Box-Cox Transformation Research Articles

Gradient Boosting Machine, Random Forest dan Light GBM untuk Klasifikasi Kacang Kering

Bean seed classification is critical in determining the quality of beans. Previously, the same dataset was tested using the MLP, SVM, KNN, and DT algorithms, with SVM producing the best results. The purpose of this study is to determine the most effective model through the use of the BoxCox transformation selection feature and the random forest (RF) algorithm, as well as the gradient boosting machine (GBM), light GBM, and repeated k-folds evaluation model. The bean dataset is available on the UCI Repository website. The BoxCox transformation and repeated k-folds improved the classification prediction's accuracy. The model is used in the optimal training phase for a random forest with decision tree parameters 50 and depth 10, a gradient boosting machine model with a learning rate of 1, and a light gradient boosting machine model with a learning rate of 0.5 and estimator of 500. The best training accuracy results are obtained with light GBM. which is 99 percent accurate, but only 91 percent accurate in terms of validation. According research, the Barbunya, Bombay, Cali, Dermason, Horoz, Seker, and Sira beans classes provided accuracy values of 91 percent, 100 percent, 92 percent, 92 percent, 95 percent, 94 percent, and 84 percent, respectively.

System reliability assessment of ductile frame structures using methods of moment

Reliability assessment of ductile frame structures in a systematic manner has remained a challenging issue because of the difficulties in searching for important failure modes and evaluating the system probability of failure stemmed from these important modes. In this paper, based on the Box-Cox transformation, a new failure mode independent performance function with the probability distribution of weak non-normality is proposed for the system reliability assessment of ductile frame structures. An efficient approach is then developed for estimating the failure probability of the proposed performance function, which includes two steps: first, the point-estimate method based on hybrid dimension-reduction integrated with structural limit analysis is developed to evaluate the first four central moments (i.e., mean, standard deviation, skewness, and kurtosis) of the proposed performance function; next, the system probability of failure corresponding to the proposed performance function is then estimated using the moment-based reliability method. Three numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method, where the method of subset simulation is employed for comparison. It can be concluded that the developed methodology successfully overcomes the two difficulties including the identification of important failure modes and the evaluation of system probability of failure stemmed from these important modes in system reliability assessment of ductile frame structures.

Comparison of 8 methods for univariate statistical exclusion of pathological subpopulations for indirect reference intervals and biological variation studies

BackgroundIndirect reference intervals and biological variation studies heavily rely on statistical methods to separate pathological and non-pathological subpopulations within the same dataset. In recognition of this, we compare the performance of eight univariate statistical methods for identification and exclusion of values originating from pathological subpopulations. MethodsThe eight approaches examined were: Tukey’s rule with and without Box-Cox transformation; median absolute deviation; double median absolute deviation; Gaussian mixture models; van der Loo (Vdl) methods 1 and 2; and the Kosmic approach. Using four scenarios including lognormal distributions and varying the conditions through the number of pathological populations, central location, spread and proportion for a total of 256 simulated mixed populations. A performance criterion of ± 0.05 fractional error from the true underlying lower and upper reference interval was chosen. ResultsOverall, the Kosmic method was a standout with the highest number of scenarios lying within the acceptable error, followed by Vdl method 1 and Tukey’s rule. Kosmic and Vdl method 1 appears to discriminate better the non-pathological reference population in the case of log-normal distributed data. When the proportion and spread of pathological subpopulations is high, the performance of statistical exclusion deteriorated considerably. DiscussionsIt is important that laboratories use a priori defined clinical criteria to minimise the proportion of pathological subpopulation in a dataset prior to analysis. The curated dataset should then be carefully examined so that the appropriate statistical method can be applied.

Frequency-based ensemble forecasting model for time series forecasting

The M4 forecasting competition challenged the participants to forecast 100,000 time series with different frequencies: hourly, daily, weekly, monthly, quarterly, and yearly. These series come mainly from the economic, finance, demographics, and industrial areas. This paper describes the model used in the competition, which is a combination of statistical methods, namely auto-regressive integrated moving-average, exponential smoothing (ETS), bagged ETS, temporal hierarchical forecasting method, Box-Cox transformation, ARMA errors, Trend and Seasonal components (BATS), and Trigonometric seasonality BATS (TBATS). Forty-nine submissions were evaluated by the organizers and compared with 12 benchmarks and standards for comparison forecasting methods. Based on the results, the proposed model is listed among the 17 submissions that outperform the 12 benchmarks and standards for comparison forecasting methods, ranked 15th on average and 4th with the weekly time series. In addition, a further comparison was conducted between the proposed model and other forecasting methods on forecasting EUR/USD exchange rate and Bitcoin closing price time series. It is apparent from the results that the proposed model can produce accurate results compared to many forecasting methods.

