Social scientists are often faced with data that have a nested structure: pupils are nested within schools, employees are nested within companies, or repeated measurements are nested within individuals. Nested data are typically analyzed using multilevel models. However, when data sets are extremely large or when new data continuously augment the data set, estimating multilevel models can be challenging: the current algorithms used to fit multilevel models repeatedly revisit all data points and end up consuming much time and computer memory. This is especially troublesome when predictions are needed in real time and observations keep streaming in. We address this problem by introducing the Streaming Expectation Maximization Approximation (SEMA) algorithm for fitting multilevel models online (or “row-by-row”). In an extensive simulation study, we demonstrate the performance of SEMA compared to traditional methods of fitting multilevel models. Next, SEMA is used to analyze an empirical data stream. The accuracy of SEMA is competitive to current state-of-the-art methods while being orders of magnitude faster.

This study delves into the comprehensive examination of an anta capital discovered during the 2008 excavations at the ancient site of Alabanda in Caria, now housed in the Aydın Archaeological Museum. Employing a typological and stylistic analysis, the research attributes the capital to the latter part of the fifth century BC, emphasising its intricate architectural ornamentation and sculptural details that reflect significant artistic and cultural developments of the period. The capital features elaborate ornament bands and mythological reliefs, including depictions of Bellerophon-Pegasus and Chimera, and a griffin attacking a horse, which are analysed for their iconographic and symbolic significance within the broader Anatolian and Mediterranean contexts. The study also explores the potential original architectural setting of the capital, suggesting its use in a monumental tomb, a hypothesis supported by its dimensions and decorative complexity. Furthermore, the article discusses the role of such imagery in asserting local identities and engaging with wider Hellenic cultural and political themes, particularly considering the complex interactions between local Carian traditions and the dominant Greek culture of the period. The findings not only contribute to our understanding of Carian art and architecture but also highlight the region’s active participation in the cultural dialogues of the Classical world.

The present paper introduces a new explanatory item response model to account for the learning that takes place during a psychometric test due to the repeated use of the operations involved in the items. The proposed model is an extension of the operation-specific learning model (Fischer and Formann in Appl Psychol Meas 6:397–416, 1982; Scheiblechner in Z für Exp Angew Psychol 19:476–506, 1972; Spada in Spada and Kempf (eds.) Structural models of thinking and learning, Huber, Bern, Germany, pp 227–262, 1977). The paper discusses special cases of the model, which, together with the general formulation, differ in the type of response in which the model states that learning occurs: (1) correct and incorrect responses equally (non-contingent learning); (2) correct responses only (contingent learning); and (3) correct and incorrect responses to a different extent (differential contingent learning). A Bayesian framework is adopted for model estimation and evaluation. A simulation study is conducted to examine the performance of the estimation and evaluation methods in recovering the true parameters and selecting the true model. Finally, an empirical study is presented to illustrate the applicability of the model to detect learning effects using real data.

The polychoric correlation is a popular measure of association for ordinal data. It estimates a latent correlation, i.e., the correlation of a latent vector. This vector is assumed to be bivariate normal, an assumption that cannot always be justified. When bivariate normality does not hold, the polychoric correlation will not necessarily approximate the true latent correlation, even when the observed variables have many categories. We calculate the sets of possible values of the latent correlation when latent bivariate normality is not necessarily true, but at least the latent marginals are known. The resulting sets are called partial identification sets, and are shown to shrink to the true latent correlation as the number of categories increase. Moreover, we investigate partial identification under the additional assumption that the latent copula is symmetric, and calculate the partial identification set when one variable is ordinal and another is continuous. We show that little can be said about latent correlations, unless we have impractically many categories or we know a great deal about the distribution of the latent vector. An open-source R package is available for applying our results.

Big cats are of conservation concern throughout their range, and genetic tools are often employed to study them for various purposes. However, there are several difficulties in using genetic tools for big cat conservation that could be resolved by modern methods of DNA sequencing. Recent reports of the sighting of a putative Javan tiger Panthera tigris sondaica in West Java, Indonesia, highlight some of the difficulties of studying the genetics of big cats. We reanalysed the data of the original reports and found that the conclusions were drawn based on incorrect copies of the genes. Specifically, the nuclear copy of the mitochondrial gene was analysed with the mitochondrial sequence, leading to discordance in the results. However, re-sequencing of the remaining DNA confirms that the sighting could have been that of a tiger, but the subspecies cannot be confirmed. This work highlights the urgency of developing high-throughput sequencing infrastructure in the tropics and the need for reliable databases for the study of big cats.

In this rejoinder, we discuss substantive and methodological validity issues of large-scale assessments of trends in student achievement, commenting on the discussion paper by Van den Heuvel-Panhuizen, Robitzsch, Treffers, and Köller (2009). We focus on methodological challenges in deciding what to measure, how to measure it, and how to foster stability. Next, we discuss what to do with trends that are found. Finally, we reflect on how the research findings were received.

