Assumption Of Constant Variance Research Articles

Thinking Inside the Bounds: Improved Error Distributions for Indifference Point Data Analysis and Simulation Via Beta Regression using Common Discounting Functions

Standard nonlinear regression is commonly used when modeling indifference points due to its ability to closely follow observed data, resulting in a good model fit. However, standard nonlinear regression currently lacks a reasonable distribution-based framework for indifference points, which limits its ability to adequately describe the inherent variability in the data. Software commonly assumes data follow a normal distribution with constant variance. However, typical indifference points do not follow a normal distribution or exhibit constant variance. To address these limitations, this paper introduces a class of nonlinear beta regression models that offers excellent fit to discounting data and enhances simulation-based approaches. This beta regression model can accommodate popular discounting functions. This work proposes three specific advances. First, our model automatically captures non-constant variance as a function of delay. Second, our model improves simulation-based approaches since it obeys the natural boundaries of observable data, unlike the ordinary assumption of normal residuals and constant variance. Finally, we introduce a scale-location-truncation trick that allows beta regression to accommodate observed values of 0 and 1. A comparison between beta regression and standard nonlinear regression reveals close agreement in the estimated discounting rate k obtained from both methods.

Spatial Dependence of Poverty Rate and Socio-Economic Indicators in Nigeria: An Empirical Analysis

This study investigates the spatial dependence between the poverty rate and various socio-economic indicators in Nigeria. The analysis is based on a dataset comprising unique geographic identifiers and the poverty rate along with other relevant variables. Descriptive statistics reveal that the poverty rate exhibits moderate variability with an average of 4.1240. The correlation analysis shows significant relationships between the poverty rate and household size as well as income level, indicating that larger households and higher incomes are associated with higher and lower poverty rates, respectively. Spatial regression models, including Spatial Autoregressive (SAR), Spatial Error (SEM), Spatial Durbin (SDM), and Spatial Autoregressive Conditional (SAC) models, are employed to explore the spatial dependence. Results indicate the presence of spatial clustering and positive autocorrelation in the poverty rate, as indicated by the Moran's I index with a value of 0.3579 (p-value = 0.0012). However, tests for spatial heteroscedasticity do not reveal significant departures from the assumption of constant error variance. The findings suggest that spatial factors play a crucial role in explaining the poverty rate in Nigeria. The positive spatial autocorrelation indicates the presence of localized poverty clusters, emphasizing the importance of considering spatial effects in policy formulation and targeted interventions. The significant relationships between the poverty rate and household size and income level underscore the need for comprehensive strategies to address these socio-economic indicators for poverty reduction.

PEMODELAN INDEKS HARGA PERDAGANGAN BESAR (IHPB) SEKTOR EKSPOR MENGGUNAKAN ARFIMA-GARCH

Indonesia's price index serves as a barometer for the nation's economic condition. One of the Indonesia’s price index is Wholesale Price Index (WPI). WPI is a price index that tracks the average change in wholesale prices over time. Time series analysis can be used for forecasting because WPI is one of the time series data. WPI is long memory, which is a condition in which data from different time periods have a high link despite being separated by a large amount of time. The Autoregressive Fractional Integrated Moving Average (ARFIMA) model can be used to overcome this feature when modeling time series data. The assumption of constant error variance is not fulfilled in the IHPB data analysis, indicating that the data is heteroscedastic. The GARCH (Generalized Auto Regressive Conditional Heteroscedasticity) model is one of the models used to overcome heteroscedasticity. The data used is the export sector of WPI from January 2003 to June 2021. The best model for forecasting WPI is ARFIMA(1,b,2) – GARCH(1,1) with b=0,7345333, and MAPE value is 3,150875%.

A case and framework for expanding the use of model‐free evidence

A case and framework for expanding the use of model‐free evidence

Multivariate change point detection for heterogeneous series

The multivariate change point detection problem has been encountered across various fields. Most approaches to this problem assume the series is homogeneous, i.e., all the coordinates change concurrently. Hence, the specific subset of the coordinates containing the change points cannot be determined. In this work, we propose S-MCPD, which is capable of detecting the position of multivariate change points for heterogeneous series by identifying specific coordinates of those changed. Specifically, the problem is discussed in the context of variable selection and transformed into the form of sparse group lasso. In simulation studies, we compared S-MCPD with four existing methods, inspect, sbs, dc, and cpm. The results showed that the performance of S-MCPD was comparable to that of inspect and was superior to other methods in terms of evaluation metrics. In addition, S-MCPD can determine not only the positions of change points, but also the subset of coordinates containing the change points, while other existing methods are unable to achieve this. Moreover, S-MCPD does not depend on the constant variance assumption and works quite well even when the covariance changes, which makes our method more practical. These are the two important contributions of our work. Finally, we applied S-MCPD to two real-world datasets to show its effectiveness.