A NONLINEAR REGRESSION MODEL TO ESTIMATE THE SIZE OF WEB APPS CREATED USING THE CAKEPHP FRAMEWORK

Context. The problem of estimating the software size in the early stage of a software project is important because a software size estimate is used for predicting the software development effort, including Web apps created using the CakePHP framework. The object of the study is the process of estimating the size of Web apps created using the CakePHP framework. The subject of the study is the nonlinear regression models to estimate the size of Web apps created using the CakePHP framework.
 Objective. The goal of the work is the building the nonlinear regression model with three predictors for estimating the size of Web apps created using the CakePHP framework on the basis of the Box-Cox four-variate normalizing transformation to increase the confidence in early size estimation of these apps.
 Method. The model, confidence and prediction intervals of multiply nonlinear regression to estimate the size of Web apps created using the CakePHP framework are constructed based on the Box-Cox multivariate normalizing transformation for non-Gaussian data with the help of appropriate techniques. The techniques to build the models, confidence, and prediction intervals of nonlinear regressions are based on the multiple nonlinear regression analysis using the multivariate normalizing transformations. The techniques allow taking into account the correlation between dependent and independent variables in the case of normalization of multivariate non-Gaussian data. In general, this leads to a reduction of the mean magnitude of relative error, the widths of the confidence, and prediction intervals in comparison with nonlinear models constructed using univariate normalizing transformations.
 Results. Comparison of the constructed model with the nonlinear regression models based on the decimal logarithm and the BoxCox univariate transformation has been performed.
 Conclusions. The nonlinear regression model with three predictors to estimate the size of Web apps created using the CakePHP framework is constructed on the basis of the Box-Cox four-variate transformation. This model, in comparison with other nonlinear regression models, has a larger multiple coefficient of determination, a smaller value of the mean magnitude of relative error and smaller widths of the confidence and prediction intervals. The prospects for further research may include the application of other multivariate normalizing transformations and data sets to construct the nonlinear regression model to estimate the size of Web apps created using the other frameworks.

Characteristics of Ordinary Portland Cement Paste Containing Rice Husk Ash and Conplast

An experimental investigation on rice husk ash (RHA) and Conplast SP 430 (CP-admixture) was carried out to evaluate their effects on the paste characteristics (soundness, consistency, initial and final setting times). The cement content used was 300g and the brand was ‘Ashaka’ Portland cement conforming to BS EN 12 1973. Various combinations of the mixtures OPC-RHA-CP-admixture were used to establish performance characteristics of the pastes. Statistical characteristics, and linear regression models (no-transformation, λ = 0.5, and Box-Cox transformation) were developed on the experimental data for decisions on their performances.

Improvement of Misclassification Rates of Classifying Objects under Box Cox Transformation and Bootstrap Approach

Discrimination and classification rules are based on different types of assumptions. Also, all most statistical methods are based on some necessary assumptions. Parametric methods are the best choice if it follows all the underlying assumptions. When assumptions are violated, parametric approaches do not provide a better solution and nonparametric techniques are preferred. After Box-Cox transformation, when assumptions are satisfied, parametric methods provide fewer misclassification rates. With this problem in mind, our concern is to compare the classification accuracy of parametric and non-parametric approaches with the aid of Box-Cox transformation and Bootstrapping. We carried Support Vector Machines (SVMs) and different discrimination and classification rules to classify objects. The attention is to critically compare the SVMs with Linear discrimination Analysis (LDA), and Quadratic discrimination Analysis (QDA) for measuring the performance of these techniques before and after Box-Cox transformation using misclassification rates. From the apparent error rates, we observe that before Box-Cox transformation, SVMs perform better than existing classification techniques, on the other hand, after Box-Cox transformation, parametric techniques provide fewer misclassification rates compared to nonparametric method. We also investigated the performances of classification techniques using the Bootstrap approach and observed that Bootstrap-based classification techniques significantly reduce the classification error rate than the usual techniques of small samples. Thus, this paper proposes to apply classification techniques under the Bootstrap approach for classifying objects in case of small sample. A real and simulated datasets application is carried out to see the performance.

