Approximate Invariance Research Articles

Minimax A‐, c‐, and I‐optimal regression designs for models with heteroscedastic errors

It is well known that it is difficult to construct minimax optimal designs. Furthermore, since in practice we never know the true error variance, it is important to allow small deviations and construct robust optimal designs. We investigate a class of minimax optimal regression designs for models with heteroscedastic errors that are robust against possible misspecification of the error variance. Commonly used A‐, c‐, and I‐optimality criteria are included in this class of minimax optimal designs. Several theoretical results are obtained, including a necessary condition and a reflection symmetry for these minimax optimal designs. In this article, we focus mainly on linear models and assume that an approximate error variance function is available. However, we also briefly discuss how the methodology works for nonlinear models. We then propose an effective algorithm to solve challenging nonconvex optimization problems to find minimax designs on discrete design spaces. Examples are given to illustrate minimax optimal designs and their properties.

An examination of model fit and measurement invariance of general mental ability and personality measures used in the multilingual context of the Swiss Armed Forces: A Bayesian structural equation modeling approach

ABSTRACT Measurement invariance of psychological test batteries is an essential quality criterion when the test batteries are administered in different cultural and language contexts. The purpose of this study was to examine to what extent measurement model fit and measurement invariance across the two largest language groups in Switzerland (i.e., German and French speakers) can be assumed for selected general mental ability and personality tests used in the Swiss Armed Forces’ cadre selection process. For the model fit and invariance testing, we used Bayesian structural equation modeling (BSEM). Because the sizes of the language group samples were unbalanced, we reran the invariance testing with the subsampling procedure as a robustness check. The results showed that at least partial approximate scalar invariance can be assumed for the constructs. However, comparisons in the full sample and subsamples also showed that certain test items function differently across the language groups. The results are discussed regarding the three following issues: First, we critically discuss the applied criterion and alternative effect size measures for assessing the practical importance of non-invariances. Second, we highlight potential remedies and further testing options, that can be applied, once certain items have been detected to function differently. Third, we discuss alternative modeling and invariance testing approaches to BSEM and outline future research avenues.

Approximate Mei Symmetries and Invariants of the Hamiltonian

It is known that corresponding to each Noether symmetry there is a conserved quantity. Another class of symmetries that corresponds to conserved quantities is the class of Mei symmetries. However, the two sets of symmetries may give different conserved quantities. In this paper, a procedure of finding approximate Mei symmetries and invariants of the perturbed/approximate Hamiltonian is presented that can be used in different fields of study where approximate Hamiltonians are under consideration. The results are presented in the form of theorems along with their proofs. A simple example of mechanics is considered to elaborate the method of finding these symmetries and the related Mei invariants. At the end, a comparison of approximate Mei symmetries and approximate Noether symmetries is also given. The comparison shows that there is only one common symmetry in both sets of symmetries. Hence, rest of the symmetries in the two sets correspond to two different sets of conserved quantities.

Lifting dual tree complex wavelets transform

We describe the lifting dual tree complex wavelet transform (LDTCWT), a type of lifting wavelets remodeling that produce complex coefficients by employing a dual tree of lifting wavelets filters to get its real part and imaginary part. Permits the remodel to produce approximate shift invariance, directionally selective filters and reduces the computation time (properties lacking within the classical wavelets transform). We describe a way to estimate the accuracy of this approximation and style appropriate filters to attain this. These benefits are often exploited among applications like denoising, segmentation, image fusion and compression. The results of applications shrinkage denoising demonstrate objective and subjective enhancements over the dual tree complex wavelet transform (DTCWT). The results of the shrinkage denoising example application indicate empirical and subjective enhancements over the DTCWT. The new transform with the DTCWT provide a trade-off between denoising computational competence of performance, and memory necessities. We tend to use the PSNR (peak signal to noise ratio) alongside the structural similarity index measure (SSIM) and the SSIM map to estimate denoised image quality.

Rigorous derivation of the Whitham equations from the water waves equations in the shallow water regime

We derive the Whitham equations from the water waves equations in the shallow water regime using two different methods, thus obtaining a direct and rigorous link between these two models. The first one is based on the construction of approximate Riemann invariants for a Whitham–Boussinesq system and is adapted to unidirectional waves. The second one is based on a generalisation of Birkhoff’s normal form algorithm for almost smooth Hamiltonians and is adapted to bidirectional propagation. In both cases we clarify the improved accuracy on the fully dispersive Whitham model with respect to the long wave Korteweg–de Vries approximation.

