loading matrix
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Biochar, a carbon-rich material obtained by pyrolysis of organic wastes, is an attractive matrix for loading nutrients and producing enhanced efficiency fertilizers. In this study, poultry litter (PL) was enriched with phosphoric acid (H3PO4) and MgO to produce a biochar-based fertilizer (PLB), which was loaded with urea in a 4:5 ratio (PLB:urea, w/w) to generate a 15–15% N–P slow-release fertilizer (PLB–N) to be used in a single application to soil. A greenhouse experiment was carried out in which a common bean was cultivated followed by maize to evaluate the agronomic efficiency and the residual effect of fertilization with PLB–N in Ultisol. Six treatments were tested, including four doses of N (100, 150, 200, and 250 mg kg−1) via PLB–N in a single application, a control with triple superphosphate (TSP—applied once) and urea (split three times), and a control without N-P fertilization. The greatest effect of PLB–N was the residual effect of fertilization, in which maize showed a linear response to the N doses applied via PLB–N but showed no response to conventional TSP + urea fertilization. Biochar has the potential as a loading matrix to preserve N availability and increase residual effects and N-use efficiency by plants.

Accelerated testing (AT) is an effective testing method for evaluating the reliability of highly reliable products. In many applications, such products are often subject to multiple stresses in actual working environments. Then, how to design the load spectra for multi-stress AT becomes a critical issue. In this paper, a new load spectra design method is proposed to overcome this challenge. Considering the properties of multiple stresses, a novel multi-stress loading matrix (MSLM) is modified to fully describe the load spectra in actual working environments and to generate the corresponding load spectra for AT. For illustration purposes, an inverse Gaussian (IG) process incorporating life-stress relationships is adopted to model product degradation under multiple stresses. A case study on a type of hydraulic piston pump is provided to demonstrate the use of the proposed method in guiding the load spectra design for multi-stress AT.

Compositional items – a form of forced-choice items – require respondents to allocate a fixed total number of points to a set of statements. To describe the responses to these items, the Thurstonian item response theory (IRT) model was developed. Despite its prominence, the model requires that items composed of parts of statements result in a factor loading matrix with full rank. Without this requirement, the model cannot be identified, and the latent trait estimates would be seriously biased. Besides, the estimation of the Thurstonian IRT model often results in convergence problems. To address these issues, this study developed a new version of the Thurstonian IRT model for analyzing compositional items – the lognormal ipsative model (LIM) – that would be sufficient for tests using items with all statements positively phrased and with equal factor loadings. We developed an online value test following Schwartz’s values theory using compositional items and collected response data from a sample size of N = 512 participants with ages from 13 to 51 years. The results showed that our LIM had an acceptable fit to the data, and that the reliabilities exceeded 0.85. A simulation study resulted in good parameter recovery, high convergence rate, and the sufficient precision of estimation in the various conditions of covariance matrices between traits, test lengths and sample sizes. Overall, our results indicate that the proposed model can overcome the problems of the Thurstonian IRT model when all statements are positively phrased and factor loadings are similar.

Diagonal loading technology is widely used in array antenna beamforming because of its simple method, low computational complexity and the ability to improve the robustness of beamformer. On this basis, this paper proposes a robust adaptive beamforming method based on automatic variable loading technology. The automatic variable loading matrix (AVLM) of the method is composed of two parts. The non-uniform loading matrix dominants when the input signal-to-noise ratio (SNR) is small, effectively control the influence of noise disturbance without affecting the ability of array antenna to suppress interference. The variable diagonal loading matrix dominants when the input SNR is high to improve the output performance of array antenna. Simulated results show that compared to other methods, the proposed method has better output performance for both low and high input SNR cases.

Discovering causal structures among latent factors from observed data is a particularly challenging problem. Despite some efforts for this problem, existing methods focus on the single-domain data only. In this paper, we propose Multi-Domain Linear Non-Gaussian Acyclic Models for LAtent Factors (MD-LiNA), where the causal structure among latent factors of interest is shared for all domains, and we provide its identification results. The model enriches the causal representation for multi-domain data. We propose an integrated two-phase algorithm to estimate the model. In particular, we first locate the latent factors and estimate the factor loading matrix. Then to uncover the causal structure among shared latent factors of interest, we derive a score function based on the characterization of independence relations between external influences and the dependence relations between multi-domain latent factors and latent factors of interest. We show that the proposed method provides locally consistent estimators. Experimental results on both synthetic and real-world data demonstrate the efficacy and robustness of our approach.

How strongly are foreign exchange markets linked in terms of their similarities in long-run fluctuations? Are they cointegrating? To analyze such “comovements,” we present a time-varying cointegration model for the foreign exchange rates of the currencies of Canada, Japan, and the UK vis-à-vis the U.S. dollar from May 1990 through July 2015. Unlike previous studies, we allow the loading matrix in the vector error-correction (VEC) model to be varying over time. Because the loading matrix in the VEC model is associated with the speed at which deviations from the long-run relationship disappear, we propose a new degree of market comovement based on the time-varying loading matrix to measure the strength or robustness of the long-run relationship over time. Since exchange rates are determined by macrovariables, cointegration among exchange rates implies these variables share common stochastic trends. Therefore, the proposed degree measures the degree of market comovement. Our main finding is that the market comovement has become stronger over the past quarter-century, but at a decreasing rate with two major turning points: one in 1995 and the other one in 2008.

Recent research has demonstrated that the network measure node strength or sum of a node’s connections is roughly equivalent to confirmatory factor analysis (CFA) loadings. A key finding of this research is that node strength represents a combination of different latent causes. In the present research, we sought to circumvent this issue by formulating a network equivalent of factor loadings, which we call network loadings. In two simulations, we evaluated whether these network loadings could effectively (1) separate the effects of multiple latent causes and (2) estimate the simulated factor loading matrix of factor models. Our findings suggest that the network loadings can effectively do both. In addition, we leveraged the second simulation to derive effect size guidelines for network loadings. In a third simulation, we evaluated the similarities and differences between factor and network loadings when the data were generated from random, factor, and network models. We found sufficient differences between the loadings, which allowed us to develop an algorithm to predict the data generating model called the Loadings Comparison Test (LCT). The LCT had high sensitivity and specificity when predicting the data generating model. In sum, our results suggest that network loadings can provide similar information to factor loadings when the data are generated from a factor model and therefore can be used in a similar way (e.g., item selection, measurement invariance, factor scores).