Saline-Sodic Soil EC Retrieval Based on Box-Cox Transformation and Machine Learning

Electrical conductivity (EC) is an important index of soil salinity level and an essential factor in judging whether improvement can be made and assessing the improvement, if any. However, saline soils of different types show different spectral characteristic bands, which affects the retrieval precision to a certain extent. To tackle this issue, we present a novel way of modeling. Specifically, we compare the correlation of sensitive bands, multiplication of sensitive bands, and spectral indexes with EC data to determine the optimal input parameters, and take the EC data after Box-Cox transformation as the output. We then try out several machine-learning algorithms to establish retrieval models for soil EC. Validation results show that the model precision increases by 3.23–85.71% after EC data transformation and machine learning models produce 29.41–86.67% higher precision than the linear regression model. Finally, using the optimal model, we retrieve pixel-level (10 m × 10 m) EC for the soil in our study areas. This provides necessary data support for working out soil desalinization initiatives and evaluating the effectiveness of such initiatives.

Prediction Analysis of Shenzhen GDP Based on ARIMA Model and Implementation in R Language

GDP can measure the development level and economic situation of a region to a certain extent. This paper selects the GDP data of Shenzhen from 1980 to 2020, and constructs the Arima(2, 2, 3) model to predict the GDP data in the next 5 years. First, after Box-Cox transformation and difference operation are performed on the selected data, the Augmented Dickey-Fuller (ADF) stationarity test is carried out. Under the condition of passing the ADF test, this paper uses the maximum likelihood method to iteratively estimate the parameters of the model based on the initial value of the least squares’ estimation, and then performs a mixed test on the residual data to verify the validity of the parameters. Finally, the h steps forward method is used to predict the GDP data of Shenzhen in the next five years, and the corresponding confidence interval is obtained. The relative error between the prediction results in 2021 and the actual data is 2.9%, indicating that the prediction results of the model are good and have certain feasibility.

The prediction power of machine learning on estimating the sepsis mortality in the intensive care unit

BackgroundThe prediction of sepsis mortality of intensive care unit (ICU) observations using machine learning (ML) methods is hypothesized to yield better or as good as performance compared to the prognostic scores. This paper aims to show that the accuracy of ML in sepsis mortality estimation can be superior and supportive knowledge to SAPS II, APACHE II, and SOFA (traditional) scores even under small sample restrictions. MethodsThe retrospective collection of data from the patients (n = 200) admitted to ICU of Acibadem Hospital, Istanbul-Turkey, between 2015 and 2020 is utilized to detect the sepsis mortality risk using eight ML methods and a generated ensemble model along with the traditional prognostic scores. The mortality as a decisive indicator is evaluated according to the explanatory variables included quantifying the traditional scores. In the calibration of the data, five different predetermined splits of the random samples are used for the training and the validation of the ML methods. The efficiency of the prediction results of ML methods and the traditional scoring methods are investigated by AUC-ROC curves and other accuracy indicators. Consecutive processes of Box-Cox and Min-Max transformations on data and parameter optimization are performed to increase the efficiency of algorithms. ResultsThe accuracy in the mortality prediction is achieved the best by the Multi-Layer Perceptron algorithm compared to SAPS II and APACHE II methods and is as good as the one with what SOFA predicts. The prediction power of the best performing ML methods for APACHE II, SAPS II, and SOFA are found to be 84.45%, 85.25% and 73.47%, respectively. The ensemble of eight ML methods is found to increase the performance around 2% in APACHE II score. ConclusionsThe outcomes of this study have clinical merits in evaluating the potential use of ML methods in predicting ICU mortality superior to traditional scores APACHE II, SAPS II, and as good as SOFA. Additionally, it explores which of the variables contributing to sepsis mortality risk should be taken as apriori information in treating the patients and requires fewer number of explanatory variables, with reliable prediction powers even for considerably small sample size data sets.

Hospitalisation costs of primary liver cancer in Australia: evidence from a data-linkage study.

