneous covariance structures and displayed slightly higher Type I error rates than the CIM. These were mostly associated with main and interaction effects for the ARH and RC structures and a marked tendency toward liberality. Future research needs to assess the power levels exhibited by covariance structure selectors.

Correction: “Influence of Selection Bias on the Test Decision – A Simulation Study”

2014 ◽  
Vol 53 (05) ◽  
pp. 343-343
Keyword(s):  
Selection Bias ◽  
Simulation Study ◽  
Error Rate ◽  
Type I Error ◽  
Block Size ◽  
Error Rates ◽  
Type I ◽  
Type I Error Rate ◽  
Representation Error ◽  
Numeric Representation

We have to report marginal changes in the empirical type I error rates for the cut-offs 2/3 and 4/7 of Table 4, Table 5 and Table 6 of the paper “Influence of Selection Bias on the Test Decision – A Simulation Study” by M. Tamm, E. Cramer, L. N. Kennes, N. Heussen (Methods Inf Med 2012; 51: 138 –143). In a small number of cases the kind of representation of numeric values in SAS has resulted in wrong categorization due to a numeric representation error of differences. We corrected the simulation by using the round function of SAS in the calculation process with the same seeds as before. For Table 4 the value for the cut-off 2/3 changes from 0.180323 to 0.153494. For Table 5 the value for the cut-off 4/7 changes from 0.144729 to 0.139626 and the value for the cut-off 2/3 changes from 0.114885 to 0.101773. For Table 6 the value for the cut-off 4/7 changes from 0.125528 to 0.122144 and the value for the cut-off 2/3 changes from 0.099488 to 0.090828. The sentence on p. 141 “E.g. for block size 4 and q = 2/3 the type I error rate is 18% (Table 4).” has to be replaced by “E.g. for block size 4 and q = 2/3 the type I error rate is 15.3% (Table 4).”. There were only minor changes smaller than 0.03. These changes do not affect the interpretation of the results or our recommendations.

The Use of Theory of Linear Mixed-Effects Models to Detect Fraudulent Erasures at an Aggregate Level

2021 ◽  
pp. 001316442199489
Author(s):  
Luyao Peng ◽  
Sandip Sinharay
Keyword(s):  
Type I Error ◽  
Real Data ◽  
Mixed Effects ◽  
Error Rates ◽  
Mixed Effects Models ◽  
Type I ◽  
Aggregate Level ◽  
Linear Mixed Effects Models ◽  
Linear Mixed Effects ◽  
Best Linear Unbiased

Wollack et al. (2015) suggested the erasure detection index (EDI) for detecting fraudulent erasures for individual examinees. Wollack and Eckerly (2017) and Sinharay (2018) extended the index of Wollack et al. (2015) to suggest three EDIs for detecting fraudulent erasures at the aggregate or group level. This article follows up on the research of Wollack and Eckerly (2017) and Sinharay (2018) and suggests a new aggregate-level EDI by incorporating the empirical best linear unbiased predictor from the literature of linear mixed-effects models (e.g., McCulloch et al., 2008). A simulation study shows that the new EDI has larger power than the indices of Wollack and Eckerly (2017) and Sinharay (2018). In addition, the new index has satisfactory Type I error rates. A real data example is also included.

The Robustness of the Likelihood Ratio Chi-Square Test for Structural Equation Models: A Meta-Analysis

2001 ◽  
Vol 26 (1) ◽  
pp. 105-132 ◽  
Author(s):  
Douglas A. Powell ◽  
William D. Schafer
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Type I Error ◽  
Meta Analysis ◽  
Generalized Least Squares ◽  
Error Rates ◽  
Type I ◽  
Chi Square ◽  
Distribution Free ◽  
Projection Techniques

The robustness literature for the structural equation model was synthesized following the method of Harwell which employs meta-analysis as developed by Hedges and Vevea. The study focused on the explanation of empirical Type I error rates for six principal classes of estimators: two that assume multivariate normality (maximum likelihood and generalized least squares), elliptical estimators, two distribution-free estimators (asymptotic and others), and latent projection. Generally, the chi-square tests for overall model fit were found to be sensitive to non-normality and the size of the model for all estimators (with the possible exception of the elliptical estimators with respect to model size and the latent projection techniques with respect to non-normality). The asymptotic distribution-free (ADF) and latent projection techniques were also found to be sensitive to sample sizes. Distribution-free methods other than ADF showed, in general, much less sensitivity to all factors considered.

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