Multivariate Regression Splines Research Articles

Prediction of compressive strength of geopolymer concrete using a hybrid ensemble of grey wolf optimized machine learning estimators

Geopolymer concrete (GPC) has the potential to replace conventional concrete. But, the mixed proportion of GPC poses several difficulties due to various contributing factors. The design of a reliable prediction model becomes challenging because of the non-linear relationship between the proportion of GPC mix and compressive strength (CS). This study implements a hybrid ensemble machine learning model (HEML) from grey wolf optimized conventional machine learning (CML) models to predict the CS of GPC. An experimental database of 1123 records was compiled from different published research work. The database was used to train and test three optimized CML models namely random forest regressor (RFR), Neural network (NN), and Multivariate regression spline (MARS). Utilizing a meta-learner XGBoost algorithm, the CML models' predicted outputs were trained to develop HEML. Statistical parameters notably R2, Adjusted R2, RMSE, MAE, MAPE, VAF, index, and the Shapiro-Wilk statistical test were used to compare the HEML and CML models' predicted outputs. The HEML model showed better performance in both the training and testing phase than the CML models. Two sensitivity analysis methods were adopted to analyze the impact of various parameters on the compressive strength of geopolymer concrete based on the model with the highest prediction accuracy.

Nomograms predicting local and distant recurrence and disease-specific mortality for R0/R1 soft tissue sarcomas of the extremities.

BackgroundPrognostic models for patients with soft tissue sarcoma (STS) of the extremities have been developed from large multi-institutional datasets with mixed results. We aimed to develop predictive nomograms for sarcoma-specific survival (SSS) and, for the first time, long-term local recurrence (LR) and distant recurrence (DR) in patients with STS of the extremities treated at our institution.Patients and methodsData from patients treated at Humanitas Cancer Center from 1997 to 2015 were analyzed. Variable selection was based on the clinical knowledge and multivariable regression splines algorithm. Perioperative treatments were always included in the model. Prognostic models were developed using Cox proportional hazards model, and model estimates were plotted in nomograms predicting SSS at 5 and 10 years and LR and DR at 2, 5, and 10 years. Model performance was estimated internally via bootstrapping, in terms of optimism-corrected discrimination (Harrell C-index) and calibration (calibration plots).ResultsData on 517 patients were analyzed. At 5 and 10 years, SSS was 68.1% [95% confidence interval (CI), 63.8–72.1] and 55.6% (50.5–60.3), respectively. LR was 79.1% (95% CI, 75.3–82.4), 71.1% (95% CI, 66.7–75.1), and 66.0% (95% CI, 60.7–70.7) at 2, 5, and 10 years, respectively, whereas DR was 65.9% (95% CI, 61.6–69.9), 57.5% (95% CI, 53.0–61.8), and 52.1% (95% CI, 47.1–56.8) at 2, 5, and 10 years, respectively. SSS nomogram included age, gender, margins, tumor size, grading, and histotype. LR and DR nomograms incorporated mostly the same variables, except for age for DR; LR nomogram did not include gender but included anatomic site. The optimism-corrected C-indexes were 0.73 and 0.72 for SSS at 5 and 10 years, respectively; 0.65, 0.64, and 0.64 for LR at 2, 5, and 10 years, respectively; and 0.68 for DR at 2, 5, and 10 years. Predicted probabilities were close to the observed ones for all outcomes.ConclusionsWe developed and validated three nomograms for STS of the extremities predicting the probability of SSS at 5 and 10 years and LR and DR at 2, 5, and 10 years. By accounting for the perioperative treatment, these models allow prediction for future patients who had no perioperative treatment, thus being useful in the clinical decision-making process.

Assessing the performance and accuracy of invasive plant habitat suitability models in detecting new observations in Wisconsin

AbstractLand managers require tools that improve understanding of suitable habitat for invasive plants and that can be incorporated into survey efforts to improve efficiency. Habitat suitability models (HSMs) contain attributes that can meet these requirements, but it is not known how well they perform, as they are rarely field-tested for accuracy. We developed ensemble HSMs in the state of Wisconsin for 15 species using five algorithms (boosted regression trees, generalized linear models, multivariate regression splines, MaxEnt, and random forests), evaluated performance, determined variables that drive suitability, and tested accuracy. All models had good model performance during the development phase (Area Under the Curve [AUC] > 0.7 and True Skills Statistic [TSS] > 0.4). While variable importance and directionality was species specific, the most important predictor variables across all of the species’ models were mean winter minimum temperatures, total summer precipitation, and tree canopy cover. Post model development, we obtained 5,005 new occurrence records from community science observations for all 15 focal species to test the models’ abilities to accurately predict results. Using a correct classification rate of 80%, just 8 of the 15 species correctly predicted suitable habitat (α ≤ 0.05). Exploratory analyses found the number of reporters of these new data and the total number of new occurrences reported per species contributed to increasing correct classification. Results suggest that while some models perform well on evaluation metrics, relying on these metrics alone is not sufficient and can lead to errors when utilized for surveying. We recommend any model should be tested for accuracy in the field before use to avoid this potential issue.