Longitudinal measurement invariance in urbanization index of Chinese communities across 2000 and 2015: a Bayesian approximate measurement invariance approach

BackgroundThe Urbanicity Scale was developed based on the China Health and Nutrition Survey (CHNS) to measure the urbanization index of communities according to 12 components. The present study was designed to systematically investigate the factorial validity, reliability, and longitudinal measurement invariance (LMI) of the Urbanicity Scale.MethodsSix waves of CHNS data from 2000 to 2015 were adopted. The factor structure and reliability of the Urbanicity Scale for 301 communities were examined using Bayesian exploratory factor analysis. Metric and scalar LMIs were evaluated using both the conventional exact and a novel approximate LMI approach via Bayesian structural equation modeling across various timeframes.ResultsThe findings verified the one-factor structure for the Urbanicity Scale, with adequate reliability. LMI was established for the Urbanicity Scale only over a shorter timeframe from 2006 to 2009 but not over a longer timeframe from 2000 to 2015. Partial LMI was found in the factor loadings and item intercepts for the Urbanicity Scale over the 2004 to 2011 period.ConclusionInterpretation of the temporal change in urbanicity was supported only for a shorter (2006 to 2009) but not a longer timeframe (2000 to 2015). Adjustments addressing the partial non-invariance of the measurement parameters are needed for the analysis of temporal changes in urbanicity between 2004 and 2011.

Small-scale shear: Peeling off diffuse subhalos with gravitational waves

Subhalos at subgalactic scales ($M\lesssim 10^7 M_\odot$ or $k\gtrsim 10^3 \,{\rm Mpc}^{-1}$) are pristine test beds of dark matter (DM). However, they are too small, diffuse and dark to be visible, in any existing observations. In this paper, we develop a complete formalism for weak and strong diffractive lensing, which can be used to probe such subhalos with chirping gravitational waves (GWs). Also, we show that Navarro-Frenk-White(NFW) subhalos in this mass range can indeed be detected individually, albeit at a rate of ${\cal O}(10)$ or less per year at BBO and others limited by small merger rates and large required SNR $\gtrsim 1/\gamma(r_0) \sim 10^3$. It becomes possible as NFW scale radii $r_0$ are of the right size comparable to the GW Fresnel length $r_F$, and unlike all existing probes, their lensing is more sensitive to lighter subhalos. Remarkably, our formalism further reveals that the frequency dependence of weak lensing (which is actually the detectable effect) is due to shear $\gamma$ at $r_F$. Not only is it consistent with an approximate scaling invariance, but it also offers a new way to measure the mass profile at a successively smaller scale of chirping $r_F \propto f^{-1/2}$. Meanwhile, strong diffraction that produces a blurred Einstein ring has a universal frequency dependence, allowing only detections. These are further demonstrated through semianalytic discussions of power-law profiles. Our developments for a single lens can be generalized and will promote diffractive lensing to a more concrete and promising physics in probing DM and small-scale structures.

The information capacity of adolescent alcohol consumption indicators along a continuum of severity: A cross-national comparison of sixteen Central and Eastern European countries.

Because there is high variability among European countries in prevalence levels of various alcohol consumption measures, the informational value of adolescent's alcohol consumption indicators is uncertain. The present study aimed to examine information capacity and measurement invariance of different alcohol consumption indicators in adolescents from countries of the former Soviet (Eastern) Bloc in Central and Eastern Europe (CEE). Data were collected in 16 CEE countries, as part of the 2013/2014 wave of the Health Behavior in School-aged Children study. Data from adolescents (age 15) who reported having consumed alcohol at least once in their lifetime were analyzed. Four binary items selected for analysis measured the presence or absence of alcohol consumption in the last 30days, lifetime drunkenness, weekly drinking frequency, and binge drinking on a typical occasion. Multiple group confirmatory factor analysis and item response theory analysis were used to examine the data. In most of the included countries, alcohol consumption in the last 30days and lifetime drunkenness were indicative at lower severity levels, while binge drinking and weekly drinking frequency were informative at higher levels of alcohol use severity. A low proportion of the estimated intercepts and factor loadings were noninvariant, which indicated approximate cross-national invariance of these indicators. Adolescent alcohol consumption indicators are informative for different severity levels and enable cross-nationally invariant measurement. However, different indicators suggested the presence of diverging drinking cultures in the CEE regions, with the highest discrimination capacity at the lower and higher ends of the continuum of alcohol use severity.

