Classical Multiple Linear Regression Research Articles

Adaptive neural fuzzy inference systems for the daily flow forecast in Algerian coastal basins

Exceptional hydrological events represent one of the most important natural risks which are responsible for the loss of human lives and material goods. During recent decades, many automated or computerized approaches have been implemented to model this process. However, the complexity of hydrological regimes requires the use of specific tools for dynamical and non-linear systems. In order to model the rainfall–runoff transformation, we propose the employment of an adaptive neural network-based fuzzy inference system to predict the flow at the outlet of Algerian coastal basins. The neural network-based fuzzy inference system can be considered as an unlooped neural network for which each layer is a component of a neuro-fuzzy system. The obtained results show that the performances of neuro-fuzzy models exceed those of neural network models and classical multiple linear regression models.

Erratum to: Ultrahigh dimensional variable selection through the penalized maximum trimmed likelihood estimator

The penalized maximum likelihood estimator (PMLE) has been widely used for variable selection in high-dimensional data. Various penalty functions have been employed for this purpose, e.g., Lasso, weighted Lasso, or smoothly clipped absolute deviations. However, the PMLE can be very sensitive to outliers in the data, especially to outliers in the covariates (leverage points). In order to overcome this disadvantage, the usage of the penalized maximum trimmed likelihood estimator (PMTLE) is proposed to estimate the unknown parameters in a robust way. The computation of the PMTLE takes advantage of the same technology as used for PMLE but here the estimation is based on subsamples only. The breakdown point properties of the PMTLE are discussed using the notion of $$d$$ -fullness. The performance of the proposed estimator is evaluated in a simulation study for the classical multiple linear and Poisson linear regression models.

Annual Rainfall Prediction Using Neuro-Fuzzy and Wavelet Approach

Rainfall prediction has become an integral part of the hydrological model. This paper presents the method of annual rainfall forecasting using wavelet transform and neuro-fuzzy approach based on the past history. The historical data have been decomposed into wavelet domain constitutive sub-series. The behaviour of the wavelet domain constitutive series has been studied based on the statistical analysis. Forecasting performance of the wavelet-coupled model has been compared with classical neuro-fuzzy, neural network and multiple linear regression models. The benchmark result shows that wavelet coupled model produces significantly better results in comparison with the neuro-fuzzy, neural network and regression models.

Effects of meteorological forcing on coastal eutrophication: Modeling with model trees

The exploration of processes leading to coastal eutrophication is a major challenge in ecological research, particularly in light of important new policies such as the European Water Framework Directive. In the present study primary production (in terms of chlorophyll α – chl α) is modeled based on a number of abiotic parameters using model trees (MTs), a machine learning (ML) approach whereby linear regressions are induced within homogeneous subsets of samples (tree leaves). Standardized regression was applied to determine the relative weight of abiotic parameters in the MT tree leaves whereas the efficiency of the MT method in chl α prediction was tested against neural networks (NNs) which is the most frequently used ML approach, and the classical multiple linear regression (MLR). To assess the efficiency of models to describe eutrophication-related responses under different environmental conditions, the methods were applied on a coastal ecosystem affected by terrestrial runoff for two meteorologically contrasting annual cycles: a typical dry ('04–'05) and a typical wet ('09–'10). MTs showed increased predictive power in chl α prediction attributed to the discrimination of input data space into tree leaves, instead of using a uniform space as in NNs and MLR. By grouping samples of each tested annual cycle (wet and dry) on a seasonal basis into discrete groups/leaves, MTs offer a much more explanatory description of ecosystem status than NNs and MLR. The discriminating variables forming tree leaves and the weighing coefficients of Linear Models (LMs) in each leaf provided a useful scaling of abiotic parameters driving chl α dynamics. The MT method is thus proposed as an efficient tool for obtaining insights into ecosystem processes leading to eutrophication events in coastal ecosystems and a useful component in integrated coastal zone management.

