Principal Component Regression Approach Research Articles

Predicting health outcomes with intensive longitudinal data collected by mobile health devices: a functional principal component regression approach

BackgroundIntensive longitudinal data (ILD) collected in near real time by mobile health devices provide a new opportunity for monitoring chronic diseases, early disease risk prediction, and disease prevention in health research. Functional data analysis, specifically functional principal component analysis, has great potential to abstract trends in ILD but has not been used extensively in mobile health research.ObjectiveTo introduce functional principal component analysis (fPCA) and demonstrate its potential applicability in estimating trends in ILD collected by mobile heath devices, assessing longitudinal association between ILD and health outcomes, and predicting health outcomes.MethodsfPCA and scalar-to-function regression models were reviewed. A case study was used to illustrate the process of abstracting trends in intensively self-measured blood glucose using functional principal component analysis and then predicting future HbA1c values in patients with type 2 diabetes using a scalar-to-function regression model.ResultsBased on the scalar-to-function regression model results, there was a slightly increasing trend between daily blood glucose measures and HbA1c. 61% of variation in HbA1c could be predicted by the three preceding months’ blood glucose values measured before breakfast (P < 0.0001, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{adjusted}^{2}=0.61$$\\end{document}).ConclusionsFunctional data analysis, specifically fPCA, offers a unique tool to capture patterns in ILD collected by mobile health devices. It is particularly useful in assessing longitudinal dynamic association between repeated measures and outcomes, and can be easily integrated in prediction models to improve prediction precision.

Supervised Machine Learning and Multiple Regression Approach to Predict Successfulness of Matrix Acidizing in Hydraulic Fractured Sandstone Formation

The success rate of matrix acidizing in hydraulic fractured sandstone formation is less than 55%, much lower compared to the more than 91% success rate in carbonate formation. The need for alternative approaches to help the success ratio in matrix acidizing is crucial. This paper demonstrates a modeling technique to improve the success ratio of matrix acidizing in a hydraulic fractured sandstone formation. Supervised machine learning with 4 models of a neural network, logistic regression, tree, and random forest was selected to predict the successfulness of matrix acidizing in hydraulic fracturing. In parallel, multivariate analysis of principal component regression and partial least square regression approach were utilized to predict the oil gain of the job. For qualitative prediction, the results showed that the random forest was the best model to predict the successfulness of the job with the area under the curve (AUC) of 0.68 and precision of 0.73 in the training model with 70% of the data. Subsequently, the validation test with the rest of the data (30% data) gave 0.51 AUC and 61% precision. For quantitative prediction, the net oil gain was evaluated by using principal component regression (PCR) and partial least square regression (PLS-R). The PCR and PLS-R model gave a coefficient of determination (Rsquare) of 0.22 and 0.35, respectively. The p-value of PLS-R was 0.047 (95% confidence interval) which indicates that the model is significant. The results of this work demonstrate the potential application of supervised machine learning, principal component regression, and partial least square regression to improve candidate selection of oil wells for matrix acidizing especially in hydraulic fractured wells with limited design data.

Hydroclimate Variations across North-Central China during the Past 530 Years and Their Relationships with Atmospheric Oscillations

Detailed study of historical drought events in North-Central China (NCC) is important to understand current hydroclimate variability in the background of global warming. Here, we combined 12 published tree-ring chronologies and 12 dryness/wetness indices (DWI) to reconstruct dry and wet climate variability across NCC. These 24 proxy records showed similarly significant responses to warm season (May–June–July–August–September, MJJAS) moisture signals. A new 530-year-long reconstruction of self-calibrating Palmer Drought Severity Index (scPDSI) values for the warm season in NCC was determined using a nested principal component regression (PCR) approach. The new reconstruction shows significant correlations with the instrumental MJJAS scPDSI data across NCC during the period AD 1901–2012. The reconstructed MJJAS scPDSI revealed seven severe dry/wet events from AD 1470 to 2012. The periods AD 1701–1727 and AD 1985–2011 represent the longest dry periods, and the drought during the 1920s is identified as the most severe one over the past 530 years. Our reconstruction shows significant interannual spectral peaks at the frequency domain of 2–7 years, together with relatively weaker decadal frequencies of 16, 24, and 78 years. The results of superposed epoch analysis (SEA) show that extreme North Atlantic Oscillation (NAO) years may modulate drought variability in NCC.

