A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

Using compositional data analysis to explore accumulation of sedentary behavior,physical activity and youth health

Purpose:The study aimed to describe youth time-use compositions,focusing on time spent in shorter and longer bouts of sedentary behavior and physical activity(PA),and to examine associations of these time-use compositions with cardiometabolic biomarkers.Methods:Accelerometer and cardiometabolic biomarker data from 2 Australian studies involving youths 7-13 years old were pooled(complete cases with accelerometry and adiposity marker data,n=782).A 9-component time-use composition was formed using compositional data analysis:time in shorter and longer bouts of sedentary behavior;time in shorter and longer bouts of light-,moderate-,or vigorous-intensity PA;and"other time"(i.e.,non-wear/sleep).Shorter and longer bouts of sedentary time were defined as<5 min and>5 min,respectively.Shorter bouts of light-,moderate-,and vigorous-intensity PA were defined as<1 min;longer bouts were defined as≥1 min.Regression models examined associations between overall time-use composition and cardiometabolic biomarkers.Then,associations were derived between ratios of longer activity patterns relative to shorter activity patterns,and of each intensity level relative to the other intensity levels and"other time",and cardiometabolic biomarkers.Results:Confounder-adjusted models showed that the overall time-use composition was associated with adiposity,blood pressure,lipids,and the summary score.Specifically,more time in longer bouts of light-intensity PA relative to shorter bouts of light-intensity PA was significantly associated with greater body mass index z-score(zBMI)(β=1.79;SE=0.68)and waist circumference(β=18.35,SE=4.78).When each activity intensity was considered relative to all higher intensities and"other time",more time in light-and vigorous-intensity PA,and less time in sedentary behavior and moderate-intensity PA,were associated with lower waist circumference.Conclusion:Accumulating PA,particularly light-intensity PA,in frequent short bursts may be more beneficial for limiting adiposity compared to accumulating the same amount of PA at these intensities in longer bouts.

Data processing for the Active Particle-induced X-ray Spectrometer and initial scientific results from Chang'e-3 mission

The Active Particle-induced X-ray Spectrometer （APXS） is an important payload mounted on the Yutu rover, which is part of the Chang＇e-3 mission. The sci- entific objective of APXS is to perform in-situ analysis of the chemical composition of lunar soil and rock samples. The radioactive sources, 55Fe and 109Cd, decay and produce a-particles and X-rays. When X-rays and a-particles interact with atoms in the surface material, they knock electrons out of their orbits, which release energy by emitting X-rays that can be measured by a silicon drift detector （SDD）. The elements and their concentrations can be determined by analyzing their peak energies and in- tensities. APXS has analyzed both the calibration target and lunar soil once during the first lunar day and again during the second lunar day. The total detection time lasted about 266 min and more than 2000 frames of data records have been acquired. APXS has three operating modes： calibration mode, distance sensing mode and detection mode. In detection mode, work distance can be calculated from the X-ray counting rate collected by SDD. Correction for the effect of temperature has been performed to convert the channel number for each spectrum to X-ray energy. Dead time correction is used to eliminate the systematic error in quantifying the activity of an X-ray pulse in a sample and derive the real count rate. We report APXS data and initial results during the first and second lunar days for the Yutu rover. In this study, we analyze the data from the calibration target and lunar soil on the first lunar day. Seven major elements, including Mg, A1, Si, K, Ca, Ti and Fe, have been identified. Comparing the peak areas and ratios of calibration basalt and lunar soil the landing site was found to be depleted in K, and have lower Mg and A1 but higher Ca, Ti, and Fe. In the future, we will obtain the elemental concentrations of lunar soil at the Chang＇e-3 landing site using APXS data.

Short-Term Impact of Elemental Sulfur on Cranberry Nutrition and Crop Performance

Cranberry (Vaccinium macrocarpon Ait.) is an ammophilous plant grown on acid soils (pH 4.0 - 5.5). Elemental sulfur is commonly applied at a recommended rate of 1120 kg S ha−1 per pH unit to acidify cranberry soils, potentially impacting the plant mineral nutrition. The general recommendation may not fit all conditions encountered in the field. Our objective was to develop an equation to predict the sulfur requirement to reach pHwater of 4.2 to tackle nitrification in acidic cranberry soils varying in initial pH values, and to measure the effect of elemental sulfur on the mineral nutrition and the performance of cranberry crops. A 3-yr experiment was designed to test the effect of elemental sulfur on soil and tissue tests and on berry yield and quality. Four S treatments (0, 250, 500 and 1000 kg S ha−1) were established on three duplicated sites during two consecutive years. We ran soil, foliar tissue, berry tissue tests, and measured berry yield, size, anthocyanin content (TAcy), Brix, and firmness. Nutrients were expressed as centered log ratios to reflect nutrient interactions. Results were analyzed using a mixed model. Soil Ca decreased while soil Mn and S increased significantly (p ≤ 0.05). Sulfur showed no significant effects on nutrient balances in uprights. The S impacted negatively berry B balance, and positively berry Mn and S balances. A linear regression model relating pH change to S dosage and elapsed time (R2 = 0.53) showed that to reach pHwater of 4.2 two years after S application, 250 - 1000 kg S ha−1 could be applied depending on initial soil pH value. The stratification of surface-applied elemental S in the soil profile should be further examined in relation to plant rooting and nutrient leaching.