Geostatistical modelling of regional bird species richness: exploring environmental proxies for conservation purpose

Identifying spatial patterns in species diversity represents an essential task to be accounted for when establishing conservation strategies or monitoring programs. Predicting patterns of species richness by a model-based approach has recently been recognised as a significant component of conservation planning. Finding those environmental predictors which are related to these patterns is crucial since they may represent surrogates of biodiversity, indicating in a fast and cheap way the spatial location of biodiversity hotspots and, consequently, where conservation efforts should be addressed. Predictive models based on classical multiple linear regression or generalised linear models crowded the recent ecological literature. However, very often, problems related with spatial autocorrelation in observed data were not adequately considered. Here, a spatially-explicit data-set on birds presence and distribution across the whole Tuscany region was analysed. Species richness was calculated within 1 × 1 km grid cells and 10 environmental predictors (e.g. altitude, habitat diversity and satellite-derived landscape heterogeneity indices) were included in the analysis. Integrating spatial components of variation with predictive ecological factors, i.e. using geostatistical models, a general model of bird species richness was developed and used to obtain predictive regional maps of bird diversity hotspots. A meaningful subset of environmental predictors, namely habitat productivity, habitat heterogeneity, combined with topographic and geographic information, were included in the final geostatistical model. Conservation strategies based on the predicted hotspots as well as directions for increasing sampling effort efficiency could be extrapolated by the proposed model.

A Quantitative Structure-Activity Relationship Model

Structure-activity relationships were studied for a series of 46 2.6-dimethyl-3.5-dicabomethoxy-4-phenyl-1.4-dihydropyridine derivatives by means of multiple linear regression (MLR) and artificial neural network (ANN) techniques. The values of log (1/EC50), which represents the 50% effective concentration for blocking the Ca2+ channel of the studied compounds were correlated with the descriptors encoding the chemical structures. Using the pertinent descriptors revealed by the regression analysis, a correlation coefficient of 0.99 (s = 0.23) for the training set (n = 46) was obtained for the ANN using the Levenberg-Marquardt algorithm with a 3-10-1 configuration. The results obtained from this study indicate that the activity of 2.6-dimethyl-3.5-dicabomethoxy-4-phenyl-1.4-dihydropyridine derivatives is strongly dependent on molar refractivity (MR), electronic factors (especially on the connectivity indices (IC0)) and hydrogen-bond donor's (HBD) of the molecule. Comparison of the descriptor's contribution obtained with MLR and ANN models indicates the presence of non-linearity in the data and the interaction effect between them since the efficiency of these descriptors was increased by the ANN model.On the other hand, we have used a new, robust structure-activity mapping technique, a Bayesian-regularized neural network, to develop a quantitative structure-activity relationship (QSAR) model, and the ability of the model was tested by using the cross validation technique. The results show that the method is robust and reliable and gives good results. Comparisons of Bayesian neural net models with those derived by classical MLR model analysis showed its superiority in generalization.

Modeling the removal of hemicellulose from cereal straw at lab-scale using self-organizing maps followed by multiple linear regression

Modeling is widely accepted to be an important tool for developing reactor management and control strategies. A statistical approach based on self-organizing maps (SOMs) followed by multiple linear regression (MLR) was used in this study to model the digestion process of cereal straw. Thus, a black-box modeling strategy was followed in which the reactor was considered as a system that could be described with four input variables ( W, the ratio between straw weight and the volume of NaOH solution; C, concentration of NaOH; T, operating temperature inside the reactor; H, contact time) and a single output variable (DE, the amount of degraded hemicellulose). In order to apply a classical MLR analysis, the original database of 45 cases was divided into two groups: a development data set to build the model and an independent test data set. It is important that both data sets have the same statistical properties and SOM were used for this purpose. Subsequently, a classical MLR analysis was carried out. The model included all candidate inputs ( W, C, T and H) in the equation proposed to model reactor response. Nevertheless, W appeared to be the most relevant variable to explain changes in the DE, and nearly 50% of the overall variability can be attributed to its influence. The proposed model explained 86% of the overall variability, thus making it possible to adopt decision-making strategies during reactor operation under different operating conditions.

A New Approach to Variable Selection Using the TLS Approach

The problem of variable selection is one of the most important model selection problems in statistical applications. It is also known as the subset selection problem and arises when one wants to explain the observations or data adequately by a subset of possible explanatory variables. The objective is to identify factors of importance and to include only variables that contribute significantly to the reduction of the prediction error. Numerous selection procedures have been proposed in the classical multiple linear regression model. We extend one of the most popular methods developed in this context, the backward selection procedure, to a more general class of models. In the basic linear regression model, errors are present on the observations only, if errors are present on the regressors as well, one gets the errors-in-variables model which for Gaussian noise becomes the total-least-squares (TLS) model, this is the context considered here