Using graph theory as a common language to combine neural structure and function in models of healthy cognitive performance.

Graph theory has been used in cognitive neuroscience to understand how organisational properties of structural and functional brain networks relate to cognitive function. Graph theory may bridge the gap in integration of structural and functional connectivity by introducing common measures of network characteristics. However, the explanatory and predictive value of combined structural and functional graph theory have not been investigated in modelling of cognitive performance of healthy adults. In this work, a Principal Component Regression approach with embedded Step-Wise Regression was used to fit multiple regression models of Executive Function, Self-regulation, Language, Encoding and Sequence Processing with a collection of 20 different graph theoretic measures of structural and functional network organisation used as regressors. The predictive ability of graph theory-based models was compared to that of connectivity-based models. The present work shows that using combinations of graph theory metrics to predict cognition in healthy populations does not produce a consistent benefit relative to making predictions based on structural and functional connectivity values directly.

Heterogeneous Beliefs and the Phillips Curve

We establish a set of novel empirical facts concerning cross-section distributions of inflation expectations reported in surveys. Almost all the variation in expectations about their mean may be summarized via three factors we call disagreement, skew, and shape. We adopt a functional principal component regression approach to estimating forward-looking models of inflation that exploits the heterogeneity present in individual-level data. By using survey information more effectively, our approach reveals an enhanced role for expectations in inflation dynamics that is robust to lagged inflation, trend inflation, and supply factors. Our findings hold in similar form across two major economies.

Optical characteristics of fermented cocoa pod husk based on Nears Infrared Reflectance Spectroscopy and evaluation of its quality as animal feed materials

Near Infrared Spectroscopy (NIRs) is one of the alternative methods to determine chemical characteristic of the animal feed due to its several benefits. The purpose of this study was to determine optical characteristics and the quality of fermented cacao pod husk as animal feed by NIRs method. Totally eighteen samples of fermented cocoa pod husk were analyzed by wet analysis consisting of as dry matter, crude protein, crude fiber, crude fat, crude ash, and nitrogen-free extract material. Spectrum acquisition was carried out using a Thermo Nicolet Antaris II tool. Chemical analysis is intended to compare the data from chemical analysis and the NIRS method. Spectrum data were processed using partial least squares (PLS) with multiplicative scatter correction (MSC) and de-Trending (DT) pre-treatment methods. The results of the study indicated that the NIRS was good prediction for dry matter, crude protein, and crude fat with the model of MSC pre-treatment. The crude ash parameter is only able to predict well on the MSC pre-treatment method with evaluation values. In conclusion, NIRS can be applied to determine animal nutritive values by means of using partial least squares (PLS), principal component regression (PCR) and other regression approaches.

Combination of structural and functional connectivity explains unique variation in specific domains of cognitive function

The relationship between structural and functional brain networks has been characterised as complex: the two networks mirror each other and show mutual influence but they also diverge in their organisation. This work explored whether a combination of structural and functional connectivity can improve the fit of regression models of cognitive performance. Principal Component Analysis (PCA) was first applied to cognitive data from the Human Connectome Project to identify latent cognitive components: Executive Function, Self-regulation, Language, Encoding and Sequence Processing. A Principal Component Regression approach with embedded Step-Wise Regression (SWR-PCR) was then used to fit regression models of each cognitive domain based on structural (SC), functional (FC) or combined structural-functional (CC) connectivity. Executive Function was best explained by the CC model. Self-regulation was equally well explained by SC and FC. Language was equally well explained by CC and FC models. Encoding and Sequence Processing were best explained by SC. Evaluation of out-of-sample models’ skill via cross-validation showed that SC, FC and CC produced generalisable models of Language performance. SC models performed most effectively at predicting Language performance in unseen sample. Executive Function was most effectively predicted by SC models, followed only by CC models. Self-regulation was only effectively predicted by CC models and Sequence Processing was only effectively predicted by FC models. The present study demonstrates that integrating structural and functional connectivity can help explaining cognitive performance, but that the added explanatory value (in-sample) may be domain-specific and can come at the expense of reduced generalisation performance (out-of-sample).

