scholarly journals A critical issue in model-based inference for studying trait-based community assembly and a solution

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e2885 ◽  
Author(s):  
Cajo J.F. ter Braak ◽  
Pedro Peres-Neto ◽  
Stéphane Dray
Keyword(s):  
Linear Models ◽  
Type I Error ◽  
Computing Time ◽  
Random Effect ◽  
Correlation Method ◽  
Statistical Testing ◽  
Type I ◽  
Promising Alternative ◽  
Species Response ◽  
Random Variation

Statistical testing of trait-environment association from data is a challenge as there is no common unit of observation: the trait is observed on species, the environment on sites and the mediating abundance on species-site combinations. A number of correlation-based methods, such as the community weighted trait means method (CWM), the fourth-corner correlation method and the multivariate method RLQ, have been proposed to estimate such trait-environment associations. In these methods, valid statistical testing proceeds by performing two separate resampling tests, one site-based and the other species-based and by assessing significance by the largest of the twop-values (thepmaxtest). Recently, regression-based methods using generalized linear models (GLM) have been proposed as a promising alternative with statistical inference via site-based resampling. We investigated the performance of this new approach along with approaches that mimicked thepmaxtest using GLM instead of fourth-corner. By simulation using models with additional random variation in the species response to the environment, the site-based resampling tests using GLM are shown to have severely inflated type I error, of up to 90%, when the nominal level is set as 5%. In addition, predictive modelling of such data using site-based cross-validation very often identified trait-environment interactions that had no predictive value. The problem that we identify is not an “omitted variable bias” problem as it occurs even when the additional random variation is independent of the observed trait and environment data. Instead, it is a problem of ignoring a random effect. In the same simulations, the GLM-basedpmaxtest controlled the type I error in all models proposed so far in this context, but still gave slightly inflated error in more complex models that included both missing (but important) traits and missing (but important) environmental variables. For screening the importance of single trait-environment combinations, the fourth-corner test is shown to give almost the same results as the GLM-based tests in far less computing time.

scholarly journals Testing for treatment effect in covariate-adaptive randomized trials with generalized linear models and omitted covariates

2021 ◽  
pp. 096228022110082
Author(s):  
Yang Li ◽  
Wei Ma ◽  
Yichen Qin ◽  
Feifang Hu
Keyword(s):  
Generalized Linear Models ◽  
Treatment Effect ◽  
Linear Models ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
Asymptotic Results ◽  
Adaptive Randomization ◽  
Adjustment Method ◽  
Inflated Type

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two-sample t-test for treatment effect is typically conservative. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method.

scholarly journals Implementation of the Omega (ω) Index to detect large-scale systematic cheating

2019 ◽  
Author(s):  
Alvin Vista
Keyword(s):  
Standardized Testing ◽  
Large Scale ◽  
Type I Error ◽  
R Package ◽  
Statistical Testing ◽  
System Level ◽  
Control Group ◽  
Type I ◽  
Data Contamination ◽  
Cheating Detection

Cheating detection is an important issue in standardized testing, especially in large-scale settings. Statistical approaches are often computationally intensive and require specialised software to conduct. We present a two-stage approach that quickly filters suspected groups using statistical testing on an IRT-based answer-copying index. We also present an approach to mitigate data contamination and improve the performance of the index. The computation of the index was implemented through a modified version of an open source R package, thus enabling wider access to the method. Using data from PIRLS 2011 (N=64,232) we conduct a simulation to demonstrate our approach. Type I error was well-controlled and no control group was falsely flagged for cheating, while 16 (combined n=12,569) of the 18 (combined n=14,149) simulated groups were detected. Implications for system-level cheating detection and further improvements of the approach were discussed.

