Conventional Stepwise Regression Research Articles

Prediction of the Compressive Strength of Concrete Admixed with Metakaolin Using Gene Expression Programming

One of the problems of optimization of concrete is to formulate a mathematical equation that shows the relationship between the various constituents of concrete and its properties. In this work, modelling of the compressive strength of concrete admixed with metakaolin was carried out using the Gene Expression Programming (GEP) algorithm. The dataset from laboratory experimentation was used for the analysis. The mixture proportions were made of three different water/binder ratios (0.4, 0.5, and 0.6), and the grades of concrete produced were grade M15 and M20. The compressive strength of the concrete was determined after 28 days of curing. The parameters used in the GEP algorithm are the input variables which include cement content, water, metakaolin content, and fine and coarse aggregate, while the response was designated as the compressive strength. The model was trained and tested using the parameters. The R‐square value from the GEP algorithm was compared with the use of conventional stepwise regression analysis. With a coefficient of determination (R‐square value) of 0.95, the GEP algorithm has shown to be a good alternative for modelling concrete compressive strength.

Time series modeling of the ring laser gyroscope's bias considering the temperature delay effect.

Due to the temperature delay effect, the coefficients of the traditional ring laser gyroscope's (RLG) bias temperature model usually change with environmental temperature. In order to improve the applicability of the temperature model in complex temperature-varying environments, a modified RLG bias modeling method based on the temperature delay effect is proposed. The time series model (TSM), whose coefficients are independent of the environmental temperature variation, is established through theoretical analysis according to the temperature delay effect. The forecasting accuracy of the proposed method is compared with the conventional stepwise regression model (SRM) when both the temperature and temperature-varying rate exceed their boundaries. The experimental results indicate that the proposed TSM can overcome the defect that the compensation accuracy will decline or even diverge when outside the boundaries of temperature and temperature-varying rate. Therefore, the TSM is more suitable for the RLG bias temperature modeling in complex temperature-varying environments.

A stepwise regression algorithm for high-dimensional variable selection

We propose a new stepwise regression algorithm with a simple stopping rule for the identification of influential predictors and interactions among a huge number of variables in various statistical models. Like conventional stepwise regression, at each forward selection step, a variable is included in the current model if the test statistic of the enlarged model with the predictor against the current model has the minimum -value among all the candidates and is smaller than a predetermined threshold. Instead of using conventional information types of criteria, the threshold is determined by a lower percentile of the beta distribution. We conducted extensive simulation studies to evaluate the performance of the proposed algorithm for various statistical models and found it to be very competitive and robust compared with several popular high-dimensional variable selection methods.

Modeling of Dissolved Oxygen Applying Stepwise Regression and a Template-Based Fuzzy Logic System

This paper develops a template-based fuzzy inference system (TFIS) capable of simulating the dissolved oxygen (DO) concentration of an example stream by using daily data (2009–2012). Stepwise regression (SR) analysis and Mallows’ Cp statistic were employed to select the best set of independent parameters for the input vector of the TFIS and the regressive models. The most effective inputs were determined for temperature and specific conductivity (P-value=0.000), whereas flow rate (P-value=0.002) and pH (P-value=0.004) were found to be less effective parameters. The TFIS and SR models undersimulated the magnitude of high DO concentrations (>12.5 mg/L), whereas the low and medium DO concentrations were oversimulated. However, they were closer to the observed data. A comparison of the prediction accuracy of the TFIS and SR methods indicated that the TFIS approach was more accurate in simulating DO concentrations, except for low concentrations of DO (<10 mg/L). The TFIS method was found to be superior to the conventional SR model.

Stepwise Paring down Variation for Identifying Influential Multi-factor Interactions Related to a Continuous Response Variable

Although several model-based methods are promising for the identifica- tion of influential single factors and multi-factor interactions, few are widely used in real applications for most of the model-selection procedures are complex and/or infeasible in computation for high-dimensional data. In particular, the ability of the methods to reveal more true factors and fewer false ones often relies heavily on the selection of appropriate values of tuning parameters, which is still a difficult task to practical analysts. This article provides a simple algorithm modified from stepwise forward regression for the identification of influential factors. Instead of keeping the identified factors in the next models for adjustment in stepwise regression, we pro- pose to subtract the effects of identified factors in each run and always fit a single- term model to the effect-subtracted responses. The computation is lighter as the pro- posed method only involves calculations of a simple test statistic; and therefore it could be applied to screen ultrahigh-dimensional data for important single factors and multi-factor interactions. Most importantly, we have proposed a novel stopping rule of using a constant threshold for the simple test statistic, which is different from the conventional stepwise regression with AIC or BIC criterion. The performance of the new algorithm has been confirmed competitive by extensive simulation studies com- pared to several methods available in R packages, including the popular group lasso, surely independence screening, Bayesian quantitative trait locus mapping methods and others. Findings from two real data examples, including a genome-wide associ- ation study, demonstrate additional useful information of high-order interactions that can be gained from implementing the proposed algorithm.

Quantitative calibration of multi-component systems with a known range of possibly co-existing species

The quantitative calibration of multi-component spectrophotometric systems with a known range of possibly co-existing species was studied. A modified stepwise regression method (MSR) was used for treating such systems. Compared with conventional stepwise regression (CSR), the MSR method does not use an F-test in the variable selection process and the result of selection is an optimum sequence of regression equations with all possible numbers of variables. The Akaike information criterion ( AIC) was used for the evaluation of a variable's contribution in the stepwise process and as a criterion for choosing the best equation from the optimum sequence. A numerical example is treated to show the essential difference between MSR and CSR and how MSR works. Spectrophotometric data for real analytical systems were treated by the proposed method, and the results of simultaneous detection and determination were satisfactory.

Modeling and variable selection in epidemiologic analysis.

This paper provides an overview of problems in multivariate modeling of epidemiologic data, and examines some proposed solutions. Special attention is given to the task of model selection, which involves selection of the model form, selection of the variables to enter the model, and selection of the form of these variables in the model. Several conclusions are drawn, among them: a) model and variable forms should be selected based on regression diagnostic procedures, in addition to goodness-of-fit tests; b) variable-selection algorithms in current packaged programs, such as conventional stepwise regression, can easily lead to invalid estimates and tests of effect; and c) variable selection is better approached by direct estimation of the degree of confounding produced by each variable than by significance-testing algorithms. As a general rule, before using a model to estimate effects, one should evaluate the assumptions implied by the model against both the data and prior information.

FRACTURE FORCE, HARDNESS AND BRITTLENESS IN CRISP BREAD, WITH A GENERALIZED REGRESSION ANALYSIS APPROACH TO INSTRUMENTAL‐SENSORY COMPARISONS

AbstractFlexure/compression data and sensory judgements of breaking force, hardness and brittleness were obtained for 8 brands of crisp bread, and compared with crushing vibration data obtained in another study for 6 of these brands.Besides relating instrumental and sensory data to each other by ordinary correlation analysis, a generalized regression analysis approach was tried as an alternative to using conventional stepwise regression as a prediction tool. This approach involved the checking of all possible combinations of regression variables, combined up to 4 at a time by certain composition rules. The results showed that there was no ‘best solution’ but rather a whole set of equally well or almost equally well fitting equations.