Despite the versatility of generalized linear mixed models in handling complex experimental designs, they often suffer from misspecification and convergence problems. This makes inference on the values of coefficients problematic. In addition, the researcher’s choice of random and fixed effects directly affects statistical inference correctness. To address these challenges, we propose a robust extension of the “two-stage summary statistics” approach using sign-flipping transformations of the score statistic in the second stage. Our approach efficiently handles within-variance structure and heteroscedasticity, ensuring accurate regression coefficient testing for 2-level hierarchical data structures. The approach is illustrated by analyzing the reduction of health issues over time for newly adopted children. The model is characterized by a binomial response with unbalanced frequencies and several categorical and continuous predictors. The proposed approach efficiently deals with critical problems related to longitudinal nonlinear models, surpassing common statistical approaches such as generalized estimating equations and generalized linear mixed models.

A method for robust canonical discriminant analysis via two robust objective loss functions is discussed. These functions are useful to reduce the influence of outliers in the data. Majorization is used at several stages of the minimization procedure to obtain a monotonically convergent algorithm. An advantage of the proposed method is that it allows for optimal scaling of the variables. In a simulation study it is shown that under the presence of outliers the robust functions outperform the ordinary least squares function, both when the underlying structure is linear in the variables as when it is nonlinear. Furthermore, the method is illustrated with empirical data.

Tukey's scheme for finding separations in univariate data strings is described and tested. It is found that one can use the size of a data gap coupled with its ordinal position in the distribution to determine the likelihood of its having arisen by chance. It was also shown that this scheme is relatively robust for fatter-tailed-than-Gaussian distributions and has some interesting implications in multidimensional situations.

A test is proposed for the equality of the variances of k ≥ 2 correlated variables. Pitman's test for k = 2 reduces the null hypothesis to zero correlation between their sum and their difference. Its extension, eliminating nuisance parameters by a bootstrap procedure, is valid for any correlation structure between the k normally distributed variables. A Monte Carlo study for several combinations of sample sizes and number of variables is presented, comparing the level and power of the new method with previously published tests. Some nonnormal data are included, for which the empirical level tends to be slightly higher than the nominal one. The results show that our method is close in power to the asymptotic tests which are extremely sensitive to nonnormality, yet it is robust and much more powerful than other robust tests.

Item response theory (IT) models are now in common use for the analysis of dichotomous item responses. This paper examines the sampling theory foundations for statistical inference in these models. The discussion includes: some history on the “stochastic subject” versus the random sampling interpretations of the probability in IRT models; the relationship between three versions of maximum likelihood estimation for IRT models; estimating θ versus estimating θ-predictors; IRT models and loglinear models; the identifiability of IRT models; and the role of robustness and Bayesian statistics from the sampling theory perspective.

In the framework of a robustness study on maximum likelihood estimation with LISREL three types of problems are dealt with: nonconvergence, improper solutions, and choice of starting values. The purpose of the paper is to illustrate why and to what extent these problems are of importance for users of LISREL. The ways in which these issues may affect the design and conclusions of robustness research is also discussed.

Taxicab correspondence analysis is based on the taxicab singular value decomposition of a contingency table, and it shares some similar properties with correspondence analysis. It is more robust than the ordinary correspondence analysis, because it gives uniform weights to all the points. The visual map constructed by taxicab correspondence analysis has a larger sweep and clearer perspective than the map obtained by correspondence analysis. Two examples are provided.

This paper addresses methodological issues that concern the scaling model used in the international comparison of student attainment in the Programme for International Student Attainment (PISA), specifically with reference to whether PISA’s ranking of countries is confounded by model misfit and differential item functioning (DIF). To determine this, we reanalyzed the publicly accessible data on reading skills from the 2006 PISA survey. We also examined whether the ranking of countries is robust in relation to the errors of the scaling model. This was done by studying invariance across subscales, and by comparing ranks based on the scaling model and ranks based on models where some of the flaws of PISA’s scaling model are taken into account. Our analyses provide strong evidence of misfit of the PISA scaling model and very strong evidence of DIF. These findings do not support the claims that the country rankings reported by PISA are robust.