The intersections of Islam, Christianity, and Judaism are well known, but scholars tend to treat each as largely independent from the others, at least after some initial point of origin. We seek rather to emphasize their ongoing inter-dependence and demonstrate the implications for both historical and theological work. Christianity, Islam, and Judaism have continuously formed, re-formed, and transformed themselves by interacting with or thinking about one another. That co-production, in all the ambivalence it entails, has shaped not only the rituals and teachings of these traditions but also some of our most enduring forms of prejudice as well as the conceptual tools with which we undertake the study of these religions. After first offering a definition of religious co-production, we then give an example, in the monk Sergius-Baḥīrā, of what historical and theological insights a methodology of co-production can yield. Finally, we offer an exploration of the critical and constructive potentials of that insight, gesturing toward the possibility of both a history and a theology of co-production.

Leprocaulon inexpectatum is described here as a new lichen species and the fourth member of the genus known from Europe. It is characterized by the crustose-granulose, blue-grey to bluish green thallus composed of ±discrete, soredia-like granules c. 45–70 μm in diameter, and the production of usnic acid and zeorin. Based on ITS rDNA, the lichen is closely related to the saxicolous American species L. beechingii. The new species is reported here from numerous localities in north-western Italy. It occurs on the bark of oaks, chestnut, and black locust in open deciduous forests, often in floodplain ecosystems. Our investigation of its photobiont identity using ITS, 18S and rbcL demonstrated that its symbiotic partner represents an undescribed species within the genus Symbiochloris (Trebouxiophyceae). We provide an identification key to sterile crustose sorediate lichens containing usnic acid and zeorin found in Europe.

The likelihood ratio test (LRT) is widely used for comparing the relative fit of nested latent variable models. Following Wilks’ theorem, the LRT is conducted by comparing the LRT statistic with its asymptotic distribution under the restricted model, a χ2 distribution with degrees of freedom equal to the difference in the number of free parameters between the two nested models under comparison. For models with latent variables such as factor analysis, structural equation models and random effects models, however, it is often found that the χ2 approximation does not hold. In this note, we show how the regularity conditions of Wilks’ theorem may be violated using three examples of models with latent variables. In addition, a more general theory for LRT is given that provides the correct asymptotic theory for these LRTs. This general theory was first established in Chernoff (J R Stat Soc Ser B (Methodol) 45:404–413, 1954) and discussed in both van der Vaart (Asymptotic statistics, Cambridge, Cambridge University Press, 2000) and Drton (Ann Stat 37:979–1012, 2009), but it does not seem to have received enough attention. We illustrate this general theory with the three examples.

In this paper, I examine the Oratio habita in enarratione Lucii Apuleii, the written version of a speech pronounced by the Bolognese master Filippo Beroaldo the Elder. An inaugural speech for his commentary on Apuleius’s Golden Ass, this text was printed in November 1500 and has, until now, remained unedited and untranslated. In the introduction, I argue that Beroaldo, by imitating Aulus Gellius in his speech, reproduces a distinctive trait of Apuleius, the embodiment of one’s model, thus reducing the distance that separates him from Apuleius. This technique, I contend, reflects a very close relationship with the text and its author (Apuleius), who is not only read and commented on but also ‘lived’ and embodied. In the commentary, I highlight the complex structure of Beroaldo’s speech, analyzing the rich intertextual relationship that he entertains with the ancient authors.

When the future Brazilian independence hero José Bonifácio de Andrada e Silva turned 20 years old in 1783, he left Brazil to study at the University of Coimbra, as his generation’s privileged sons did. Upon graduating, he embarked on a lengthy government-sponsored trip to study mineralogy across Europe. From 1790, he immersed himself in the latest scientific doctrines and mining techniques in France, Denmark, Sweden, northern Italy, and most importantly German territories. After 10 years of traveling, he began teaching at Coimbra and Portugal’s Mint and then took over a new Intendancy of Mines tailor-made for his new qualifications. He returned to Brazil only in 1819 after 36 years away.

The sum score on a psychological test is, and should continue to be, a tool central in psychometric practice. This position runs counter to several psychometricians’ belief that the sum score represents a pre-scientific conception that must be abandoned from psychometrics in favor of latent variables. First, we reiterate that the sum score stochastically orders the latent variable in a wide variety of much-used item response models. In fact, item response theory provides a mathematically based justification for the ordinal use of the sum score. Second, because discussions about the sum score often involve its reliability and estimation methods as well, we show that, based on very general assumptions, classical test theory provides a family of lower bounds several of which are close to the true reliability under reasonable conditions. Finally, we argue that eventually sum scores derive their value from the degree to which they enable predicting practically relevant events and behaviors. None of our discussion is meant to discredit modern measurement models; they have their own merits unattainable for classical test theory, but the latter model provides impressive contributions to psychometrics based on very few assumptions that seem to have become obscured in the past few decades. Their generality and practical usefulness add to the accomplishments of more recent approaches.