Measurement Invariance of the SQWLi Instrument Over Time

The SQWLi questionnaire was developed for the long-term measurement of subjectively perceived quality of working life. The aim of this study is to test the instrument's measurement invariance between 2009 and 2019 and determine whether - despite the modifications made to the instrument over the years - the results remain comparable. Data from eight representative surveys of the economically active population in the Czech Republic were analysed (total N = 6909) using the MG CFA method (configural, metric, and scalar invariance) and the alignment method (approximate measurement invariance). The findings from the MG CFA tests for measurement invariance indicate that the SQWLi instrument achieves configural and metric invariance over time but not full scalar invariance. Achieving a partial scalar invariance would be challenging because of the many high modification indices; therefore, an approximate measurement invariance approach, namely the Alignment Method, was applied. The results suggest that comparisons of latent means across all years can be made. Consequently, it is possible to make meaningful comparisons of overall indices of dimensions (batteries) and of more general domains. However, not all the individual items can be compared. The results confirm that the biggest risk of invariance is caused by conceptual changes to items and by substantial or frequent modifications to item wording. Conversely, the results also show that a conceptual change to an entire dimension may not necessarily cause any problem on the general level, and that a disruption of invariance caused by changes to the range of scales used can be rectified by means of their harmonisation ex post.

Longitudinal Measurement Invariance of the PHQ-9 and GAD-7

Intraindividual change over time is commonly used to estimate treatment effectiveness. However, patients may not respond similarly to a scale after treatment, rendering pre-post change an unreliable metric. The current objective was to investigate longitudinal measurement invariance of the Patient Health Questionnaire-9 and Generalized Anxiety Disorder Scale-7 among 4,323 patients completing a partial hospital program. We used confirmatory factor analysis to determine (1) factor structure at pretreatment and posttreatment and (2) longitudinal invariance, accounting for dependent observations, using both classical and approximate measurement invariance approaches. Results indicated a two-factor solution for both scales. Longitudinal invariance was not established for either scale, thus, using raw score differences from the Patient Health Questionnaire-9 and Generalized Anxiety Disorder Scale-7 for measuring symptom change over time may be problematic. The most longitudinally consistent items captured somatic as opposed to affective/cognitive symptoms. We discuss the potential use of these measures for diagnostic screening and between-group comparisons and suggest alternative ways to monitor client progress over time. Limitations included a majority White sample and uniqueness of a partial hospital setting.

A cautionary note on the variance of empirical pair correlation function

Point processes are popular models for data consisting of a random configuration of points, such as positions of trees of a given species in a forest stand, locations of earthquakes' epicentres or positions of proteins in a cell membrane. Pair correlation function is a functional summary characteristic quantifying the interactions between pairs of points of the process at different distances. In practice, kernel estimators of the pair correlation function are mostly used, which require the user to choose the bandwidth of the smoothing kernel. When looking for the optimal bandwidth, higher order terms of the variance of the estimator are often neglected. We present the detailed formulas for the variance and argue that the higher order terms contribute the most to the variance and should not be ignored. Furthermore, we adapt a well‐known variance approximation formula to accommodate the popular translation edge correction factor. We compare the original and the adjusted approximation formula to the exact variance obtained by numerical integration and to the empirical variance obtained from simulated realizations. We conclude that the variance approximations do not perform well and that modern cross‐validation approaches to bandwidth selection should be preferred in practice.

Measurement invariance of the Childhood Autism Rating Scale (CARS) across six countries.

The Childhood Autism Rating Scale (CARS) is a simple and inexpensive tool for Autism spectrum disorder (ASD) assessments, with evidenced psychometric data from different countries. However, it is still unclear whether ASD symptoms are measured the same way across different societies and world regions with this tool, since data on its cross-cultural validity are lacking. This study evaluated the cross-cultural measurement invariance of the CARS among children with ASD from six countries, for whom data were aggregated from previous studies in India (n=101), Jamaica (n=139), Mexico (n=72), Spain (n=99), Turkey (n=150), and the United States of America (n=186). We analyzed the approximate measurement invariance based on Bayesian structural equation modeling. The model did not fit the data and its measurement invariance did not hold, with all items found non-invariant across the countries. Items related to social communication and interaction (i.e., relating to people, imitation, emotional response, and verbal and nonverbal communication) displayed lower levels of cross-country non-invariance compared to items about stereotyped behaviors/sensory sensitivity (i.e., body and object use, adaptation to change, or taste, smell, and touch response). This study found that the CARS may not provide cross-culturally valid ASD assessments. Thus, cross-cultural comparisons with the CARS should consider first which items operate differently across samples of interest, since its cross-cultural measurement non-invariance could be a source of cross-cultural variability in ASD presentations. Additional studies are needed before drawing valid recommendations in relation to the cultural sensitivity of particular items.

