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Comparative public health research makes wide use of self-report instruments. For example, research identifying and explaining health disparities across demographic strata may seek to understand the health effects of patient attitudes or private behaviors. Such personal attributes are difficult or impossible to observe directly and are often best measured by self-reports. Defensible use of self-reports in quantitative comparative research requires not only that the measured constructs have the same meaning across groups, but also that group comparisons of sample estimates (eg, means and variances) reflect true group differences and are not contaminated by group-specific attributes that are unrelated to the construct of interest. Evidence for these desirable properties of measurement instruments can be established within the confirmatory factor analysis (CFA) framework; a nested hierarchy of hypotheses is tested that addresses the cross-group invariance of the instrument's psychometric properties. By name, these hypotheses include configurai, metric (or pattern), strong (or scalar), and strict factorial invariance. The CFA model and each of these hypotheses are described in nontechnical language. A worked example and technical appendices are included.

T-welded joints are commonly seen in various industrial assemblies. An effort is made to check the applicability of friction stir welding for producing T-joints made of AA6063-T6 using a developed fixture. Quality T-joints were produced free from any surface defects. The effects of three parameters, such as the speed of rotation of the tool, axial force, and travel speed were analyzed. Correspondingly, mechanical characteristics such as tensile strength, hardness in three zones (thermal heat affected zone, heat affected zone, and nugget zone) and temperature distribution were measured. The full factorial analysis was performed with various combinations of parameters generated using factorial design and responses. Evident changes in the strength, hardness, and temperature profile were noticed for each combination of parameters. The three main parameters were significant in every response with p-values less than 0.05, indicating their importance in the friction stir welding process. Mathematical models developed for investigated responses were satisfactory with high R-sq and least percentage error.

Background: Analysis of subgroups such as different ethnic, language, or education groups selected from among a parent population is common in health disparities research. One goal of such analyses is to examine measurement equivalence, which includes both qualitative review of the meaning of items as well as quantitative examination of different levels of factorial invariance and differential item functioning. Objectives: The purpose of this essay is to review the definitions and assumptions associated with factorial invariance, placing this formulation in the context of bias, fairness, and equity. The connection between the concepts of factorial invariance and item bias (differential item functioning) using a variant of item response theory is discussed. The situations under which different forms of invariance (weak, strong, and strict) are required are discussed. Methods: Establishing factorial invariance involves a hierarchy of levels that include tests of weak, strong, and strict invariance. Pattern (metric or weak) factorial invariance implies that the regression slopes are invariant across groups. Pattern invariance requires only invariant factor loadings. Strong factorial invariance implies that the conditional expectation of the response, given the common and specific factors, is invariant across groups. Strong factorial invariance requires that specific factor means (represented as invariant intercepts) also be identical across groups. Strict factorial invariance implies that, in addition, the conditional variance of the response, given the common and specific factors, is invariant across groups. Strict factorial invariance requires that, in addition to equal factor loadings and intercepts, the residual (specific factor plus error variable) variances are equivalent across groups. The concept of measurement invariance that is most closely aligned to that of item response theory considers the latent variable as a common factor measured by manifest variables; the specific factors can be characterized as nuisance variables. Conclusions: Invariance of factor loadings across studied groups is required for valid comparisons of scale score or latent variable means. Strong and strict invariance may be less important in the context of basic research in which group differences in specific factors are indicative of individual differences that are important for scientific exploration. However, for most applications in which the aim is to ensure fairness and equity, strict factorial invariance is required. Health disparities research often focuses on self-reported clinical outcomes such as quality of life that are not observed directly. Latent variable models such as factor analyses are central to establishing valid assessment of such outcomes.

How can we extract hidden relations from a tensor and a matrix data simultaneously in a fast, accurate, and scalable way? Coupled matrix-tensor factorization (CMTF) is an important tool for this purpose. Designing an accurate and efficient CMTF method has become more crucial as the size and dimension of real-world data are growing explosively. However, existing methods for CMTF suffer from lack of accuracy, slow running time, and limited scalability. In this paper, we propose S.sup.3 CMTF, a fast, accurate, and scalable CMTF method. In contrast to previous methods which do not handle large sparse tensors and are not parallelizable, S.sup.3 CMTF provides parallel sparse CMTF by carefully deriving gradient update rules. S.sup.3 CMTF asynchronously updates partial gradients without expensive locking. We show that our method is guaranteed to converge to a quality solution theoretically and empirically. S.sup.3 CMTF further boosts the performance by carefully storing intermediate computation and reusing them. We theoretically and empirically show that S.sup.3 CMTF is the fastest, outperforming existing methods. Experimental results show that S.sup.3 CMTF is up to 930x faster than existing methods while providing the best accuracy. S.sup.3 CMTF shows linear scalability on the number of data entries and the number of cores. In addition, we apply S.sup.3 CMTF to Yelp rating tensor data coupled with 3 additional matrices to discover interesting patterns.

