One of the frequent questions by users of the mixed model function lmer of the lme4 package has been: How can I get p values for the F and t tests for objects returned by lmer? The lmerTest package ...extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing p values for tests for fixed effects. We have implemented the Satterthwaite's method for approximating degrees of freedom for the t and F tests. We have also implemented the construction of Type I - III ANOVA tables. Furthermore, one may also obtain the summary as well as the anova table using the Kenward-Roger approximation for denominator degrees of freedom (based on the KRmodcomp function from the pbkrtest package). Some other convenient mixed model analysis tools such as a step method, that performs backward elimination of nonsignificant effects - both random and fixed, calculation of population means and multiple comparison tests together with plot facilities are provided by the package as well.
From Many to One: Consensus Inference in a MIP Cressie, Noel; Bertolacci, Michael; Zammit‐Mangion, Andrew
Geophysical research letters,
28 July 2022, Letnik:
49, Številka:
14
Journal Article
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A Model Intercomparison Project (MIP) consists of teams who estimate the same underlying quantity (e.g., temperature projections to the year 2070). A simple average of the ensemble of the teams' ...outputs gives a consensus estimate, but it does not recognize that some outputs are more variable than others. Statistical analysis of variance (ANOVA) models offer a way to obtain a weighted frequentist consensus estimate of outputs with a variance that is the smallest possible. Modulo dependence between MIP outputs, the ANOVA approach weights a team's output inversely proportional to its variance, from which optimally weighted estimates follow. ANOVA weights can also provide a prior distribution for Bayesian Model Averaging of the MIP outputs when external evaluation data are available. We use a MIP of carbon‐dioxide‐flux inversions to illustrate the ANOVA‐based weighting and subsequent frequentist consensus inferences.
Plain Language Summary
There can be disagreement between different teams of scientists on the best way to model and hence estimate complex geophysical phenomena. Model Intercomparison Projects (MIPs) address this in a scientific manner, where a common protocol about data and certain basic geophysical features is agreed upon by the teams. The collection of the different teams' outputs is analyzed, often using the ensemble mean and a measure of the ensemble variability. However, the results may indicate that it is inappropriate to treat all teams' outputs equally, which can happen when some teams have superior models or better numerical approximations. It may also happen that some teams share code or their models have common features beyond those specified in the protocol. We adapt a statistical technique called the analysis of variance (ANOVA) to this complex setting, obtain optimal weights on the outputs, and then estimate those weights. This results in a statistically optimal (i.e., most precise) consensus summary of the MIP; other weights give less‐precise inferences. We call this inference framework for MIPs, Statistically Unbiased Prediction and Estimation‐ANOVA, and we apply it to a MIP designed to estimate the sources and sinks of carbon dioxide.
Key Points
Consensus inference is provided for Multiple Intercomparison Project (MIP) outputs when little or no evaluation data are available
The statistical analysis of variance method quantifies the MIP outputs' variabilities to obtain optimally weighted frequentist consensus inference
Variance parameters for optimal weighting of outputs and consensus inference are estimated using likelihood‐based methodology
Researchers often rely on analysis of variance (ANOVA) when they report results of experiments. To ensure that a study is adequately powered to yield informative results with an ANOVA, researchers ...can perform an a priori power analysis. However, power analysis for factorial ANOVA designs is often a challenge. Current software solutions do not allow power analyses for complex designs with several within-participants factors. Moreover, power analyses often need
η
p
2
or Cohen’s f as input, but these effect sizes are not intuitive and do not generalize to different experimental designs. We have created the R package Superpower and online Shiny apps to enable researchers without extensive programming experience to perform simulation-based power analysis for ANOVA designs of up to three within- or between-participants factors. Predicted effects are entered by specifying means, standard deviations, and, for within-participants factors, the correlations. The simulation provides the statistical power for all ANOVA main effects, interactions, and individual comparisons. The software can plot power across a range of sample sizes, can control for multiple comparisons, and can compute power when the homogeneity or sphericity assumption is violated. This Tutorial demonstrates how to perform a priori power analysis to design informative studies for main effects, interactions, and individual comparisons and highlights important factors that determine the statistical power for factorial ANOVA designs.