Application of cluster analysis to geochemical compositional data for identifying ore-related geochemical anomalies

Cluster analysis is a well-known technique that is used to analyze various types of data. In this study, cluster analysis is applied to geochemical data that describe 1444 stream sediment samples collected in northwestern Xinjiang with a sample spacing of approximately 2 km. Three algorithms （the hierarchical, k-means, and fuzzy cmeans algorithms） and six data transformation methods （the z-score standardization, ZST; the logarithmic transformation, LT; the additive log-ratio transformation, ALT; the centered log-ratio transformation, CLT; the isometric log-ratio transformation, ILT; and no transformation, NT） are compared in terms of their effects on the cluster analysis of the geochemical compositional data. The study shows that, on the one hand, the ZST does not affect the results of columnor variable-based （R-type） cluster analysis, whereas the other methods, including the LT, the ALT, and the CLT, have substantial effects on the results. On the other hand, the results of the row- or observation-based （Q-type） cluster analysis obtained from the geochemical data after applying NT and the ZST are relatively poor. However, we derive some improved results from the geochemical data after applying the CLT, the ILT, the LT, and the ALT. Moreover, the k-means and fuzzy cmeans clustering algorithms are more reliable than the hierarchical algorithm when they are used to cluster the geochemical data. We apply cluster analysis to the geochemical data to explore for Au deposits within the study area, and we obtain a good correlation between the results retrieved by combining the CLT or the ILT with the k-means or fuzzy c-means algorithms and the potential zones of Au mineralization. Therefore, we suggest that the combination of the CLT or the ILT with the k-means or fuzzy c-means algorithms is an effective tool to identify potential zones of mineralization from geochemical data.

Simplicial Indicator Kriging

Indicator kriging （IK） is a spatial interpolation technique devised for estimating a conditional cumulative distribution function at an unsampled location. The result is a discrete approximation, and its corresponding estimated probability density function can be viewed as a composition in the simplex. This fact suggested a compositional approach to IK which, by construction, avoids all its standard drawbacks （negative predictions, not-ordered or larger than one）. Here, a simple algorithm to develop the procedure is presented.

Onion Response to Added N in Histosols of Contrasting C and N Contents

Adjusting the N fertilization to soil potentially mineralizable N in Histosols is required to secure high vegetable yields while mitigating nitrate contamination of surface waters. However, there is still no soil test N (STN) relating the response of Histosol-grown onion (Allium cepa L.) to added N. Compositional data analysis can integrate soil C and N composition into a STN index computed as Mahalanobis distance (M2) across isometric log ratios (ilr) of diagnosed and reference soil C and N compositions. Our objective was to calibrate onion response to added N against a compositional STN index for Histosols. Reference compositions were computed from high N-mineralizing Histosols reported in the literature. Soil analyses were total C and N, and a residual soil mass (Fv) was computed as 100%-%C-%N to close the compositional vector to 100%. The C, N, and Fv proportions were synthesized into two ilrs. We conducted thirteen onion N fertilization trials in Histosols of south-western Quebec showing contrasting C, N, and Fv proportions. Each crop received four N rates broadcast before seeding or split-applied. We derived two STN classes separating weakly to highly responsive crops about the M2 value of 5.5. Onion crops grown on soils showing M2 values >5.5 required more N and yielded less in control treatments compared with soils showing M2 values 5.5) soils responded significantly (P < 0.10) to 60 and 180 kg N ha-1, respectively. Using literature data and the results of this study, we elaborated a provisory N requirement model for Histosol-grown onions in Quebec.

Linear mixed-effects model for longitudinal complex data with diversified characteristics

The increasing richness of data encourages a comprehensive understanding of economic and financial activities,where variables of interest may include not only scalar(point-like)indicators,but also functional(curve-like)and compositional(pie-like)ones.In many research topics,the variables are also chronologically collected across individuals,which falls into the paradigm of longitudinal analysis.The complicated nature of data,however,increases the difficulty of modeling these variables under the classic longitudinal frame-work.In this study,we investigate the linear mixed-effects model(LMM)for such complex data.Different types of variables arefirst consistently represented using the corresponding basis expansions so that the classic LMM can then be conducted on them,which gener-alizes the theoretical framework of LMM to complex data analysis.A number of simulation studies indicate the feasibility and effectiveness of the proposed model.We further illustrate its practical utility in a real data study on Chinese stock market and show that the proposed method can enhance the performance and interpretability of the regression for complex data with diversified characteristics.

Research progress of 24-hour movement behaviors in chronic non-communicable disease

Chronic non-communicable diseases(NCDs)represent a significant impediment to improve life expectancy and remain a focal point in global public health and disease prevention efforts.24-hour movement behaviors,which include sleep,sedentary behavior(SED),and physical activity,underscore the inherent connections between different daily activities and the comprehensive impact of overall movement patterns on health.Evidence suggested that modifying patterns of 24-hour movement behaviors can aid in preventing and attenuating the progression of NCDs.This study systematically delineated the concept,evolution,analytical methods,and intrinsic associations of 24-hour movement behaviors,emphasizing their pivotal role in the prevention and management of NCDs such as obesity,mental disorders,cardiovascular diseases,diabetes,and renal diseases.Future research endeavors should focus on refining methodologies,broadening study populations,developing research tools,and exploring precise intervention strategies and interdisciplinary approaches to comprehensively enhance the effectiveness of NCDs prevention and management from a temporal perspective.Such efforts are poised to provide substantive guidance and support for public health practices.