We examine how the seemingly arbitrary way a prompt is posed, which we term “prompt architecture,” influences responses provided by large language models (LLMs). Five large-scale, full-factorial experiments performing standard (zero-shot) similarity evaluation tasks using GPT-3, GPT-4, and Llama 3.1 document how several features of prompt architecture (order, label, framing, and justification) interact to produce methodological artifacts, a form of statistical bias. We find robust evidence that these four elements unduly affect responses across all models, and although we observe differences between GPT-3 and GPT-4, the changes are not necessarily for the better. Specifically, LLMs demonstrate both response-order bias and label bias, and framing and justification moderate these biases. We then test different strategies intended to reduce methodological artifacts. Specifying to the LLM that the order and labels of items have been randomized does not alleviate either response-order or label bias, and the use of uncommon labels reduces (but does not eliminate) label bias but exacerbates response-order bias in GPT-4 (and does not reduce either bias in Llama 3.1). By contrast, aggregating across prompts generated using a full factorial design eliminates response-order and label bias. Overall, these findings highlight the inherent fallibility of any individual prompt when using LLMs, as any prompt contains characteristics that may subtly interact with a multitude of hidden associations embedded in rich language data.

The paper describes the factorial design of the experiment with three input factors that change on two levels. For given values of the input parameters, it is shown how to obtain a variance analysis table and which factors and interactions between factors are significant. The example was done in the software intended for the design of the experiment and in the software R. It is shown how to use the software R to arrive at the final solution of the given example.

This paper aims to investigate the mechanical properties of specimens printed by 3D open-source printers. It discusses the effect of five factors (part orientation, layer height, extrusion width, nozzle diameter, and filament temperature) on the ultimate tensile strength and the impact toughness of the 3D-printed samples. A 2 5–1 resolution V fractional factorial experiment was run with the 16 samples printed on a Prusa I3 MK3S in PLA. Tensile strength and impact toughness were tested using Instron 3367 and Tinius Olsen 66 testers, respectively. In analyzing the data, a normal probability plot of the effects complimented with ANOVA (Analysis Of Variance) revealed that, for both responses, only part orientation was statistically significant at p  = 0 . 05. Regression equations were used to predict the ultimate tensile strength and the impact toughness as a function of the part orientation. Both the toughness response and the tensile strength response are maximized with horizontal part orientation. Verification experiments have been implemented to validate the adopted regression equations’ predictions under different circumstances, and the results of those experiments appear to confirm the model.

This study analyses future changes in temperature and precipitation over the Yangtze River Basin (YRB) throughout the twenty-first century by developing a regional factorial cluster analysis (RFCA) model on the basis of bias correction and spatial disaggregation (BCSD), cluster analysis and multilevel factorial analysis (MFA). In detail, BCSD is presented to downscale climate variables (i.e., daily mean temperature, maximum temperature, and total precipitation) of multiple global climate models (GCMs) under four shared socioeconomic pathways (SSPs). Evaluations shows BCSD can reasonably reproduce high spatial resolution climate predictions, especially temperature variables with great spatial correlation coefficients (i.e., larger than 0.9). Future climate changes are quantified by the Standard Euclidean Distance (SED), indicating climate change over YRB would spatially and seasonally undergo uneven distribution. Temperature changes have an overall south-to-north trend, with high variations in winter and summer. Precipitation changes over the upper reaches in winter and summer have larger variations than lower ones. Two hotspots are clustered with SED stabilities greater than 1.8, distributed in the Tibetan Plateau and the Yunnan–Guizhou Plateau, respectively. The effects of uncertainties (i.e., periods, GCMs and SSPs) and their interactions on predictions are analyzed through MFA. The individual effects of SSPs factor and its interactions with periods are worthy of consideration. The largest variation is observed under SSP585, with a total SED of 1.050; the smallest variation is observed under SSP370, with a total SED of 1.034. The interaction of SSPs and periods leads to a relatively stable interdecadal total SED under SSP126, which remains around 1.040.

To move society toward an AIDS-free generation, behavioral interventions for prevention and treatment of HIV/AIDS must be not only effective, but also cost-effective, efficient, and readily scalable. The purpose of this article is to introduce to the HIV/AIDS research community the multiphase optimization strategy (MOST), a new methodological framework inspired by engineering principles and designed to develop behavioral interventions that have these important characteristics. Many behavioral interventions comprise multiple components. In MOST, randomized experimentation is conducted to assess the individual performance of each intervention component, and whether its presence/absence/setting has an impact on the performance of other components. This information is used to engineer an intervention that meets a specific optimization criterion, defined a priori in terms of effectiveness, cost, cost-effectiveness, and/or scalability. MOST will enable intervention science to develop a coherent knowledge base about what works and does not work. Ultimately this will improve behavioral interventions systematically and incrementally.