Sufficient Dimension Reduction for Poisson Regression

Poisson regression is popular and commonly employed to analyze frequency of occurrences in a fixed amount of time. In practice, data collected from many scientific disciplines tend to grow in both volume and complexity. One characteristic of such complexity is the inherent sparsity in high-dimensional covariates space. Sufficient dimension reduction (SDR) is known to be an effective cure for its advantage of making use of all available covariates. Existing SDR techniques for a continuous or binary response do not naturally extend to count response data. It is challenging to detect the dependency between the response variable and the covariates due to the curse of dimensionality. To bridge the gap between SDR and its applications in count response models, an efficient estimating procedure is developed to recover the central subspace through estimating a finite dimensional parameter in a semiparametric model. The proposed model is flexible which does not require model assumption on the conditional mean or multivariate normality assumption on covariates. The resulting estimators achieve optimal semiparametric efficiency without imposing linearity or constant variance assumptions. The finite sample performance of the estimators is examined via simulations, and the proposed method is further demonstrated in the baseball hitter example and pathways to desistance study.

Estimation and variable selection in joint mean and dispersion models applied to mixture experiments

In industrial experiments, controlling variability is of paramount importance to ensure product quality. Classical regression models for mixture experiments are widely used in industry, however, when the assumption of constant variance is not satisfied, the building of procedures that allow minimizing the variability becomes necessary and other methods of statistical modeling should be considered. In this article, we use the class of generalized linear models (GLMs) to build statistical models in mixture experiments. The GLMs class is general and very flexible, generalizing some of the most important probability distributions, and allows modeling the variability through the methodology of the joint modeling of mean and dispersion (JMMD). This paper shows how the JMMD can be used to obtain models for mean and variance in mixture experiments. We give a comprehensive understanding of the procedures for estimating parameters and selecting variables in the JMMD. The variable selection procedure was adapted for the case of mixture experiments, where the verification of constant dispersion is ensured by the existence of only the constant term in the dispersion model; the absence of the constant term or the existence of any other term in the dispersion model implies non-constant dispersion. A simulation study, considering the most common case of Normal distribution, was used to verify the effectiveness of the proposed variable selection procedure. A practical example from the Food Industry was used to illustrate the proposed methodology.

The re-parameterized inverse Gaussian regression to model length of stay of COVID-19 patients in the public health care system of Piracicaba, Brazil

Among the models applied to analyze survival data, a standout is the inverse Gaussian distribution, which belongs to the class of models to analyze positive asymmetric data. However, the variance of this distribution depends on two parameters, which prevents establishing a functional relation with a linear predictor when the assumption of constant variance does not hold. In this context, the aim of this paper is to re-parameterize the inverse Gaussian distribution to enable establishing an association between a linear predictor and the variance. We propose deviance residuals to verify the model assumptions. Some simulations indicate that the distribution of these residuals approaches the standard normal distribution and the mean squared errors of the estimators are small for large samples. Further, we fit the new model to hospitalization times of COVID-19 patients in Piracicaba (Brazil) which indicates that men spend more time hospitalized than women, and this pattern is more pronounced for individuals older than 60 years. The re-parameterized inverse Gaussian model proved to be a good alternative to analyze censored data with non-constant variance.

Increased Use of Antibiotics in the Intensive Care Unit During Coronavirus Disease (COVID-19) Pandemic in a Brazilian Hospital.

Background: Microbial drug resistance is one of the biggest public health problems. Antibiotic consumption is an essential factor for the emergence and spread of multiresistant bacteria. Therefore, we aimed to analyze the antibiotics consumption in the Intensive Care Unit (ICU), identifying trends in the antibiotics use profile and microbiological isolates throughout the COVID-19 pandemic. Methods: We performed this retrospective observational study in intensive care units of a Brazilian tertiary hospital from January 2019 to December 2020. The primary outcome was antimicrobial consumption in the ICU, measured by defined daily doses (DDDs) per 100 bed-days. As a secondary outcome, bacterial infections (microbiological isolates) were calculated in the same fashion. Outcomes trends were analyzed using Joinpoint regression models, considering constant variance (homoscedasticity) and first-order autocorrelation assumptions. A monthly percent change (MPC) was estimated for each analyzed segment. Results: Seven thousand and nine hundred fifty-three patients had data available on prescribed and received medications and were included in the analyses. Overall, the use of antibiotics increased over time in the ICU. The reserve group (World Health Organization Classification) had an increasing trend (MPC = 7.24) from February to April 2020. The azithromycin consumption (J01FA) increased rapidly, with a MPC of 5.21 from January to April 2020. Polymyxin B showed a relevant increase from March to June 2020 (MPC = 6.93). The peak of the antibiotic consumption of Reserve group did not overlap with the peak of the pathogenic agents they are intended to treat. Conclusion: Overall antimicrobial consumption in ICU has increased in the context of the COVID-19 pandemic. The peaks in the antimicrobial’s use were not associated with the rise of the pathogenic agents they intended to treat, indicating an empirical use, which is especially concerning in the context of treating multidrug-resistant (MDR) infections. This fact may contribute to the depletion of the therapeutic arsenal for MDR treatment.