No counts, no variance: allowing for loss of degrees of freedom when assessing biological variability from RNA-seq data

2017 ◽  
Vol 16 (2) ◽  
Author(s):  
Aaron T. L. Lun ◽  
Gordon K. Smyth
Keyword(s):  
Software Package ◽  
Error Control ◽  
Degrees Of Freedom ◽  
Linear Models ◽  
Type I Error ◽  
Real Data ◽  
Type I ◽  
Rna Seq ◽  
Study Gene Expression ◽  
Complex Models

AbstractRNA sequencing (RNA-seq) is widely used to study gene expression changes associated with treatments or biological conditions. Many popular methods for detecting differential expression (DE) from RNA-seq data use generalized linear models (GLMs) fitted to the read counts across independent replicate samples for each gene. This article shows that the standard formula for the residual degrees of freedom (d.f.) in a linear model is overstated when the model contains fitted values that are exactly zero. Such fitted values occur whenever all the counts in a treatment group are zero as well as in more complex models such as those involving paired comparisons. This misspecification results in underestimation of the genewise variances and loss of type I error control. This article proposes a formula for the reduced residual d.f. that restores error control in simulated RNA-seq data and improves detection of DE genes in a real data analysis. The new approach is implemented in the quasi-likelihood framework of the edgeR software package. The results of this article also apply to RNA-seq analyses that apply linear models to log-transformed counts, such as those in the limma software package, and more generally to any count-based GLM where exactly zero fitted values are possible.

Misspecification of the random effect structure: Implications for the linear mixed model

2020 ◽  
Author(s):  
Brandon LeBeau
Keyword(s):  
Fixed Effects ◽  
Serial Correlation ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Type I Error ◽  
Random Effect ◽  
Correlated Data ◽  
Unbiased Estimation ◽  
Type I ◽  
Nested Data

<p>The linear mixed model is a commonly used model for longitudinal or nested data due to its ability to account for the dependency of nested data. Researchers typically rely on the random effects to adequately account for the dependency due to correlated data, however serial correlation can also be used. If the random effect structure is misspecified (perhaps due to convergence problems), can the addition of serial correlation overcome this misspecification and allow for unbiased estimation and accurate inferences? This study explored this question with a simulation. Simulation results show that the fixed effects are unbiased, however inflation of the empirical type I error rate occurs when a random effect is missing from the model. Implications for applied researchers are discussed.</p>

scholarly journals Statistical model specification and power: recommendations on the use of test-qualified pooling in analysis of experimental data

2017 ◽  
Vol 284 (1851) ◽  
pp. 20161850 ◽  
Author(s):  
Nick Colegrave ◽  
Graeme D. Ruxton
Keyword(s):  
Experimental Data ◽  
Statistical Model ◽  
Statistical Power ◽  
Error Term ◽  
Degrees Of Freedom ◽  
Type I Error ◽  
Error Rates ◽  
Statistical Testing ◽  
Model Specification ◽  
Type I

A common approach to the analysis of experimental data across much of the biological sciences is test-qualified pooling. Here non-significant terms are dropped from a statistical model, effectively pooling the variation associated with each removed term with the error term used to test hypotheses (or estimate effect sizes). This pooling is only carried out if statistical testing on the basis of applying that data to a previous more complicated model provides motivation for this model simplification; hence the pooling is test-qualified. In pooling, the researcher increases the degrees of freedom of the error term with the aim of increasing statistical power to test their hypotheses of interest. Despite this approach being widely adopted and explicitly recommended by some of the most widely cited statistical textbooks aimed at biologists, here we argue that (except in highly specialized circumstances that we can identify) the hoped-for improvement in statistical power will be small or non-existent, and there is likely to be much reduced reliability of the statistical procedures through deviation of type I error rates from nominal levels. We thus call for greatly reduced use of test-qualified pooling across experimental biology, more careful justification of any use that continues, and a different philosophy for initial selection of statistical models in the light of this change in procedure.

scholarly journals Including random effects in statistical models in ecology: fewer than five levels?

2021 ◽  
Author(s):  
Dylan G.E. Gomes
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Linear Models ◽  
Random Effect ◽  
Mixed Effects ◽  
Parameter Estimates ◽  
Type I ◽  
Type I Errors ◽  
Ecological Sites ◽  
Generalized Linear Mixed Effects

