Mallow's Cp Research Articles

Factors influencing the health-related quality of life of older men and women living with HIV in Spain

ABSTRACT The number of older people living with HIV (OPLHIV) is increasing worldwide. However, little is known about the factors that better predict their health-related quality of life (HRQoL). We administered the validated WHOQoL-HIV BREF questionnaire to 247 Spanish OPLHIV (192 men and 55 women). In addition to the six domains of the questionnaire, we constructed a seventh domain as theaverage of punctuations of all domains. Multivariable Poisson regression models with robust estimates by sex were constructed for the seven domains (14 in total). The best-subset selection method together with Mallow's Cp metric was used to select the model factors. The percentage of variability explained by Poisson models ranged from15-38% for men and 29-70% for women. The analysis showed that women were most affected by ageing (four domains), mobility impairments (five domains), and mental disorders (five domains). The factors with the greatest negative influence on men were heterosexuality (six domains), mental disorders (six domains), being single (five domains), and poverty risk (three domains). Physical activity was found to improve HRQoL in both men (six domains) and women (four domains). Future OPLHIV programmes would benefit from considering sex specific HRQoL factors. This could also improve the cost-effectiveness of interventions.

Information criteria for structured parameter selection in high-dimensional tree and graph models

Parameter selection in high-dimensional models is typically fine-tuned in a way that keeps the (relative) number of false positives under control. This is because otherwise the few true positives may be dominated by the many possible false positives. This happens, for instance, when the selection follows from a naive optimisation of an information criterion, such as AIC or Mallows's Cp. It can be argued that the overestimation of the model comes from the optimisation process itself changing the statistics of the selected variables, in a way that the information criterion no longer reflects the true divergence between the selected model and the data generating process. Using lasso, the overestimation can also be linked to the shrinkage estimator, which makes the selection too tolerant of false positive selections. For these reasons, this paper works on refined information criteria, carefully balancing false positives and false negatives, for use with estimators without shrinkage. In particular, the paper develops corrected Mallows's Cp criteria for structured selection in trees and graphical models.

Estimation of body weight using body measurements in female water buffaloes reared in southeastern Mexico

Buffalo farming is an important livestock activity in Mexico. However, the low technological level of the farms makes it difficult to monitor the growth rates of the animals. The objectives of this study were to analyse the body measurements of 107 adult female Murrah buffaloes, to estimate the interrelationships between those measurements and body weight, and to develop equations to predict body weight (BW) using body measurements including withers at height (WH), rump height (RH), body height (BH), heart girth (HG), abdominal girth (AG), pelvic girth (PG), body length (BL), girth circumference (GC), diagonal body length (DBL), pelvic circumference (PC), and abdomen circumference (AC). The study was conducted on two commercial farms in southern Mexico. Pearson correlation and stepwise regression techniques were used for the data analysis. To find out the best regression models, we used model quality criteria such as coefficient of determination (R2), adjusted R2 (Adj.R2), root mean square error (RMSE), Mallow's Cp, Akaike's information criteria (AIC), Bayesian information criteria (BIC), and coefficient of variation (CV). Correlation results indicated that BW had a positive high correlation (P < 0.01) of all the measured traits. Model 4 (-780.56 + 311.76GC + 383.51DBL + 51.82PC + 47.65AC-106.78BL) was the best regression model with a higher R2 (0.87), Adj. R2 (0.86) smaller Cp (4.24), AIC (749.19), BIC (752.16), and RMSE (36.91). The current study suggests that GC, DBL, PC, AC, and BL might be used in combination to estimate BW of adult female Murrah buffaloes.