Design of Double- and Multi-Bend Achromat Lattices with Large Dynamic Aperture and Approximate Invariants

A numerical method to design nonlinear double- and multi-bend achromat (DBA and MBA) lattices with approximate invariants of motion is investigated. The search for such nonlinear lattices is motivated by Fermilab's Integrable Optics Test Accelerator (IOTA), whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing DBA and MBA lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions $J_x$ and $J_y$ at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread.

The Fusion of Multi-Focus Images Based on the Complex Shearlet Features-Motivated Generative Adversarial Network

The traditional methods for multi-focus image fusion, such as the typical multi-scale geometric analysis theory-based methods, are usually restricted by sparse representation ability and the transferring efficiency of the fusion rules for the captured features. Aiming to integrate the partially focused images into the fully focused image with high quality, the complex shearlet features-motivated generative adversarial network is constructed for multi-focus image fusion in this paper. Different from the popularly used wavelet, contourlet, and shearlet, the complex shearlet provides more flexible multiple scales, anisotropy, and directional sub-bands with the approximate shift invariance. Therefore, the features in complex shearlet domain are more effective. With of help of the generative adversarial network, the whole procedure of multi-focus fusion is modeled to be the process of adversarial learning. Finally, several experiments are implemented and the results prove that the proposed method outperforms the popularly used fusion algorithms in terms of four typical objective metrics and the comparison of visual appearance.

Measurement Invariance of Liberal and Authoritarian Notions of Democracy: Evidence From the World Values Survey and Additional Methodological Considerations

This article offers a gentle introduction to the measurement invariance (MI) literature with a focus on its relevance to comparative political research. It reviews 1) the conceptual foundations of MI; 2) standard procedures of testing for MI in practical applications within the multiple-group confirmatory factor analysis (MGCFA) paradigm; and 3) two novel approaches to MI, Bayesian approximate measurement invariance, and MGCFA alignment optimization, which are especially suitable for dealing with extremely heterogeneous data from large-scale comparative surveys typical for modern political science. It then provides an empirical illustration of the key concepts and methods from the MGCFA-MI literature by applying them to testing for MI of two recently introduced measures of democracy attitudes, so-called liberal and authoritarian notions of democracy, across 60 countries in the sixth round of the World Values Survey. These analyses show that both measures can be considered reliable comparative measures of democratic attitudes, although for different reasons. Finally, this study emphasizes that some survey-based constructs, e.g., authoritarian notions of democracy, do not follow the reflective (correlation-based) logic of construct development. These alternative measures, known as formative measures, do not assume strong correlations between their indicators, for which reason it is inappropriate to test their comparability using the reflective MGCFA approach. Instead, their comparability can be tied to their correlations with theoretically relevant external variables.

Approximate Measurement Invariance of Willingness to Sacrifice for the Environment Across 30 Countries: The Importance of Prior Distributions and Their Visualization.

Nationwide opinions and international attitudes toward climate and environmental change are receiving increasing attention in both scientific and political communities. An often used way to measure these attitudes is by large-scale social surveys. However, the assumption for a valid country comparison, measurement invariance, is often not met, especially when a large number of countries are being compared. This makes a ranking of countries by the mean of a latent variable potentially unstable, and may lead to untrustworthy conclusions. Recently, more liberal approaches to assessing measurement invariance have been proposed, such as the alignment method in combination with Bayesian approximate measurement invariance. However, the effect of prior variances on the assessment procedure and substantive conclusions is often not well understood. In this article, we tested for measurement invariance of the latent variable “willingness to sacrifice for the environment” using Maximum Likelihood Multigroup Confirmatory Factor Analysis and Bayesian approximate measurement invariance, both with and without alignment optimization. For the Bayesian models, we used multiple priors to assess the impact on the rank order stability of countries. The results are visualized in such a way that the effect of different prior variances and models on group means and rankings becomes clear. We show that even when models appear to be a good fit to the data, there might still be an unwanted impact on the rank ordering of countries. From the results, we can conclude that people in Switzerland and South Korea are most motivated to sacrifice for the environment, while people in Latvia are less motivated to sacrifice for the environment.

Stabilization of semi-Markovian jump systems via a quantity limited controller

This paper addresses the stabilization problem of continuous-time semi-Markovian jump systems (s-MJSs), where the quantity of a controller to be designed has a limitation. A principle designing such a controller is proposed based on its stationary probability sequence. Sufficient conditions for the existence of the designed controller are obtained by applying a Lyapunov function approach and presented with LMIs. The controller mentioned above is proved to be a minimal variance approximation of mode-dependent controllers having total modes. More special cases about Markovian switching and without minimal variance approximation are further studied. A practical example is used to demonstrate the effectiveness and superiority of the proposed methods.