Identifying cause of quality defect in cheese using qualitative variables in a statistical experimental design

AbstractStatistical experimental design was used to identify the stage or stages in a cheesemaking process that caused a quality defect. A full factorial design with five qualitative variables was constructed and a total of 32 experiments, each representing a unique combination of treatments, were then evaluated by a trained sensory panel. The average score for each sample was used as a response, and classical multiple linear regression (MLR) was used to find the relationship between the treatments (X) and the rate of quality defect (y). Evaluation of the design and the regression coefficients clearly showed that one of the factors, process step 3 (x3) at location B, was mainly responsible for high rates of the quality defect. In addition, process step 5 at location B, especially in combination with process step 2 or 4 at location A or step 3 at location B, increased the rate of quality defect in the cheese. The other factors had little or no effect. Copyright © 2004 John Wiley & Sons, Ltd.

Statistical Prediction of the Presence of Salt-Affected Soils by Using Digitalized Hydrogeological Maps

Since spatial databases created from maps in Geographical Information Systems (GIS) do not typically meet the requirements of multivariate tests such as multiple linear regression analyses, we used novel, more robust statistical techniques for predicting the occurrence of certain categories of a soil map. Based on published maps of salt-affected soils (SASs), (hydro) geological conditions (all at the scale of 1:500,000) and regionalization, we showed that the spatial occurrence of SASs in the Great Hungarian Plain can be predicted with an overall precision of 91; 96% for the SASs and 99% for the non-SASs. When we separated the non-SASs into potential SAS and non-SAS categories, the overall precision was 91%, and 87% for the SASs, 92% for the potential SASs and 94% for the non-SASs. The technique of classification trees proved to be better than the classical Multiple Linear Regression, since it does not have limitations regarding the distribution of the data set created from the maps and because it flexibly provided a possibility for incorporating nominal variables through the previous use of homogeneity analysis by means of alternating least squares (HOMALS). Inside the multidimensional space, the first and most important (regarding spatial extent) splits for the separation of non-salt-affected cases from salt-affected ones were realized in the plane of two variables derived with HOMALS from the map of "Textural classes of near-surface geological formations" and the map of "Dominant ion type of groundwater" combined with the map of "Taxonomical division of the regions of Hungary." The plane of these variables was split into five main bands. The clay band has 70% of SASs and the mixed silty layer was divided to a bicarbonatic one with 12% SAS, and a sulfatic one with 65% SAS cover. The remaining sandy band has few SAS, but the dominance of sulfate in the groundwater indicates a higher cover of SASs and these soils constituted the two last bands. Other variables entering the classification were the groundwater level above sea level and the depth to groundwater.

Vegetation water and dry matter contents estimated from top-of-the-atmosphere reflectance data: A simulation study

Leaf (PROSPECT), soil, canopy (SAIL), and atmosphere (6S) models were coupled and used to create a large set of simulated reflectance spectra with corresponding water content per unit leaf area (C W), dry matter content per unit leaf area (SLW, i.e., the specific leaf weight), leaf area index (LAI), whole canopy water content (C W.LAI), and whole canopy dry matter content (SLW LAI). Multiple linear regression was used to estimate these canopy variables from the simulated satellite reflectance spectra within the 880 2380-nm domain. Our data set was subdivided into calibration and validation subsets to evaluate the predictive power of the relations. Canopy-level variables (C,.LAI,SLWLAI,LAI) were retrieved with a good accuracy, whereas leaf-level variables (C W SLW) were less accurately retrieved. The radiometric resolution of the simulated sensor greatly affected the accuracy of the estimation. Conversely the spectral resolution between 10 and 20 nm was not critical, the largest spectral resolution providing the most accurate estimates because it smoothed the instrument noise. We used multiple linear regression to select between five and eight wave bands for each canopy variable. Several wave bands selected were common to different canopy variables. Therefore, a set of ten wavebands centered on about 890, 1080, 1210, 1290, 1535, 1705, 2035, 2205, 2260, and 2295 nm efficiently allowed reasonable estimates of the variables investigated with varying coefficients for each of the canopy variables. For each variable, neural networks were trained over the wave bands selected by the multiple regression. Results showed better performances than classical multiple linear regression. Shifting the wave bands by 10 or 20 nm when calibrating and testing the networks slightly decreased the accuracy of the estimation. The difference was more pronounced for C W and SLW. Conversely, when equations were generated with the use of the wave bands at their optimal position and validated by using wave bands shifted by 10 or 20 nm, the accuracy of estimation for all variables except LAI was low. These results are discussed with emphasis on the design of future sensors.