Modeling Internet Search Behavior of Cross-Laminated Timber

Abstract The Internet is a powerful tool that can be leveraged to explore user search behavior. Google Trends is a compelling database that tracks the frequency with which all users search any given word. There is thus an opportunity to see if the search histories obtained from Google Trends can be merged with data analytics to tease out underlying relationships with similar searches for cross-laminated timber (CLT). In this study, multiple linear regression was used to predict the search strength of the term cross laminated timber from 60 possible variables that may be directly or indirectly associated with CLT. This study was able to model the search term CLT (R2 = 0.76) using a reduced model of 20 variables. However, while prediction strength was strong, our primary interest was to statistically classify and rank important variables that might be important to CLT. To achieve this, the Mallow's Cp statistic was used to build the most robust model possible. To confirm with the literature, we also compared our study with another Web-based study and found a significant linear relationship between the t statistic in our study and the frequency of the same or similar search term in their study (R2 = 0.76). This agreement between studies helps to support our hypothesis that multiple linear regression coupled with Google Trends is a new tool that may assist marketers to identify emerging trends important to CLT.

On improvability of model averaging by penalized model selection

We propose MMAe, a modified MMA based on penalized Mallow's Cp. A weighted elastic net penalty is added to handle the inevitable collinearity among models, which is beneficial to high‐dimensional data modelling. We proved the sparsity, the asymptotic optimality of its weight solution and also proved that its candidate model set can be exponentially enlarged under Gaussian noises. We further proved that an MMAe adjusted by generalized cross validation (GCV) has an asymptotically lower risk than MMA under more relaxed conditions. Our approach can be implemented efficiently by convex optimization algorithms. In simulation and real‐life analysis, MMAe achieves higher prediction accuracy compared with other methods.

Comparative study using design experiment to assess an anionic dye degradation in aqueous solution through the application of different advanced oxidation processes

AbstractThis study aims to compare the anionic dye degradation (Titan yellow dye: DY9) in synthetic solution using three advanced oxidation processes, namely, Fenton process (FP) (H2O2/Fe2+), photo‐Fenton process (PhFP) (UV/H2O2/Fe2+), and photocatalytic process (PhCP) (TiO2/UV). To perform this study, design of experiments methodology was applied. A full factorial design was used to investigate the effect of operating parameters on the degradation yield. For each process, four parameters were considered, for “FP” and “PhFP,” the initial dye concentration ([DY9]0), the ratio R1 = [H2O2]/[Fe2+], the ratio R2 = [DY9] / [Fe2+], and the pH of solution and for “PhCP,” the initial dye concentration (([DY9]0), initial concentration of hydrogen peroxide [H2O2], dose of titanium oxide [TiO2], and the pH of solution. The averages of degradation yield obtained are 47.1%, 56.7%, and 68.5% for “FP,” “PhFP,” and “PhCP,” respectively. Main and interaction effects plots were constructed. An interaction index (In (%)) was defined, which allowed to quantify the impact of the interaction on the response. Three regression models were proposed and validated on basis of analysis of variance (ANOVA) and statistical criteria as corrected Akaike Information Criterion (AICc), Mallows Cp statistic, coefficient of determination (R2), and adjusted coefficient of determination (R2adj). These models showed that the “PhCP” model was the most statistically significant, including more interaction effect terms. Iso‐responses curves were plotted to predict the optimal conditions for each process. To achieve a full degradation of DY9, the predicting optimal conditions were expressed on intervals.

Prediction model for left ventricular ejection fraction recovery in atrial fibrillation-induced cardiomyopathy