A distributed principal component regression method for quality-related fault detection and diagnosis

Modern industrial processes are confronted with a large-scale challenge in recent years. In this paper, a novel distributed kernel principal component regression (DKPCR) approach is proposed to study the plant-wide problem of quality-related process monitoring. Along with reducing the scale of abundant measurements, the proposed approach also focuses on the robust issues that arise from the large outliers. In the local phase, every agent of the DKPCR technique processes the data of the partial sections and sends the selected information to the centralized mainframe. The engineer gathers the data from the local agents and then makes a decision based on the Bayesian inference. Additionally, the corresponding weight diagnosis approach is devised to isolate the fault-relevant variables under the smear effect by virtue of the detection results and information. In the end, the Tennessee Eastman case (TEC) and the three-phase flow system (TPFS) are leveraged to demonstrate the detection and diagnosis performance of the proposed approach.

Season Onset Prediction Based on Statistical Model for Malang Regency, East Java

Prediction of season onset is important for many sectors, particularly on agricultural practices, as its usage for reducing climate risk and planning activities. Current knowledge on season onset prediction mainly focused on large area, which remains research challenge for local level. This research developed model prediction of season onset for Malang Regency, East Java based on global climate data. The research specifically aimed to: (i) determine the onset date of rainy and dry season, (ii) generate equation for onset date prediction using principal component regression (PCR) approach, and (iii) evaluate the model performance. We depend on statistical model based on a combine of domain time and principal component analysis (PCA) for atmospheric variables, namely sea level pressure, outgoing longwave radiation, and zonal wind. We used the Tropical Rainfall Measuring Mission (TRMM) data for model evaluation, especially for determination of onset date. Based on cumulative anomalies rainfall, the onset date for dry season occurred in the early May, whereas for rainy season it was in early November. The results showed that regression models of the principal components had a good skill to predict onset date for both seasons. It has been confirmed by a low error and a high correlation. Visually, the dynamic of onset dates from model was mostly identical to the observation. The predictive model for rainy season had higher performance compared to the model for dry season. This finding was confirmed by insignificant difference resulted from the independent t-test between model and observed onset dates. The best model for dry season was conducted by domain time of February, whereas for rainy season was domain time of August. This research can be used to complement previous studies regarding season onset prediction in Indonesia.

Application of PCR and PLS Tools for the Simultaneous Quantification of Praziquantel and Ivermectin Binary Mixtures in Veterinary Tablets

Two chemometric calibration methods, principal component regression (PCR) and partial least squares regression (PLS) were proposed for the simultaneous spectrophotometric determination of praziquantel (PRA) and ivermectin (IVE) in a marketed veterinary formulation without using preliminary separation step. UV spectra of calibration set and samples including PRA and IVE were recorded in the spectral region of 225-315 nm. PCR and PLS algorithms were applied to absorbance data matrix and concentration set including PRA and IVE in the linear concentration range of 20.0-160.0 µg/mL for PRA and 2.0-44.0 µg/mL for IVE. The capability of the PCR and PLS methods were validated by analyzing validation samples. Assay results showed that both PCR and PLS approaches provided an opportunity for quantifying PRA and IVE in veterinary tablet formulation.

Framework for implementation of the Pitman-WR2012 model in seasonal hydrological forecasting: a case study of Kraai River, South Africa

Hydrological forecasting becomes an important tool in water resources management in forecasting the future state of the water resources in a catchment. The need for a reliable seasonal hydrologic forecast is significant and is becoming even more urgent under future climate conditions, as the assimilation of seasonal forecast information in decision making becomes part of the short and long-term climate change adaptation strategies in a range of contexts, such as energy supply, water supply and management, rural-urban, agriculture, infrastructure and disaster preparedness and relief. This work deals with the framework for implementation of the Pitman-WR2012 model in a hydrological forecasting mode. The Pitman-WR2012 model was forced with 10-member ensemble seasonal climate forecast from Climate Forecast Systems v.2 (CFSv2), which is downscaled using the principal components regression (PCR) approach. The generated seasonal hydrological forecast focused on the summer season, in particular on the Dec–Jan–Feb (DJF) period, which is the rainy season in the studied catchment (Kraai River catchment in the Eastern Cape Province of South Africa). The hydrological forecast issued at the end of November showed skill in December and February (assessed through Receiver Operating Characteristic (ROC) and Ranked Probability Skill Score (RPSS)), with poorer skill in January. Importantly, the skill of streamflow forecast was better than that of rainfall forecast, which likely results from the influence of the initial conditions of the hydrological model. In conclusion Pitman-WR2012 model performed realistically when implemented in seasonal hydrological forecasts mode, and it is important that in that mode the model is run with near-real-time rainfall data in order to maximize forecast skill arising from initial conditions.