The measurement of latent traits and investigation of relations between these and a potentially large set of explaining variables is typical in psychology, economics, and the social sciences. Corresponding analysis often relies on surveyed data from large-scale studies involving hierarchical structures and missing values in the set of considered covariates. This paper proposes a Bayesian estimation approach based on the device of data augmentation that addresses the handling of missing values in multilevel latent regression models. Population heterogeneity is modeled via multiple groups enriched with random intercepts. Bayesian estimation is implemented in terms of a Markov chain Monte Carlo sampling approach. To handle missing values, the sampling scheme is augmented to incorporate sampling from the full conditional distributions of missing values. We suggest to model the full conditional distributions of missing values in terms of non-parametric classification and regression trees. This offers the possibility to consider information from latent quantities functioning as sufficient statistics. A simulation study reveals that this Bayesian approach provides valid inference and outperforms complete cases analysis and multiple imputation in terms of statistical efficiency and computation time involved. An empirical illustration using data on mathematical competencies demonstrates the usefulness of the suggested approach.

In this rejoinder to McNeish (2024) and Mislevy (2024), who both responded to our focus article on the merits of the simple sum score (Sijtsma et al., 2024), we address several issues. Psychometrics education and in particular psychometricians’ outreach may help researchers to use IRT models as a precursor for the responsible use of the latent variable score and the sum score. Different methods used for test and questionnaire construction often do not produce highly different results, and when they do, this may be due to an unarticulated attribute theory generating noisy data. The sum score and transformations thereof, such as normalized test scores and percentiles, may help test practitioners and their clients to better communicate results. Latent variables prove important in more advanced applications such as equating and adaptive testing where they serve as technical tools rather than communication devices. Decisions based on test results are often binary or use a rather coarse ordering of scale levels, hence, do not require a high level of granularity (but nevertheless need to be precise). A gap exists between psychology and psychometrics which is growing deeper and wider, and that needs to be bridged. Psychology and psychometrics must work together to attain this goal.

In this article we present an exploratory tool for extracting systematic patterns from multivariate data. The technique, hierarchical segmentation (HS), can be used to group multivariate time series into segments with similar discrete-state recurrence patterns and it is not restricted by the stationarity assumption. We use a simulation study to describe the steps and properties of HS. We then use empirical data on daily affect from one couple to illustrate the use of HS for describing the affective dynamics of the dyad. First, we partition the data into three periods that represent different affective states and show different dynamics between both individuals’ affect. We then examine the synchrony between both individuals’ affective states and identify different patterns of coherence across the periods. Finally, we discuss the possibilities of using results from HS to construct confirmatory dynamic models with multiple change points or regime-specific dynamics.

What undergirds the association between religious and political conservatism and “group-serving pronatalism”; that is, support for childbearing to advance social or political goals rather than for personal fulfillment? Although recent research suggests that Christian nationalism—reflecting a desire to formally privilege conservative Christian values and identity—strongly accounts for the link, previous studies have not inquired about specific group-serving reasons to have children. Analyses of nationally representative data affirm Christian nationalism (measured in two ways) as the strongest predictor of support for group-serving pronatalism; specifically, support for having children to reverse the nation’s declining fertility, perpetuate one’s religious or racial heritage, and secure influence for one’s political group. These associations are weakly or inconsistently moderated by indicators of traditionalism, conservatism, and race. Findings affirm support for having children to advance national, religious, racial, or political goals corresponds strongly with a desire to privilege a Christian national identity and social order.

Producing and disseminating knowledge is core university business and a collaborative, global activity engaging multiple stakeholders including universities, researchers, governments, Indigenous communities, commercial bodies and the public. While ownership of university inventions attracts scholarly and policy attention, effective management of copyright in research outputs is also necessary to maximise the benefits of publicly funded research, but often neglected. This article explains current dynamics in academic publishing and research ownership. It seeks to explain the complex interface of copyright law, university policies, academic customary practices, Enterprise Bargaining Agreements (EBA), research funder mandates and policies, the guidelines and policies that pertain to Indigenous research, and publishing contracts. The article concludes with proposals for copyright management to maximise opportunities for greater public benefit from Australian research.

We show that separable nonlinear least squares (SNLLS) estimation is applicable to all linear structural equation models (SEMs) that can be specified in RAM notation. SNLLS is an estimation technique that has successfully been applied to a wide range of models, for example neural networks and dynamic systems, often leading to improvements in convergence and computation time. It is applicable to models of a special form, where a subset of parameters enters the objective linearly. Recently, Kreiberg et al. (Struct Equ Model Multidiscip J 28(5):725–739, 2021. https://doi.org/10.1080/10705511.2020.1835484) have shown that this is also the case for factor analysis models. We generalize this result to all linear SEMs. To that end, we show that undirected effects (variances and covariances) and mean parameters enter the objective linearly, and therefore, in the least squares estimation of structural equation models, only the directed effects have to be obtained iteratively. For model classes without unknown directed effects, SNLLS can be used to analytically compute least squares estimates. To provide deeper insight into the nature of this result, we employ trek rules that link graphical representations of structural equation models to their covariance parametrization. We further give an efficient expression for the gradient, which is crucial to make a fast implementation possible. Results from our simulation indicate that SNLLS leads to improved convergence rates and a reduced number of iterations.