Objective This study aimed to estimate the public hospital costs associated with primary liver cancer (PLC) in the first and second years following the cancer diagnosis. Methods This study linked administrative datasets of patients diagnosed with PLC in Victoria, Australia, from January 2008 to December 2015. The health system perspective was adopted to estimate the direct healthcare costs associated with PLC, based on inpatient and emergency costs. Costs were estimated for the first 12 months and 12-24 months after the PLC diagnosis and expressed in 2017 Australian dollars (A$). The cost estimated was then extrapolated nationally. The linear mixed model with a Box-Cox transformation of the costs was used to explore the relationship between costs and patients' sociodemographic and clinical characteristics. Results For the first 12 months, the total and annual per-patient cost was A$211.4 million and A$63 664, respectively. Costs for the subsequent year were A$49.7 million and A$46 751, respectively. Regarding the cost extrapolation to Australia, the total cost was A$137 million for the first 12 months after notification and A$42.6 million for the period from 12 to 24 months. Higher costs per episode of care were mostly associated with older age, hepatocellular carcinoma type of PLC, metropolitan hospitals, and Asian birth region. Conclusion This study showed the public hospital admission and emergency costs associated with PLC and the substantial economic burden this cancer has placed on the Australian health system.

Reference Interval, Biological Variations and Distribution of Creatinine Level in Fasting Urine: A Cross-sectional Study

Introduction: Serum creatinine, urine creatinine, and rate of urine formation are components of creatinine clearance and are under multiple influences. Of these, urine creatinine has the widest variability, especially in the tropical region. Reference intervals, biological variations, and distributions of urine creatinine in the reference individuals are related and important for clinical interpretations of kidney functions. Aim: To establish the reference intervals, biological variations, and distributions of creatinine in urine formed during morning fasting state from reference individuals in a tropical location. Materials and Methods: This observational cross-sectional study of the sample population was done from January 2017 to November 2021 for the establishment of reference interval. Reference individuals, defined by inclusion and exclusion criteria, were from the population at near sea levels plains, in Thrissur district, Kerala, avoiding the mountainous Western Ghats. Morning fasting, third sample of urine was collected to ensure that the urine collected was formed in the morning (n=156). A second set of 44 urine samples, collected from 10 reference individuals consecutively for 4 to 5 days, was used for estimating the analytical Coefficient of Variation (CVA), within-subject (CVI ), and between-subject (CVG) components of biological variation. Outliers in the creatinine data were identified and removed by the Box-Whisker plot to exclude the subclinical influences that affected the urine creatinine, followed by BoxCox transformation to bring the distribution to Gaussian and reference interval calculations of fasting urine creatinine. Results: As the total sample number was >120, non parametric percentile method was used to calculate the reference interval of 17.14 to 325.89 mg/dL. As the female sample number was between 40 and 120, double-sided, 95% reference interval, based on normal distribution was calculated as 12.41 to 328.71 mg/dL. As the male sample was <50, method of robust calculation was used to define the reference interval of 21.91 to 379.12 mg/dL. The reference interval and biological variation data showed gender differences in the distribution, CVI , and CVG due to lower concentration of fasting urine creatinine in females resulting from lower muscle mass. Conclusion: Reference intervals of creatinine in fasting urine formed in the morning were established. Gender differences were observed in the distribution of data, CVI , and CVG.

Symmetry Analysis of the Uncertain Alternative Box-Cox Regression Model

The asymmetry of residuals about the origin is a severe issue in estimating a Box-Cox transformed model. In the framework of uncertainty theory, there are such theoretical issues regarding the least-squares estimation (LSE) and maximum likelihood estimation (MLE) of the linear models after the Box-Cox transformation on the response variables. Heretofore, only weighting methods for least-squares analysis have been available. This article proposes an uncertain alternative Box-Cox model to alleviate the asymmetry of residuals and avoid λ tending to negative infinity for uncertain LSE or uncertain MLE. Such symmetry of residuals about the origin is reasonable in applications of experts’ experimental data. The parameter estimation method was given via a theorem, and the performance of our model was supported via numerical simulations. According to the numerical simulations, our proposed ‘alternative Box-Cox model’ can overcome the problems of a grossly underestimated lambda and the asymmetry of residuals. The estimated residuals neither deviated from zero nor changed unevenly, in clear contrast to the LSE and MLE for the uncertain Box-Cox model downward biased residuals. Thus, though the LSE and MLE are not applicable on the uncertain Box-Cox model, they fit the uncertain alternative Box-Cox model. Compared with the uncertain Box-Cox model, the issue of a systematically underestimated λ is not likely to occur in our uncertain alternative Box-Cox model. Both the LSE and MLE can be used directly without constructing a weighted estimation method, offering better performance in the asymmetry of residuals.