Abstract Introduction Arrhythmia-Induced Cardiomyopathy (AIC) is a cardiac disfunction secondary to fast, asynchronous or irregular ventricular contraction. Its diagnosis is usually retrospective, subsequently of the recovery of the left ventricle ejection fraction (LVEF) after controlling the responsible arrythmia (most frequently atrial fibrillation (AF)). Objective Our aim is to try to estimate the recovering of LVEF in patients diagnosed of AIC caused by AF, based on individual baseline characteristics. Methods Retrospective analysis of patients diagnosed with AIC related to AF between January 2015–2022. Clinical and demographic characteristics, as well as echocardiographic parameters prior to diagnosis and after recovery of ventricular function, were assessed. Recovered LVEF (final minus initial LVEF) was calculated in all patients. The best model was selected from the method of all possible equations, the one with the lowest Mallows Cp index, maintaining a sufficiently high multiple correlation coefficient (R2). Results 134 patients with AIC were gathered in this period, 99 of them AF-related. Baseline characteristics are summarized in Image 1. The changes in the values of LVEF, left ventricle end-diastolic diameter and (LVEDD), tricuspid annular plane systolic excursion (TAPSE), which represents both left and right ventricular ejection fraction are showed in Image 2. The LVEF recoveredwith treatment was 22±8,5%. The model was selected using up to 16 potential variables: age, sex, chronic kidney disease (CKD), obesity, enolism, hypertension, diabetes, obstructive sleeping apnoea (OSA), LVEF at the diagnosis, heart rate at diagnosis, angiotensin-converting enzyme inhibitors (ACEI) or angiotensin receptor blockers (ARBs), neprilysin inhibitors (ARNI), mineralocorticoid receptor antagonists (MRA), ablation performed, rhythm control strategy and the interaction between ablation andrhythm control (the latter being rejected because of collinearity). 32.767 models were estimated. The best model was: Recovered LVEF = 51.79 + 1.15×Female Sex − 1.11×OSA − 4.40×RNI − 091×LVEF at diagnosis + 3.43×Rhythm control. The Cp of the selected model was 2.07 and R2 0.496, which means that 49.6% of individual variability of recovered LVEF was justified by this simple model. After that, we performed an internal control using cross-validation, which did not show significative differences according to the estimation ability of the model (0.496 − 0.474 = 0.022, &amp;lt;10%). Conclusion Female sex, absence of OSA, the lower the LVEF at the diagnosis, the absence of treatment with ARNI and the rhythm control as the treatment strategy predicted higher LEVF recovery in patients with AIC caused by AF, explaining nearly half to the individual variability. Funding Acknowledgement Type of funding sources: None.

Goodness of Fit Test of an Autocorrelated Time Series Cubic Smoothing Spline Model

We investigated the finite properties as well as the goodness of fit test for the cubic smoothing spline selection methods like the Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV) and Mallow CP criterion (MCP) estimators for time-series observation when there is the presence of Autocorrelation in the error term of the model. The Monte-Carlo study considered 1,000 replication with six sample sizes: 30; 60; 120; 240; 480 and 960, four degree of autocorrelations; 0.1; 0.3; 0.5; and 0.9 and three smoothing parameters; lambdaGML= 0.07271685, lambdaGCV= 0.005146929, lambdaMCP= 0.7095105. The cubic smoothing spline selection methods were also applied to a real-life dataset. The Predictive mean square error, R-square, and adjusted R-square criteria for assessing finite properties and goodness of fit among competing models discovered that the performance of the estimators is affected by changes in the sample sizes and autocorrelation levels of the simulated and real-life data set. The study concluded that the Generalized Cross-Validation estimator provides a better fit for Autocorrelated time series observation. It is recommended that the GCV works well at the four autocorrelation levels and provides the best fit for time-series observations at all sample sizes considered. This study can be applied to; non –parametric regression, non –parametric forecasting, spatial, survival and econometric observations.

Monte Carlo methods for estimating Mallows's Cp and AIC criteria for PLSR models. Illustration on agronomic spectroscopic NIR data

AbstractMallows's Cp and Akaike information criterion (AIC) are common criteria for selecting the dimensionality of regression models, as an alternative to cross‐validation (CV) and nonparametric bootstrap. A key parameter in the calculation of Cp and AIC is the effective number of degrees of freedom of the model, or model complexity (d). Parameter d is generally easy to calculate for linear smoothers, that is, models for which the prediction of the training response y is given by = S y where S is a projector matrix that does not involve y. Nevertheless, d is more difficult to estimate for nonlinear smoothers, such as partial least squares regression (PLSR). In this article, we present two algorithms for estimating d for PLSR based on Monte Carlo simulation methods (parametric bootstrap and perturbation analysis) and with the particular case of high dimensional data. We compare these Monte Carlo methods to three other algorithms already published. We used the d estimates to compute Cp and AIC and select PLSR model dimensionalities that we then compare to CV. Two real and heterogeneous agronomic near infrared (NIR) datasets were considered as examples.