Predicting Probability of Liquefaction Susceptibility Based on a Wide Range of CPT Data

In the present study, three efficient soft computing techniques (namely, genetic programming (GP), relevance vector machine (RVM), and multivariate regression splines (MARS)) are utilized to predict the probabilistic liquefaction susceptibility of soils based on reliability analysis. For this, a sum of 253 cone penetration test (CPT) data of 19 major earthquakes occurring between 1964 and 2011 have been collected from the literature. Six liquefaction parameters such as corrected cone penetration resistance, total vertical stress, total effective stress, maximum horizontal acceleration, magnitude moment, and depth of penetration are explored. To evaluate the overall performance of the proposed models, rank analysis has been carried out. Based on the values of performance indices, the GP model outperforms the other two models in terms of RMSE=0.15, R2 =0.77, and VAF=76.86 in the training stage while the same has been found 0.14, 0.81, and 80.46 in the testing phase. Also, the rank analysis confirms the superiority of the GP model in predicting the probability of liquefaction susceptibility of soils at all stages.

Bioethanol fuel quality assessment using dielectric spectroscopy

This study first aims to determine the physical characteristics of bioethanol from its dielectric properties during the production process. For this purpose, bioethanol samples were produced from sugarcane molasses under different fermentation conditions such as temperature and reaction time. The main permittivity properties, including dielectric constant and loss factor at various frequencies, were measured as the inputs, whereas flash point and octane number, as significant physical parameters, were considered as output variables. Linear regression (LR) models were developed to predict the relationships between predictors and targets. Next, four learning algorithms – multivariate regression splines (MARS), M5 tree, multilayer perceptron (MLP), and support vector regression (SVR) – were deployed to improve the models’ performance. The results from LR models revealed that the flash point had a direct relationship with the dielectric constant and loss factor. However, the octane number was indirectly proportional to the dielectric properties. Also, analysis of the testing data set of learning algorithms indicated that the best algorithm for predicting the responses was MARS, whereas the SVR model performed with the lowest accuracy. The findings from this paper suggest that dielectric spectroscopy is a valuable approach for estimating the physical features of bioethanol.

An estimation procedure with knot selection for multivariate regression splines

Knot selection for regression splines is crucial to the approximation power of splines. For univariate splines, many knot selection algorithms are available. However, extending those univariate algorithms to the multivariate case can be challenging. In this work, an estimation procedure with knot selection for multivariate regression splines is proposed, where the knot selection part is adapted from an existing univariate knot selection algorithm. Simulation results are included to demonstrate the performance of the proposed method.

Mapping groundwater contamination risk of multiple aquifers using multi-model ensemble of machine learning algorithms

Constructing accurate and reliable groundwater risk maps provide scientifically prudent and strategic measures for the protection and management of groundwater. The objectives of this paper are to design and validate machine learning based-risk maps using ensemble-based modelling with an integrative approach. We employ the extreme learning machines (ELM), multivariate regression splines (MARS), M5 Tree and support vector regression (SVR) applied in multiple aquifer systems (e.g. unconfined, semi-confined and confined) in the Marand plain, North West Iran, to encapsulate the merits of individual learning algorithms in a final committee-based ANN model. The DRASTIC Vulnerability Index (VI) ranged from 56.7 to 128.1, categorized with no risk, low and moderate vulnerability thresholds. The correlation coefficient (r) and Willmott's Index (d) between NO3 concentrations and VI were 0.64 and 0.314, respectively. To introduce improvements in the original DRASTIC method, the vulnerability indices were adjusted by NO3 concentrations, termed as the groundwater contamination risk (GCR). Seven DRASTIC parameters utilized as the model inputs and GCR values utilized as the outputs of individual machine learning models were served in the fully optimized committee-based ANN-predictive model. The correlation indicators demonstrated that the ELM and SVR models outperformed the MARS and M5 Tree models, by virtue of a larger d and r value. Subsequently, the r and d metrics for the ANN-committee based multi-model in the testing phase were 0.8889 and 0.7913, respectively; revealing the superiority of the integrated (or ensemble) machine learning models when compared with the original DRASTIC approach. The newly designed multi-model ensemble-based approach can be considered as a pragmatic step for mapping groundwater contamination risks of multiple aquifer systems with multi-model techniques, yielding the high accuracy of the ANN committee-based model.

Decreased cord blood estradiol levels in related to mothers with gestational diabetes.