Electricity‐heat‐gas integrated demand response dependency assessment based on BOXCOX‐Pair Copula model

With the continuous development of Regional Integrated Energy System (RIES), demand response (DR) is composed of diversified loads including electric load, heat load and gas load. Their cross-dependencies reflecting the nonlinear coupling complementary relationship between each load type are one of the key factors to improve multi-energy flow optimisation modelling and utilisation efficiency on the demand side. Accordingly, this paper proposes a DR dependency assessment method considering electricity-heat-gas loads based on the BOXCOX-Pair Copula model. BOXCOX transformation is introduced to convert various probability distribution statistics of electricity-heat-gas loads into Gaussian distributed variables. C-vine Pair Copula is used to characterise an ensemble-of-trees of high-dimensional dependency structure among multi-energy demand modalities. Then the combined model of BOXCOX transformation and C-vine Pair Copula can be employed to determine the complex coupling dependency among electricity-heat-gas loads according to different DR statistics. Some metrics between the original empirical distribution and BOXCOX-Pair Copula distribution are introduced to assess the dependency evaluation precision of the proposed model. Finally, the novel dependency assessment model is numerically tested utilising the electricity load, heat load and gas load data sequences in a real RIES. The results illustrate that the cross-dependency of electricity-heat-gas integrated DR based on the BOXCOX-C-vine copula model is closer to that of actual sample data, which verify the effectiveness and superiority of the proposed approach.

A modified approach to determine suspended sediment transport effectiveness in Indian rivers

Transport Effectiveness (TE) of a discharge is defined as the product of the frequency of discharge and corresponding sediment transport rate. Maximization of TE function helps in finding the “effective discharge (Qe)” which is responsible for the transfer of the majority of sediments over a prolonged period. This approach to determine Qe is famously known as Magnitude-Frequency Analysis (MFA). Conventionally, MFA involves the construction of the TE function by assuming (i) a location-specific probability density function (PDF) for discharge and (ii) power-law relationship between discharge and sediment transport rate. There have been attempts in the past to derive expressions for Qe by assuming positively skewed PDFs for discharge. The present study proposes a modified approach to estimate TE-based Qe for general discharge distribution datasets which alleviates the limitation of assuming a location-specific PDF. The approach involves the transformation of discharge data through Box-Cox transformation and subsequently performing MFA to determine Qe. An expression for the analytical solution of TE-based Qe is derived for the proposed framework of MFA. The robustness of the approach is established through a simulation study by generating discharge data using lognormal, Gamma, and log Pearson type III distributions. In this study, the influence of the hysteresis effect was investigated for total as well as seasonal datasets according to the considerations of the rising and falling stages for 14 stream gauges in South Indian Rivers. The analysis is performed by using the suspended sediment load and discharge data whereas the bedload has been excluded. Subsequently, the estimates of Qe based on the proposed approach (QePA) were computed considering various sediment rating curves fitted for total, seasonal, stage and season-stage based datasets. Finally, the variation of QePA with various catchment descriptors was examined.

MATHEMATICAL MODELLING AS AN ELEMENT OF PLANNING RAIL TRANSPORT STRATEGIES

Effective planning and optimization of rail transport operations depends on effective and reliable forecasting of demand. The results of transport performance forecasts usually differ from measured values because the mathematical models used are inadequate. In response to this applicative need, we report the results of a study whose goal was to develop, on the basis of historical data, an effective mathematical model of rail passenger transport performance that would allow to make reliable forecasts of future demand for this service. Several models dedicated to this type of empirical data were proposed and selection criteria were established. The models used in the study are: the seasonal naive model, the Exponential Smoothing (ETS) model, the exponential smoothing state space model with Box–Cox transformation, ARMA errors, trigonometric trend and seasonal components (TBATS) model, and the AutoRegressive Integrated Moving Average (ARIMA) model. The proposed time series identification and forecasting methods are dedicated to the processing of time series data with trend and seasonality. Then, the best model was identified and its accuracy and effectiveness were assessed. It was noticed that investigated time series is characterized by strong seasonality and an upward trend. This information is important for planning a development strategy for rail passenger transport, because it shows that additional investments and engagement in the development of both transport infrastructure and superstructure are required to meet the existing demand. Finally, a forecast of transport performance in sequential periods of time was presented. Such forecast may significantly improve the system of scheduling train journeys and determining the level of demand for rolling stock depending on the season and the annual rise in passenger numbers, increasing the effectiveness of management of rail transport.