Spatiotemporal assessment of Sickle Darter ( Percina williamsi Page and Near, 2007) distribution in the upper Tennessee River Basin

The Sickle Darter Percina williamsi (Page and Near, 2007) is a species of fish endemic to the upper Tennessee River basin in eastern Tennessee, southwestern Virginia, and western North Carolina. Because of its narrow range and presumed decline in occupied sites over the last half century, it is being proposed for federal listing under the Endangered Species Act. We analyzed the current distribution of the Sickle Darter and temporal trends in its distribution in relation to temporal trends in environmental and habitat covariates for each of the historically occupied sub-basins (upper Clinch, Emory, upper French Broad, Little, Little Pigeon, Middle Fork Holston, North Fork Holston, Powell, South Fork Holston, and Watauga) with multiple linear regression modelling. A total of 154 Sickle Darters were observed at 15 sites throughout the upper Tennessee River Basin. Sickle Darters were observed in the Little River, Emory River, and Middle Fork Holston River sub-basins. A total of 133 unique historical occurrences were used for the spatiotemporal analyses. Sickle Darters have declined in 8 out of 10 historically occupied sub-basins. Our best model for the whole distribution scale (Mallow's Cp = −0.87; Adjusted R2 = .92) suggests that habitat fragmentation due to damming has had adverse effects on Sickle Darter populations across its distribution. Models were very similar for the sub-basin specific models as well. The results from this study highlight the drivers of decline in Sickle Darter distribution and outline the future research needs for this species that should be used to inform future conservation decisions regarding this species.

Forecast combination for VARs in large N and T panels

We propose a new forecast combination method for panel data vector autoregressions that permit limited forms of parameterized heterogeneity (including fixed effects or incidental trends). Models are fitted using bias-corrected least squares in order to attenuate the effects of small sample bias of forecast loss. We begin by constructing a general estimator of the quadratic forecast risk of the averaged model that is asymptotically unbiased as both n (cross sections) and T (time series) grow large. Armed with this result, we propose a specific weighting mechanism, in which weights are chosen to minimize the estimated quadratic risk of the averaged forecast error. The objective function in this minimization problem is a version of the Mallows Cp criterion modified for application to the panel data setting. The forecast combination method performs well in Monte Carlo simulations and pseudo-out-of-sample forecasting applications.

Critical shear stress approach for self-cleansing design of a rectangular channel

The current study aims at the development of an incipient motion equation and a self-cleansing design chart based on the critical shear stress approach for a rectangular channel. Data from previous experimental work on incipient motion for rectangular flumes were subjected to multiple linear regression analysis. Selected regression models were further assessed through cross validation using the remaining data from the previous experimental work and a performance test using another three sets of existing data from the literature. The best regression model from the current study was found to perform much better than two of the existing equations in the literature by Novak and Nalluri and El-Zaemey with respect to having 95% of the predicted values fall within the acceptable discrepancy ratio range of 0.5–2.0. The equations by Novak and Nalluri and El-Zaemey only managed to have 10% and 16%, respectively, of the predicted values fall within the acceptable discrepancy ratio. The developed best regression model has a coefficient of determination (Rp2) value of 0.9960, adjusted coefficient of determination (Radj2) value of 0.9960, predicted coefficient of determination (Rpre2) value of 0.9958, mean square error (MSE) value of 0.0004, and Mallow's Cp value of 3.0. The best regression model was further chosen to develop a self-cleansing design chart for rectangular channels. The design chart which relates the minimum sewer slope Smin with the minimum critical shear stress, τc, for the respective standard rectangular channel size of an open channel system could be used to check and determine the suitable minimum slope for self-cleansing design purposes.

Model Selection and Model Averaging for Nonlinear Regression Models

This paper develops a nonlinear model averaging method (NLMA) and constructs the corresponding weight choosing criterion which we call NLC criterion for models that are nonlinear with respect to their parameters. NLC can be applied as an information criterion to model selection for nonlinear regression models as well. NLC is based on the idea of Mallows Cp which can be regarded as an unbiased estimator of the mean squared error (MSE) and takes the nonlinearity of the models into consideration. Under some regularity conditions, we investigate into the properties of NLMA and NLC. We show that the weight vector chosen by minimizing NLC converges in probability to the optimal weight vector that minimizes the risk. It’s also proved that the NLMA estimator based on the weight vector selected by NLC minimizes the risk of estimation asymptotically. Furthermore, the distribution of NLMA estimator is derived. For finite sample property, simulation results show that NLMA performs much better than every single-model approximation and other model selection and model averagingmethods, achieving relatively smaller sample MSE.