Analyzing Collinear Data by Principal Component Regression Approach — An Example from Developing Countries

The aim of this paper is to identify the effects of socioeconomic factors and family planning program effort on total fertility rate with national level data from forty-three developing countries. The data used have mainly been taken from the secondary source “Family Planning and Child Survival: 100 Developing Countries” compiled by the Center for Population and Family Health, Columbia University. Because the independent variables were found to be highly correlated among themselves, component regression technique has been used to analyze the data. The analysis shows that the family planning program effort has the largest contribution in lowering the total fertility rate, followed by percent of urban population, female literacy rate, and infant mortality rate in that order. Policy implications are discussed.

Principal Component Analysis in Linear Regression Survival Model with Microarray Data

As a useful alternative to the Cox proportional hazards model, the linear regression survival model assumes a linear relationship between the covariates and a known monotone transformation, for example logarithm, of an event time of interest. In this article, we study the linear regression survival model with right censored survival data, when high-dimensional microarray measurements are present. Such data may arise in studies in vestigating the statistical influence of molecular features on survival risk. We propose using the principal component regression (PCR) technique for model reduction based on the weight least squared Stute estimate. Com pared with other model reduction techniques, the PCR approach is relatively insensitive to the number of covariates and hence suitable for high dimen sional microarray data. Component selection based on the nonparametric bootstrap, and model evaluation using the time-dependent ROC (receiver operating characteristic) technique are investigated. We demonstrate the proposed approach with datasets from two microarray gene expression pro filing studies of lymphoma cancers

Spectral Data Analysis for a Complex Drug Mixture Containing Altizide, Potassium Canrenoate, and Rescinnamine

Conventional and chemometric spectrophotometric techniques were compared for their analytical performance in determining a tri-component pharmaceutical mixture containing altizide, potassium canrenoate, and rescinnamine. These components were characterized by a notable spectral overlap, thus making their quantitative determination particularly difficult. The determination of altizide and canrenoate was performed using the technique of different order-derivative spectrophotometry, while rescinnamine was determined by fluorometry with activation and fluorescence maxima respectively at 325 and 427 nm thanks to a total absence of interference from the other two components. The analysis of the mixture was carried out by applying multivariate calibration methods, including principal component (PCR) and partial least squares (PLS) regression approaches. The calibration sample set was defined by a simplex-lattice experimental design to cover the experimental domain distributed over five concentration levels. The prediction accuracy of the defined methods was evaluated through external validation on new unknown samples and commercial pharmaceuticals. Significant advantages were found in the prediction of all the analytes when using the chemometric methods, which proved to be simpler, faster, and showing better statistical results with accuracy values between 96.12 and 103.36% and relative standard errors lower than 1.7%.

Principal components estimator for measurement error models

ABSTRACTIn this paper, we carry out the principal components regression approach to the measurement error models. We introduce the principal components estimator and then the restricted principal components estimator by combining the approaches principal components regression estimator and restricted least squares estimator for the measurement error models, when the reliability matrix known and unknown, separately. We investigate the asymptotic properties and matrix mean squared error performances of the new estimators. Also, we conduct a Monte Carlo simulation study and a numerical example to investigate the performances of the proposed estimators by the scalar mean squared error criterion.

Hybrid approach to reducing estimating overfitting and collinearity

Purpose The purpose of this paper is to present an approach to address the overfitting and collinearity problems that frequently occur in predictive cost estimating models for construction practice. A case study, modeling the cost of preliminaries is proposed to test the robustness of this approach. Design/methodology/approach A hybrid approach is developed based on the Akaike information criterion (AIC) and principal component regression (PCR). Cost information for a sample of 204 UK school building projects is collected involving elemental items, contingencies (risk) and the contractors’ preliminaries. An application to estimate the cost of preliminaries for construction projects demonstrates the method and tests its effectiveness in comparison with such competing models as: alternative regression models, three artificial neural network data mining techniques, case-based reasoning and support vector machines. Findings The experimental results show that the AIC–PCR approach provides a good predictive accuracy compared with the alternatives used, and is a promising alternative to avoid overfitting and collinearity. Originality/value This is the first time an approach integrating the AIC and PCR has been developed to offer an improvement on existing methods for estimating construction project Preliminaries. The hybrid approach not only reduces the risk of overfitting and collinearity, but also results in better predictability compared with the commonly used stepwise regression.