Dimension Reduction via Penalized GLMs for Non-Gaussian Response: Application to Stock Market Volatility

We fit U.S. stock market volatilities on macroeconomic and financial market indicators and some industry level financial ratios. Stock market volatility is non-Gaussian distributed. It can be approximated by an inverse Gaussian (IG) distribution or it can be transformed by Box–Cox transformation to a Gaussian distribution. Hence, we used a Box–Cox transformed Gaussian LASSO model and an IG GLM LASSO model as dimension reduction techniques and we attempted to identify some common indicators to help us forecast stock market volatility. Via simulation, we validated the use of four models, i.e., a univariate Box–Cox transformation Gaussian LASSO model, a three-phase iterative grid search Box–Cox transformation Gaussian LASSO model, and both canonical link and optimal link IG GLM LASSO models. The latter two models assume an approximately IG distributed response. Using these four models in an empirical study, we identified three macroeconomic indicators that could help us forecast stock market volatility. These are the credit spread between the U.S. Aaa corporate bond yield and the 10-year treasury yield, the total outstanding non-revolving consumer credit, and the total outstanding non-financial corporate bonds.

Improving Hotel Room Demand Forecasts for Vienna across Hotel Classes and Forecast Horizons: Single Models and Combination Techniques Based on Encompassing Tests

The present study employs daily data made available by the STR SHARE Center covering the period from 1 January 2010 to 31 January 2020 for six Viennese hotel classes and their total. The forecast variable of interest is hotel room demand. As forecast models, (1) Seasonal Naïve, (2) Error Trend Seasonal (ETS), (3) Seasonal Autoregressive Integrated Moving Average (SARIMA), (4) Trigonometric Seasonality, Box–Cox Transformation, ARMA Errors, Trend and Seasonal Components (TBATS), (5) Seasonal Neural Network Autoregression (Seasonal NNAR), and (6) Seasonal NNAR with an external regressor (seasonal naïve forecast of the inflation-adjusted ADR) are employed. Forecast evaluation is carried out for forecast horizons h = 1, 7, 30, and 90 days ahead based on rolling windows. After conducting forecast encompassing tests, (a) mean, (b) median, (c) regression-based weights, (d) Bates–Granger weights, and (e) Bates–Granger ranks are used as forecast combination techniques. In the relative majority of cases (i.e., in 13 of 28), combined forecasts based on Bates–Granger weights and on Bates–Granger ranks provide the highest level of forecast accuracy in terms of typical measures. Finally, the employed methodology represents a fully replicable toolkit for practitioners in terms of both forecast models and forecast combination techniques.

Early LOC Estimation of Web Apps Created Using Yii Framework by Nonlinear Regression Models

We have performed early LOC estimation of Web applications (apps) created using the Yii framework by three nonlinear regression models with three predictors based on the normalizing transformations. We used two univariate transformations (the decimal logarithm and the Box-Cox transformation) and the Box-Cox four-variate transformation for constructing nonlinear regression models. The nonlinear regression model constructed by the Box-Cox four-variate transformation has better size prediction results compared to other regression ones based on the univariate transformations.

Mapping constrained modulus differences in a highway widening project based on CPTU data and two-dimensional anisotropic geostatistics

Evaluation of differences in the field constrained modulus (Es) is key to controlling differential settlement in highway widening projects. To address this issue, a procedure based on geostatistics that considers two-dimensional soil anisotropy is developed. Regression analysis is used to check trend, and Box-Cox transformation is used to obtain weak stationary residual data. Semi-variograms are used to evaluate the anisotropy of road foundation soil with depth and horizontal distance. The cone tip resistance (qt) profiles of the field were obtained using ordinary Kriging interpolation and verified by cross and independent validation. The results show that road foundation soil has significant anisotropy in the horizontal and depth directions, which is reflected by autocorrelation distances. The low variance and uniform distribution of the interpolation of field qt residuals indicate that piezocone penetration test soundings made in the highway section are sufficient and the prediction results are reliable. Differences in the compressive moduli of old and new road foundations were evaluated through a regional empirical equation. Mapping Es differences can provide guidance for differential settlement control and monitoring design.