Linear Regression in Medical Research.

Linear Regression in Medical Research.

Assessing the composition of the soft tissue in lamb carcasses with bioimpedance and accessory measures

Consumers are demanding additional information to support their decision-making while shopping for meat. In the lamb industry, labelling carcasses with composition information is challenging. This is due to issues with conventional analytical procedures, such as the time spent with determinations and product loss or devaluing due to sampling for analysis. The objective was to evaluate the potential use of bioimpedance analysis (BIA) to determine composition of the soft tissue portion of lamb carcasses. Thirty-one Texel and Ile-de-France crossbreed ram lambs were slaughtered at 20, 26, 32, or 38 kg of body weight. Values of resistance and reactance were collected from hot and cold carcasses, which weighed 12.4 ± 2.99 kg and 11.9 ± 2.94 kg, respectively and measured 53.9 ± 3.25 cm of length. Carcass weight and length were used to calculate other BIA variables such as impedance modulus, phase angle, bioelectrical volume, and both resistive and reactive densities. These variables were used as independent variables to predict the contents of soft tissue, moisture, ash, protein, fat, lean, and crude energy of the carcasses. Multiple regression analyses were carried out to calibrate BIA models. The leave-one-out cross-validation was performed to evaluate precision and accuracy of the BIA technique. Resistive density was the most important BIA variable to predict lamb composition of hot carcasses, which explained 83% to 92% of the variation in composition. In turn, reactive density better predicted lamb carcass composition in cold carcasses, which accounted for 81% to 92% of their variation in carcass composition. In addition, prediction models of the soft tissue portion of lamb carcasses assessed on cold carcasses showed a higher coefficient of determination and smaller root mean square error and Mallows Cp values than hot carcasses. Therefore, BIA has an excellent potential to predict lamb carcass components on either hot as cold carcass; however, higher accuracy was found with cold carcasses in comparison with hot.

Seasonal Short‐Term Prediction of Dissolved Oxygen in Rivers via Nature‐Inspired Algorithms

AbstractThis study challenges the use of three nature‐inspired algorithms as learning frameworks of the adaptive‐neuro‐fuzzy inference system (ANFIS) machine learning model for short‐term modeling of dissolved oxygen (DO) concentrations. Particle swarm optimization (PSO), butterfly optimization algorithm (BOA), and biogeography‐based optimization (BBO) are employed for developing predictive ANFIS models using seasonal 15 min data collected from the Rock Creek River in Washington, DC. Four independent variables are used as model inputs including water temperature (T), river discharge (Q), specific conductance (SC), and pH. The Mallow's Cp and R2 parameters are used for choosing the best input parameters for the models. The models are assessed by several statistics such as the coefficient of determination (R2), root‐mean‐square error (RMSE), Nash–Sutcliffe efficiency, mean absolute error, and the percent bias. The results indicate that the performance of all‐nature‐inspired algorithms is close to each other. However, based on the calculated RMSE, they enhance the accuracy of standard ANFIS in the spring, summer, fall, and winter around 13.79%, 15.94%, 6.25%, and 12.74%, respectively. Overall, the ANFIS‐PSO and ANFIS‐BOA provide slightly better results than the other ANFIS models.

Artificial intelligence models for prediction of the aeration efficiency of the stepped weir