Adjusting for partial invariance in latent parameter estimation: Comparing forward specification search and approximate invariance methods.

Measurement invariance is the condition that an instrument measures a target construct in the same way across subgroups, settings, and time. In psychological measurement, usually only partial, but not full, invariance is achieved, which potentially biases subsequent parameter estimations and statistical inferences. Although existing literature shows that a correctly specified partial invariance model can remove such biases, it ignores the model uncertainty in the specification search step: flagging the wrong items may lead to additional bias and variability in subsequent inferences. On the other hand, several new approaches, including Bayesian approximate invariance and alignment optimization methods, have been proposed; these methods use an approximate invariance model to adjust for partial measurement invariance without the need to directly identify noninvariant items. However, there has been limited research on these methods in situations with a small number of groups. In this paper, we conducted three systematic simulation studies to compare five methods for adjusting partial invariance. While specification search performed reasonably well when the proportion of noninvariant parameters was no more than one-third, alignment optimization overall performed best across conditions in terms of efficiency of parameter estimates, confidence interval coverage, and type I error rates. In addition, the Bayesian version of alignment optimization performed best for estimating latent means and variances in small-sample and low-reliability conditions. We thus recommend the use of the alignment optimization methods for adjusting partial invariance when comparing latent constructs across a few groups.

Measurement Invariance of Disorder-Specific and Transdiagnostic Measures of Repetitive Negative Thinking.

Repetitive negative thinking is conceptualized to be a transdiagnostic process linked to the development and maintenance of psychopathology. Prior research distinguishes between disorder-specific exemplars (worry, rumination) and transdiagnostic measures of repetitive negative thinking with differences across disorders reported. However, establishing the measurement invariance of these measures is necessary to support meaningful comparisons across clinical groups. Bayesian structural equation modelling was used to assess the approximate invariance of the Ruminative Response Scale, Penn State Worry Questionnaire, and the Repetitive Thinking Questionnaire across individuals with a principal diagnosis of either depressive disorder, social anxiety disorder, or generalized anxiety disorder. All scales demonstrated approximate measurement invariance across the three disorder groups. The depressive disorder group reported a higher level of rumination than the generalized anxiety disorder group (Δµ = 0.25, 95% Credibility Interval [0.06, 0.45]), with no difference between the generalized anxiety disorder and social anxiety disorder groups. The depressive disorder and generalized anxiety disorder groups did not differ in their levels of trait repetitive negative thinking, but the social anxiety disorder group was markedly lower than the generalized anxiety disorder group (Δµ = -0.21 [-0.37, -0.05]). Similarly, levels of worry did not differ between the generalized anxiety disorder and depressive disorder group but were lower in the social anxiety disorder group than the generalized anxiety disorder group (Δµ = -0.23 [-0.41, -0.06]). The Ruminative Response Scale, Penn State Worry Questionnaire, and Repetitive Thinking Questionnaire are measuring trait repetitive negative thinking in a consistent manner across individuals with a principal diagnosis of depressive disorder, social anxiety disorder, or generalized anxiety disorder. This supports their use in transdiagnostic contexts and indicates that it is appropriate to directly compare the scores on these measures between diagnostic groups.

Probing low-energy Lorentz violation from high-energy modified dispersion in dipolar Bose-Einstein condensates

We theoretically propose an experimentally viable scheme to use an impurity atom in a dipolar Bose-Einstein condensate (BEC), in order to probe analogue low-energy Lorentz violation from the modified dispersion at high energies as suggested by quantum theories of gravity. We show that the density fluctuations in the dipolar BEC possess a Lorentz-violating Bogoliubov spectrum $\omega_\mathbf{k}=c_0|\mathbf{k}|f(c_0|\mathbf{k}|/M_\star)$, with recovery of approximate Lorentz invariance (LI) at energy scales much below $M_\star$. When $f$ is adjusted to dip below unity somewhere, the impurity, analogously dipole coupled to the density fluctuations, experiences analogue drastic Lorentz violation at arbitrarily low energies, reproducing the same responds of Unruh-DeWitt detector to Lorentz-violating quantum fields. Being a fundamentally quantum mechanical device, our quantum fluid platform provides an experimentally realizable test field to verify whether the effective low energy theory can reveal unexpected imprints of the theory's high energy structure, in quantum field theory.