We study the robustness of Krupka and Weber's method (2013) for eliciting social norms. In two online experiments with more than 1200 participants on Amazon Mechanical Turk, we find that participants’ response patterns are invariant to differences in the salience of the monetarily incentivized coordination aspect. We further demonstrate that asking participants for their personal first- and second-order beliefs without monetary incentives results in qualitatively identical responses in the case that beliefs and social norms are well aligned. Overall, Krupka and Weber's method produces remarkably robust response patterns.

Corrections for restriction in range due to explicit selection assume the linearity of regression and homoscedastic array variances. This paper develops a theoretical framework in which the effects of some common forms of violation of these assumptions on the estimation of the unrestricted correlation can be investigated. Simple expressions are derived for both the restricted and corrected correlations in terms of the target (unrestricted) correlation in these situations.

This paper discusses the issue of differential item functioning (DIF) in international surveys. DIF is likely to occur in international surveys. What is needed is a statistical approach that takes DIF into account, while at the same time allowing for meaningful comparisons between countries. Some existing approaches are discussed and an alternative is provided. The core of this alternative approach is to define the construct as a large set of items, and to report in terms of summary statistics. Since the data are incomplete, measurement models are used to complete the incomplete data. For that purpose, different models can be used across countries. The method is illustrated with PISA’s reading literacy data. The results indicate that this approach fits the data better than the current PISA methodology; however, the league tables are nearly identical. The implications for monitoring changes over time are discussed.

The importance of appropriate test selection for a given research endeavor cannot be overemphasized. Using samples drawn from eleven populations (differing in shape, peakedness, and density in the tails), this study investigates the small sample empirical powers of nine k-sample tests against ordered location alternatives under completely randomized designs. The results then are intended to aid the researcher in the selection of a particular procedure appropriate for a given endeavor. To highlight this an industrial psychology application involving work productivity is presented.

When some of observed variates do not conform to the model under consideration, they will have a serious effect on the results of statistical analysis. In factor analysis the model with inconsistent variates may result in improper solutions. In this article a useful method for identifying a variate as inconsistent is proposed in factor analysis. The procedure is based on the likelihood principle. Several statistical properties such as the effect of misspecified hypotheses, the problem of multiple comparisons, and robustness to violation of distributional assumptions are investigated. The procedure is illustrated by some examples.

A recent paper by Wainer and Thissen has renewed the interest in Gini’s mean difference, G, by pointing out its robust characteristics. This note presents distribution-free asymptotic confidence intervals for its population value, γ, in the one sample case and for the difference Δ = (γ1 − γ2) in the two sample situations. Both procedures are based on a technique of jackknifing U-statistics developed by Arvesen.

Noise is a ubiquitous feature for all organisms growing in nature. Noise (defined here as stochastic variation) in the availability of nutrients, water and light profoundly impacts their growth and development. Not only is noise present as an external factor but cellular processes themselves are noisy. Therefore, it is remarkable that organisms can display robust control of growth and development despite noise. To survive, various mechanisms to suppress noise have evolved. However, it is also becoming apparent that noise is not just a nuisance that organisms must suppress but can be beneficial as low noise can facilitate the response of an organism to a sub-threshold input signal in a stochastic resonance mechanism. This review discusses mechanisms capable of noise suppression or noise leveraging that might play a significant role in robust temporal regulation of an organism’s response to their noisy environment.

Text classification methods have been widely investigated as a way to detect content of low credibility: fake news, social media bots, propaganda, etc. Quite accurate models (likely based on deep neural networks) help in moderating public electronic platforms and often cause content creators to face rejection of their submissions or removal of already published texts. Having the incentive to evade further detection, content creators try to come up with a slightly modified version of the text (known as an attack with an adversarial example) that exploit the weaknesses of classifiers and result in a different output. Here we systematically test the robustness of common text classifiers against available attacking techniques and discover that, indeed, meaning-preserving changes in input text can mislead the models. The approaches we test focus on finding vulnerable spans in text and replacing individual characters or words, taking into account the similarity between the original and replacement content. We also introduce BODEGA: a benchmark for testing both victim models and attack methods on four misinformation detection tasks in an evaluation framework designed to simulate real use cases of content moderation. The attacked tasks include (1) fact checking and detection of (2) hyperpartisan news, (3) propaganda, and (4) rumours. Our experimental results show that modern large language models are often more vulnerable to attacks than previous, smaller solutions, e.g. attacks on GEMMA being up to 27% more successful than those on BERT. Finally, we manually analyse a subset adversarial examples and check what kinds of modifications are used in successful attacks.