Stepped weir is a commonly used hydraulic structure in water treatment plants to enhance the air-water transfer of oxygen or nitrogen and volatile organic components. The flow regimes on stepped weir are classified into nappe, transition and skimming flow. This study presents the novel application of artificial intelligence methods to evaluate the aeration efficiency over stepped weir for the three flow regimes. Two methods were adopted in this study, namely, the evolutionary polynomial regression (EPR) and the M5 model tree (M5 MT). A total of 151 laboratory experimental data sets were collected from the literature to train and test the artificial intelligence models. The Mallow's coefficient CP was used to determine the effective variables affecting aeration efficiency. It was found that weir steps number, slope, the flow Reynolds number, and the ratio of the critical flow depth to the step height are the most important variables providing the lowest Cp. Both the EPR and M5 MT methods provided satisfactory predictions for the aeration efficiency. The two methods have high values of correlation coefficient R> 0.93 and low values for the root mean square error RMSE< 0.052 and relative mean absolute error RMAE< 0.065. However, the EPR method has an advantage over the M5 MT method that it provides one equation for each regime, while the M5 MT method provides a number of equations for each regime. This will make the equations of the EPR method more attractive to the practitioners compared to the equations of the M5 MT method. It was found that the equations obtained from artificial intelligence methods in this study perform better than the currently existing equations in the litrature obtained from regressive methods.

Foetal weight prediction models at a given gestational age in the absence of ultrasound facilities: application in Indonesia

BackgroundBirth weight is one of the most important indicators of neonatal survival. A reliable estimate of foetal weight at different stages of pregnancy would facilitate intervention plans for medical practitioners to prevent the risk of low birth weight delivery. This study has developed reliable models to more accurately predict estimated foetal weight at a given gestation age in the absence of ultrasound facilities.MethodsA primary health care centre was involved in collecting retrospective non-identified Indonesian data. The best subset model selection criteria, coefficient of determination, standard deviation, variance inflation factor, Mallows Cp, and diagnostic tests of residuals were deployed to select the most significant independent variables. Simple and multivariate linear regressions were used to develop the proposed models. The efficacy of models for predicting foetal weight at a given gestational age was assessed using multi-prediction accuracy measures.ResultsFour weight prediction models based on fundal height and its combinations with gestational age (between 32 and 41 weeks) and ultrasonic estimates of foetal head circumference and foetal abdominal circumference have been developed. Multiple comparison criteria show that the proposed models were more accurate than the existing models (mean prediction errors between − 0.2 and 2.4 g and median absolute percentage errors between 4.1 and 4.2%) in predicting foetal weight at a given gestational age (between 35 and 41 weeks).ConclusionsThis research has developed models to more accurately predict estimated foetal weight at a given gestational age in the absence of ultrasound machines and trained ultra-sonographers. The efficacy of the models was assessed using retrospective data. The results show that the proposed models produced less error than the existing clinical and ultrasonic models. This research has resulted in the development of models where ultrasound facilities do not exist, to predict the estimated foetal weight at varying gestational age. This would promote the development of foetal inter growth charts, which are currently unavailable in Indonesian primary health care systems. Consistent monitoring of foetal growth would alleviate the risk of having inter growth abnormalities, such as low birth weight that is the most leading factor of neonatal mortality.

A Regression Equation Model for Height and Weight Prediction

Height and weight prediction has been a popular problem in ergonomics study. In this paper, we reduce the dimension by principal component analysis and choose the best regression equation using various statistical criterion such as Residual Mean Square (RMSq), Mallow Cp and Akaike information criterion (AIC). Finally, compared with the real value, we analyze the fitting accuracy of the regression equation we proposed.

Is the global sea surface temperature rise accelerating?

This is an exploratory investigation to search for the presence of an acceleration in global sea surface temperature rise, which is essential to identify anthropogenic contributions to the climate change during the 20th century. A weighted statistical model with an acceleration parameter was built progressively to reconstruct the variations in the global sea surface temperature data considering statistically significant confounders and autoregressive disturbances in the process. From the preliminary residual analysis of a weighted regression model, emerged a parsimonious model with first order autoregressive disturbances with a deterministic trend, acceleration and periodicity of 69 yr and its 138 yr subharmonic. The final model solution, selected from 29 alternative combinations of the model parameters using Mallows's Cp metric, revealed a statistically significant deterministic trend, 0.40 ± 0.03 °C/c (p < 0.01), and acceleration, 0.67 ± 0.11 °C/c2 (p < 0.01) explaining 33% of the global sea surface temperature variations. The combined yearly trend and acceleration in global sea surface temperature as predicted by the model, exhibit a strong correlation with the yearly increase in the global CO2 concentrations observed during the 20th century.