QSAR and Molecular Modelling of Catamphiphilic Drugs Able to Modulate Multidrug Resistance in Tumors

AbstractThe Free‐Wilson approach was applied to two groups of catamphiphilic multidrug resistance (MDR) modifiers using classical multiple linear regression (MLR) and genetic algorithms (GA) for feature selection. In the first group (17 thioxanthenes) the side chain length between the ring system and tertiary nitrogen, the type of the tertiary nitrogen substituent and the stereoisomery were found to be significant for anti‐MDR activity both by MLR and GA (r2 = 0.803, predictive power Q2 = 0.652). In the second data set (17 phenothiazines and related drugs) the ring system type, the stereoisomery, the side chain type, and the ring substituent kind in position two contributed significantly (r2 = 0.938 and Q2 = 0.908). The QSAR studies showed a thioxanthene ring with a ‐CF3 substituent in position two, a piperazine moiety with a 4‐bond distance from the ring system and trans‐isomery to be optimal for MDR reversal. Based on these results molecular modeling of trans‐(T) and cis‐flupentixol (C) was performed assuming that the 2 to 3‐fold difference in MDR reversing activity of T compared to C might be related to different preferable conformations in the membrane lipid environment. Among all conformations generated by the SYBYL systematic search routine those comprising local energy minima were selected and optimized with semiempirical quantum chemistry methods. The optimized conformations were compared with 1H‐NMR analysis results on drug conformations in lipid environment, some of them corresponded excellently. The electrostatic and lipophilic fields of T and C were compared to identify molecular properties related to the activity difference. The results demonstrated that T and C could have a different (mirror‐like) orientation entering the lipid bilayer by the ring system suggesting much better fitting of T compared to C to the lipid “MDR‐reversal receptor”.

A comparison of some statistical techniques for road accident analysis

At the TRRL/SWOV Workshop on Accident Analysis Methodology, held in Amsterdam in 1988, the need to establish a methodology for the analysis of road accidents was firmly stated by all participants. Data from different countries cannot be compared because there is no agreement on research methodology, data collection, and analysis. Linear and log-linear models are regularly used for the analysis of such data. This paper discusses the background of these models and the model assumptions. It is stated that two relevant and fundamentally different classes of models exist. However, in most cases the difference between these classes remains implicit. These classes of models are called design oriented and object oriented models. Within the context of linear models, the basic assumptions deal with this distinction and the generalization of linear to log-linear models. It is argued that there are advantages and disadvantages for each choice and that a check on the tenability of a particular model is to be recommended. Two different types of generalized linear models, both object-oriented, are used by SWOV and TRRL for the analysis of accidents of road users or on particular road locations. The qualitative data analysis (QDA) models used at SWOV are primarily descriptive and useful for model exploration. The generalized linear interactive modeling (GLIM) technique used at TRRL has stricter assumptions, but is better suited for model testing. In order to compare these models, a number of analyses has been carried out on roundabout data from TRRL. The outcomes are consistent and highly comparable. The results show that for this kind of data these two types of models are to be preferred over classical multiple linear regression analysis (MLR) and log-linear analysis of contingency tables (LLA). QDA turned out to be the most powerful in data exploration. A QDA analysis showed that the dominant accident type of entering and circulating accidents had a different relation with the road and traffic characteristics of the roundabouts than the other accident types and should be analyzed separately. Furthermore, it was shown by a QDA analysis that the choice of a log-link function was preferable over an identity relation as used in MLR. This log-link function in combination with the choice of a Poisson error distribution results in a GLIM model with parameter estimates and errorbounds for these estimates. The errorbounds can be used as an indication of the reliability of the parameters. It is stated that the combination of QDA and GLIM is most powerful for the analysis of this type of problems.

LIMITATIONS ON THE USE OF THE MULTIPLE LINEAR REGRESSION MODEL

This paper discusses briefly the classic multiple linear regression model and indicates the principal ways in which its assumptions are inadequately met when it is used as a model for prediction purposes in the social sciences. It also considers the damping effects of errors of measurement and of selective sampling on estimates of partial regression and multiple correlation coefficients and describes techniques whereby these effects may in part be overcome.