Recent studies have revealed a link between estradiol (E2) and glucose homeostasis. We aimed to assess the association between cord blood hormone levels and the risk of gestational diabetes mellitus (GDM).A total of 204 pregnant women with GDM and 204 pregnant women without GDM (control) were included in the study. Maternal GDM were diagnosed using a 75 g oral glucose tolerance test at 24 to 26 weeks of gestation. Cord blood samples from neonates were collected immediately post delivery. Controls, which were randomly selected from the study population, were matched (cases to controls ratio: 1:1) to cases by age, sex of fetus, and gestational week.Pregravid body mass index (BMI) (mean ± standard deviation) was (GDM vs. control): 24.5 ± 2.1 versus 22.8 ± 2.4 (P = .001). Cord blood estradiol in the GDM group was significantly lower than in the control group (P < .05). Pregravid BMI in the GDM group was significantly higher than in the control group (P < .05). Estradiol concentrations in cord blood were negatively correlated with birth weight (r = −0.121, P < .05). Conditional logistic regressions showed pregravid BMI, cord blood estradiol, and parity independently and positively predicted GDM. Multivariable regression splines characterize a nonlinear relationship between cord blood estradiol and GDM risk.These results demonstrate a relationship between cord blood estradiol levels and GDM. Estradiol might be involved in the pathophysiology of GDM. Further studies are needed to explore potential mechanism.

Using multiple adaptive regression to address the impact of track geometry on development of rail defects

This paper presents an application of multivariate regression splines (MARS) to a model looking at the railroad track defect behavior. MARS is a non-parametric function estimation technique that shows great promise for fitting non-linear multivariate functions. The MARS approach was used here, together with traditional regression analysis techniques, to develop equations to predict the life (in Millions of Gross Tons or MGT) of a rail defect in the presence of track geometry defects. The MARS approach, using extensive input data, identified and accounted for the key variables contributing to a reduction in rail life. The MARS technique allows for easy interpretation of the relative importance of the different input parameters, to include defect type, and resulted in the development of rail defect life predictive equations as a function of these key parameters. As part of this study, it was determined that there is a reduction in rail life of approximately 30%, when track geometry defects are present.

Vitamin D and executive functioning: Are higher levels better?

ABSTRACTObjectives: Insufficiency of 25-hydroxyvitamin D has been associated with cognitive impairment, particularly worse executive functioning. However, it remains unclear whether supratherapeutic levels (≥100 nmol L–1) are associated with even better performance than sufficient levels (defined as ≥50 nmol L–1 or even ≥75 nmol L–1). The current investigation sought to examine this question. Method: Healthy adults (n = 142) were tested on four measures of executive functioning, including verbal fluency, digit span backward, CANTAB® Spatial Working Memory, and One Touch Stockings of Cambridge. A measure of attention (digit span forward) and memory (CANTAB® Verbal Recognition) were also assessed. Based on blood 25-hydroxyvitamin D [25(OH)D] levels, participants were divided into four groups: insufficient (<50 nmol L–1), low sufficient (50 to <75 nmol L–1), high sufficient (75 to <100 nmol L–1), and supratherapeutic (≥100 nmol L–1). Relationships between vitamin D status and cognition were assessed by analyses of covariance and hierarchical multiple regression, adjusted for age, education, sex, body mass index, mood, and physical activity level. Multivariate regression spline analyses were utilized to investigate nonlinearity. Results: Performance on verbal fluency, but not other measures, differed by vitamin D status, analysis of covariance (ANCOVA), F(3, 127) = 2.70, p = .048; d = 0.50. Specifically, participants with supratherapeutic levels provided a greater number of words (M = 16.1, SE = 1.0) than those with insufficient (M = 12.0, SE = 1.0; p = .007, d = 0.78), low (M = 13.4, SE = 0.7; p = .026, d = 0.51), and high sufficient levels (M = 13.9, SE = 0.9; p = .080, d = 0.42). Similarly, vitamin D status was a significant independent predictor of verbal fluency (p = .025, d = 0.40). Spline analyses revealed that there is a positive, near-linear association between verbal fluency and 25(OH)D levels up to and exceeding 100 nmol L–1. Discussion: Supratherapeutic levels of vitamin D were associated with significantly better performance on verbal fluency. Importantly, commonly used cutoff levels and sufficiency categories have been based on bone health and optimal levels for cognition are unknown. These findings suggest that levels exceeding 100 nmol L–1 may be optimal for at least some aspects of executive functioning.

Ethnic density and depressive symptoms among African Americans: threshold and differential effects across social and demographic subgroups.