The bullet point of Sustainable Development Goals (SDGs) 2030 is improving of countries food security through decreasing of hungry level and providing equal conditions for food to everyone. Besides, ...according to the findings the issues with hungry index could be solved through developing the agricultural sector corresponding of SDGs principals. The findings showed that the agricultural sector is start point of decreasing the hungry. The authors proved the type of the political regime had impact on the efficiency of achieving of SDGs and countries’ food security. The hypothesis of investigation was checking the relationship between political profile of the countries and level of sustainable development of the agricultural sector (ASI). The assessment of the relationship between average level of ASI and countries' democratic profile (democracy level of public relations) for 28 countries of Post-Soviet bloc proved the non-existence of differences between countries with authoritarian and transitional regimes opposed to other political regimes (imperfect and full democracy). The authors allocated three segments of countries: authoritarian and transitional regimes, imperfect democracy and full-fledged democracy. The findings proved the hypothesis that democracy level had a statistically significant impact on the average level of ASI. Using the bivariate and multivariate models the authors empirically proved that the democracy level increase by 1-point leads to the increase of the target index by 0.087 points for countries with authoritarian and transitional regimes (to which Ukraine belongs). Thus, the transition to a more democratic model of the political regime will partially offset the threats to food security.
Aluminium alloy is the popular material in the world to produce lot of light weight parts with high strength, in additionally reinforcement is consider to these alloy is improve its strength. In this ...investigation consider the AA7050 aluminium alloy as a base material with reinforcement of Silicon Carbide (SiC) at various percentage level like as 0%, 4 % and 6 %. The wear of this composites are analysed through the design of experiments (Taguchi approach) for optimize the process parameters. This wear study is considered the parameters are Sliding velocity in m/s (1, 2 and 3), Sliding distance in m (1000, 1400 and 1800) and percentage of composition (0%, 43% and 6%). For this experimental investigation the sliding distance as most significant factor among three. The microstructure analysis demonstrated that there is a SiC particles which reduces wear of the samples.
This paper introduces the R package WRS2 that implements various robust statistical methods. It elaborates on the basics of robust statistics by introducing robust location, dispersion, and ...correlation measures. The location and dispersion measures are then used in robust variants of independent and dependent samples
t
tests and ANOVA, including between-within subject designs and quantile ANOVA. Further, robust ANCOVA as well as robust mediation models are introduced. The paper targets applied researchers; it is therefore kept rather non-technical and written in a tutorial style. Special emphasis is placed on applications in the social and behavioral sciences and illustrations of how to perform corresponding robust analyses in R. The R code for reproducing the results in the paper is given in the
Supplementary Materials
.
The robustness of F-test to non-normality has been studied from the 1930s through to the present day. However, this extensive body of research has yielded contradictory results, there being evidence ...both for and against its robustness. This study provides a systematic examination of F-test robustness to violations of normality in terms of Type I error, considering a wide variety of distributions commonly found in the health and social sciences.
We conducted a Monte Carlo simulation study involving a design with three groups and several known and unknown distributions. The manipulated variables were: Equal and unequal group sample sizes; group sample size and total sample size; coefficient of sample size variation; shape of the distribution and equal or unequal shapes of the group distributions; and pairing of group size with the degree of contamination in the distribution.
The results showed that in terms of Type I error the F-test was robust in 100% of the cases studied, independently of the manipulated conditions.
Many modern analytical methods are used to analyse samples coming from an experimental design, for example, in medical, biological, or agronomic fields. Those methods generate most of the time highly ...multivariate data like spectra or images. This is the case of “omics” technologies used to detect genes (genomics), mRNA (transcriptomics), proteins (proteomics), or metabolites (metabolomics) in a specific biological sample. Those technologies produce high‐dimensional multivariate databases where the number of variables (descriptors) tends to be much larger than the number of experimental units. Moreover, experiments in omics often follow designs aimed at understanding the effect of several factors on biological systems. Therefore, multivariate statistical tools are needed to highlight variables that are consistently modified by different biological states. It is in this context that 2 recent methods combine analysis of variance (ANOVA) and principal component analysis (PCA), namely, ASCA (ANOVA–simultaneous component analysis) and APCA (ANOVA‐PCA). They provide powerful tools to visualize multivariate structures in the space of each effect of the statistical model linked to the experimental design. Their main limitation is that they provide biased estimators of the factor effects when the design of experiment is unbalanced. This paper introduces 2 new methods, ASCA+ and APCA+, that allow, respectively, to extend the use of ASCA and APCA to unbalanced designs using several principles from the theory of general linear models. Both methods are applied on real‐life metabolomics data, clearly demonstrating the capacity of ASCA+ and APCA+ methods to highlight correct biomarkers corresponding to effects of interest in unbalanced designs.
This paper presents 2 new methods: ASCA+ and APCA+ that allow, respectively, to extend the use of ASCA and APCA to unbalanced designs. Those new methods rely on the principle of the general linear model to estimate factor effects with least squares rather than with simple differences of means as proposed by classical ASCA and APCA. Their application on real‐life metabolomics data shows their advantage in highlighting biomarkers corresponding to a factor of interest in unbalanced designs.
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