Comparison of Least Squares, Ridge Regression and Principal Component Approaches in the Presence of Multicollinearity in Regression Analysis

The aim of this study was to compare estimation methods: least squares method (LS), ridge regression (RR), Principal component regression (PCR) to estimate the parameters of multiple regression model in situations when the underlying assumptions of least squares estimation are untenable because of multicollinearity. For this aim, the effect of some body measurements on body weights (height at withers and rumps, body length, chest width, chest girth and chest depth, front, middle and hind rump width) obtained from totally 85 Karayaka lambs at weaning period raised at Research Farm of Ondokuz Mayis University was examined. Mean square error, R2 value and significance of parameters were used to evaluate estimator performance. The multicollinearity, between front and middle rump width which were used to estimate live weight, was eliminated by using RR and PCR. Although research findings showed that RR method had the smallest MSE and the highest R2 value, the estimates of PCR were determined to be more consistent when the importance tests of parameters were taken into account. The results showed that principal component regression approach should be used to estimate the live weight of Karayaka lambs at weaning period.

Outliers detection using an iterative strategy for semi‐supervised learning

AbstractAs a direct consequence of production systems' digitalization, high‐frequency and high‐dimensional data has become more easily available. In terms of data analysis, latent structures‐based methods are often employed when analyzing multivariate and complex data. However, these methods are designed for supervised learning problems when sufficient labeled data are available. Particularly for fast production rates, quality characteristics data tend to be scarcer than available process data generated through multiple sensors and automated data collection schemes. One way to overcome the problem of scarce outputs is to employ semi‐supervised learning methods, which use both labeled and unlabeled data. It has been shown that it is advantageous to use a semi‐supervised approach in case of labeled data and unlabeled data coming from the same distribution. In real applications, there is a chance that unlabeled data contain outliers or even a drift in the process, which will affect the performance of the semi‐supervised methods. The research question addressed in this work is how to detect outliers in the unlabeled data set using the scarce labeled data set. An iterative strategy is proposed using a combined Hotelling's T2 and Q statistics and applied using a semi‐supervised principal component regression (SS‐PCR) approach on both simulated and real data sets.

Application Of L1- Regularization Approach In QSAR Problem. Linear Regression And Artificial Neural Networks

One of the primary tasks of analytical chemistry and QSAR/QSPR researches is building of prognostic regression equations based on descriptors sets. The one of the most important problems here is to decrease the number of descriptors in the initial descriptor set which is usually way too big. In current investigation the descriptor set is proposed to be reduced employing the least absolute shrinkage and selection operator (LASSO) approach. Decreased descriptor sets were used for calculations with application of the following QSAR/QSPR methods: ordinary least squares (OLS), the least absolute deviation (LAD) regressions and artificial neural networks (ANN). Contrary to aforementioned methods principal component regression (PCR) and partial least squares (PLS) approaches can produce solutions containing numerous descriptors. In this article we compared the viability of these two different descriptor handling ideologies in application to molecular chemical and physical properties prediction. From the obtained results it is possible to see that there are tasks for which PCR and PLS approaches can fail to produce accurate regression equations. At the same time, methods OLS and LAD that use small amount of descriptors can provide viable solutions for the same cases. It was shown that these small sets of descriptors selected with LASSO approach can be used in ANN to obtain models with even better internal validation characteristics.

Heterogeneous Beliefs and the Phillips Curve

We establish a set of novel empirical facts concerning cross-section distributions of inflation expectations reported in surveys. Almost all the variation in expectations about their mean may be summarized via three factors we call disagreement, skew, and shape. We adopt a functional principal component regression approach to estimating forward-looking models of inflation that exploits the heterogeneity present in individual-level data. By using survey information more effectively, our approach reveals an enhanced role for expectations in inflation dynamics that is robust to lagged inflation, trend inflation, and supply factors. Our findings hold in similar form across two major economies.