We examined the association between Black ethnic density and depressive symptoms among African Americans. We sought to ascertain whether a threshold exists in the association between Black ethnic density and an important mental health outcome, and to identify differential effects of this association across social, economic, and demographic subpopulations. We analyzed the African American sample (n = 3570) from the National Survey of American Life, which we geocoded to the 2000 US Census. We determined the threshold with a multivariable regression spline model. We examined differential effects of ethnic density with random-effects multilevel linear regressions stratified by sociodemographic characteristics. The protective association between Black ethnic density and depressive symptoms changed direction, becoming a detrimental effect, when ethnic density reached 85%. Black ethnic density was protective for lower socioeconomic positions and detrimental for the better-off categories. The masking effects of area deprivation were stronger in the highest levels of Black ethnic density. Addressing racism, racial discrimination, economic deprivation, and poor services-the main drivers differentiating ethnic density from residential segregation-will help to ensure that the racial/ethnic composition of a neighborhood is not a risk factor for poor mental health.

Waist circumference-to-height ratio predicts adiposity better than body mass index in children and adolescents

Body mass index (BMI) is the surrogate measure of adiposity most commonly employed in children and adults. Waist circumference (WC) and the waist circumference-to-height ratio (WCHt) have been proposed as markers of adiposity-related morbidity in children. However, no study to date has compared WCHt, WC, BMI and skinfolds thickness for their ability to detect body adiposity. To compare WCHt, WC, BMI and skinfolds for their accuracy in predicting percent body fat (PBF), percent trunk fat (PTF) and fat mass index (FMI) in a large sample of children and adolescents. We studied 2339 children and adolescents aged 8-18 years from the US National Health and Nutrition Examination Survey 2003/2004. Body fat was measured using dual-energy X-ray absorptiometry. Multivariable regression splines were used to model the association between PBF, PTF, FMI and the predictors of interest. WCHt alone explained 64% of PBF variance as compared with 31% for WC, 32% for BMI and 72% for the sum of triceps and subscapular skinfolds (SF2) (P<0.001 for all). When age and gender were added to the predictors, the explained variance increased to 80% for the WCHt model, 72% for the WC model, 68% for the BMI model and 84% for the SF2 model. There was no practical advantage to add the ethnic group as further predictor. Similar relationships were observed with PTF and FMI. WCHt is better than WC and BMI at predicting adiposity in children and adolescents. It can be a useful surrogate of body adiposity when skinfold measurements are not available.

Optimal storm generation for evaluation of the storm surge inundation threat

To quantify the hazard of hurricane storm surge and coastal inundation in the U.S., storm surge atlas and base flood elevation (BFE) maps are developed. The traditional method for determining the BFE map is the joint probability method (JPM), which requires the simulation of over thousands of hypothetical hurricanes to accurately represent the storm climatology to determine the surge response and return frequency—a huge cost using the sophisticated surge and inundation models today. This study presents an efficient and accurate JPM-OS (optimal sampling) for determining inundation return frequencies using piecewise multivariate regression splines coupled with dimension adaptive sparse grids, based on inundation response calculated by a storm surge modeling system. This method involves the interpolation in five-dimensional space of the simulated surge response and the storm characteristics of an optimal set of storms to any set of storm parameters. The interpolated results can be combined with a probabilistic description to obtain the return frequencies. The method is used to calculate the inundation frequencies of SW Florida and compared with the JPM. The results show excellent agreement between simulated and interpolated response with two orders of magnitude reduction in computational cost. This technique can be readily applied to other coasts.

Circadian variations of infarct size in acute myocardial infarction

BackgroundThe circadian clock influences a number of cardiovascular (patho)physiological processes including the incidence of acute myocardial infarction. A circadian variation in infarct size has recently been shown in rodents, but...

Generalized Nonlinear Modeling With Multivariate Free-Knot Regression Splines

A Bayesian method is presented for the nonparametric modeling of univariate and multivariate non-Gaussian response data. Data-adaptive multivariate regression splines are used where the number and location of the knot points are treated as random. The posterior model space is explored using a reversible-jump Markov chain Monte Carlo sampler. Computational difficulties are partly alleviated by introducing a random residual effect in the model that leaves many of the posterior conditional distributions of the model parameters in standard form. The use of the latent residual effect provides a convenient vehicle for modeling correlation in multivariate response data, and as such our method can be seen to generalize the seemingly unrelated regression model to non-Gaussian data. We illustrate the method on a number of examples, including two previously unpublished datasets relating to the spatial smoothing of multivariate accident data in Texas and the modeling of credit card use across multiple retail sectors.

Multivariate regression splines

Multivariate regression splines of arbitrary order assuming known knots using the additional function are developed. Model description and possible parameter tests for obtaining regression splines are also stated in detail for the triplicate case. A simulation study of drawn data from the Lubricant nonlinear regression model, where “Lubricant” is referred to lubricant data that we use in application, to compare the mean squares errors for the multivariate regression spline models and the multivariate polynomial models show the need of employing the multivariate regression splines in the approximation of the nonlinear regression models.