AbstractAs generalized linear mixed-effects models (GLMMs) have become a widespread tool in ecology, the need to guide the use of such tools is increasingly important. One common guideline is that one needs at least five levels of a random effect. Having such few levels makes the estimation of the variance of random effects terms (such as ecological sites, individuals, or populations) difficult, but it need not muddy one’s ability to estimate fixed effects terms – which are often of primary interest in ecology. Here, I simulate ecological datasets and fit simple models and show that having too few random effects terms does not influence the parameter estimates or uncertainty around those estimates for fixed effects terms. Thus, it should be acceptable to use fewer levels of random effects if one is not interested in making inference about the random effects terms (i.e. they are ‘nuisance’ parameters used to group non-independent data). I also use simulations to assess the potential for pseudoreplication in (generalized) linear models (LMs), when random effects are explicitly ignored and find that LMs do not show increased type-I errors compared to their mixed-effects model counterparts. Instead, LM uncertainty (and p values) appears to be more conservative in an analysis with a real ecological dataset presented here. These results challenge the view that it is never appropriate to model random effects terms with fewer than five levels – specifically when inference is not being made for the random effects, but suggest that in simple cases LMs might be robust to ignored random effects terms. Given the widespread accessibility of GLMMs in ecology and evolution, future simulation studies and further assessments of these statistical methods are necessary to understand the consequences of both violating and blindly following simple guidelines.

scholarly journals On the Conditional and Unconditional Type I Error Rates and Power of Tests in Linear Models with Heteroscedastic Errors

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
Patrick J. Rosopa ◽  
Alice M. Brawley ◽  
Theresa P. Atkinson ◽  
Stephen A. Robertson
Keyword(s):  
Linear Models ◽  
Type I Error ◽  
Weighted Least Squares ◽  
Error Rates ◽  
Type I ◽  
Least Squares Regression ◽  
Type I Error Rates ◽  
Power Of Tests ◽  
Wide Range ◽  
Heteroscedastic Errors

Preliminary tests for homoscedasticity may be unnecessary in general linear models. Based on Monte Carlo simulations, results suggest that when testing for differences between independent slopes, the unconditional use of weighted least squares regression and HC4 regression performed the best across a wide range of conditions.

Statistical Significance Testing with Mahalanobis Distance for Thresholds Estimated from Constant Stimuli Method

2011 ◽  
Vol 24 (2) ◽  
pp. 91-124 ◽  
Author(s):  
Keiji Uchikawa ◽  
Takahiro Hoshino ◽  
Takehiro Nagai
Keyword(s):  
Analysis Of Variance ◽  
Type I Error ◽  
Statistical Significance ◽  
Statistical Testing ◽  
Significance Testing ◽  
Type I ◽  
Testing Methods ◽  
Statistical Significance Testing ◽  
Staircase Method ◽  
Statistical Testing Method

AbstractThe t-test and the analysis of variance are commonly used as statistical significance testing methods. However, they cannot assess the significance of differences between thresholds within individual observers estimated from the constant stimuli method; these thresholds are not defined as averages of samples, but they are rather defined as functions of parameters of psychometric functions fitted to participants' responses. Moreover, the statistics necessary for these statistical testing methods cannot be derived. In this paper, we propose a new statistical testing method to assess the statistical significance of differences between thresholds estimated from the constant stimuli method. The new method can assess not only threshold differences but also main effects and interactions in multifactor experiments, exploiting the asymptotic normality of maximum likelihood estimators and the characteristics of multivariate normal distributions. This proposed method could be used in similar cases to the analysis of variance for thresholds estimated from the adjustment method and the staircase method. Finally, we present some data on simulations in which we tested assumptions, power and type I error of the proposed method.

A more efficient three-arm non-inferiority test based on pooled estimators of the homogeneous variance

2016 ◽  
Vol 27 (8) ◽  
pp. 2437-2446 ◽  
Author(s):  
Hezhi Lu ◽  
Hua Jin ◽  
Weixiong Zeng
Keyword(s):  
Sample Size ◽  
Error Rate ◽  
Statistical Power ◽  
Type I Error ◽  
Statistical Testing ◽  
New Method ◽  
Type I ◽  
Simulation Studies ◽  
Testing Framework ◽  
Better Than

Hida and Tango established a statistical testing framework for the three-arm non-inferiority trial including a placebo with a pre-specified non-inferiority margin to overcome the shortcomings of traditional two-arm non-inferiority trials (such as having to choose the non-inferiority margin). In this paper, we propose a new method that improves their approach with respect to two aspects. We construct our testing statistics based on the best unbiased pooled estimators of the homogeneous variance; and we use the principle of intersection-union tests to determine the rejection rule. We theoretically prove that our test is better than that of Hida and Tango for large sample sizes. Furthermore, when that sample size was small or moderate, our simulation studies showed that our approach performed better than Hida and Tango’s. Although both controlled the type I error rate, their test was more conservative and the statistical power of our test was higher.

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