Prediction–variance relation in a state-space fish stock assessment model

AbstractThe state-space assessment model (SAM) is extended by allowing a functional relationship between observation variance and the corresponding prediction. An estimated relationship between observation variance and predicted value for each individual observation allows the model to assign smaller (or larger) variance to predicted larger log-observations. This relation is different from the usual assumption of constant variance of log-observations within age groups. The prediction–variance link is implemented and compared to the usual constant variance assumption for the official assessments of North East Arctic cod and haddock. For both of these stocks, the prediction–variance link is found to give a significant improvement.

Statistical detection of synergy: New methods and a comparative study.

Combination therapies are increasingly adopted as the standard of care for various diseases to improve treatment response, minimise the development of resistance and/or minimise adverse events. Therefore, synergistic combinations are screened early in the drug discovery process, in which their potential is evaluated by comparing the observed combination effect to that expected under a null model. Such methodology is implemented in the BIGL R-package which allows for a quick screening of drug combinations. We extend the meanR and maxR tests from this package by allowing non-constant variance of the responses and by extending the list of null models (Loewe, Loewe2, HSA, Bliss). These new tests are evaluated in a comprehensive simulation study under various models for additivity and synergy, various monotherapeutic dose-response models (complete, partial and incomplete responders) and various types of deviation from the constant variance assumption. In addition, the BIGL package is extended with bootstrap confidence intervals for the individual off-axis points and for the overall synergy strength, which were demonstrated to have reliable coverage and can complement the existing tests. We conclude that the differences in performance between the different null models are small and depend on the simulation scenario. As a result, the choice of null model should be driven by expert knowledge on the particular problem. Finally, we demonstrate the new features of the BIGL package and the difference between the synergy models on a real dataset from drug discovery. The BIGL package is available at CRAN (https://CRAN.R-project.org/package=BIGL) and as a Shiny app (https://synergy.openanalytics.eu/app).

A Weighted-Least-Squares Estimation Approach to Comparing Trends in Age-Adjusted Cancer Rates Across Overlapping Regions

Li and Tiwari (2008) recently developed a corrected Z-test statistic for comparing the trends in cancer age-adjusted mortality and incidence rates across overlapping geographic regions, by properly adjusting for the correlation between the slopes of the fitted simple linear regression equations. One of their key assumptions is that the error variances have unknown but common variance. However, since the age-adjusted rates are linear combinations of mortality or incidence counts, arising naturally from an underlying Poisson process, this constant variance assumption may be violated. This paper develops a weighted-least-squares based test that incorporates heteroscedastic error variances, and thus significantly extends the work of Li and Tiwari. The proposed test generally outperforms the aforementioned test through simulations and through application to the age-adjusted mortality data from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute.

Modeling inter-trial variability of pointing movements during visuomotor adaptation

Trial-to-trial variability during visuomotor adaptation is usually explained as the result of two different sources, planning noise and execution noise. The estimation of the underlying variance parameters from observations involving varying feedback conditions cannot be achieved by standard techniques (Kalman filter) because they do not account for recursive noise propagation in a closed-loop system. We therefore developed a method to compute the exact likelihood of the output of a time-discrete and linear adaptation system as has been used to model visuomotor adaptation (Smith et al. in PLoS Biol 4(6):e179, 2006), observed under closed-loop and error-clamp conditions. We identified the variance parameters by maximizing this likelihood and compared the model prediction of the time course of variance and autocovariance with empiric data. The observed increase in variability during the early training phase could not be explained by planning noise and execution noise with constant variances. Extending the model by signal-dependent components of either execution noise or planning noise showed that the observed temporal changes of the trial-to-trial variability can be modeled by signal-dependent planning noise rather than signal-dependent execution noise. Comparing the variance time course between different training schedules showed that the signal-dependent increase of planning variance was specific for the fast adapting mechanism, whereas the assumption of constant planning variance was sufficient for the slow adapting mechanisms.

The macroeconomic determinants of stock price fluctuations in Amman Stock Exchange

The purpose of this study is to identify the key macroeconomic variables that affected stock price fluctuations in Amman Stock Exchange during the period 1980-2018. Using Augmented Dickey-fuller (ADF) test, it was found that the variables did not have the same degree of integration. According to Breusch-Pagan-Godfrey test, the residuals violated the constant variance assumption under Ordinary Least Square (OLS) model. Therefore, the study employed Generalized Autoregressive Conditional Heteroskedasticity (GARCH) methodology to analyze the model after taking the first difference of natural logarithm for all variables to be stationary at the same level and to show the fluctuation in the variables. It was found that fluctuations in portfolio investment and in industrial production index are statically significant to lead fluctuations in the stock price index in Amman Stock Exchange and they follow the same direction, whereas fluctuations in real effective exchange rate, real interest rate, and Brent crude oil prices were statically significant to lead fluctuations in the stock price index but in the opposite direction.

Fuzzy Clustering Based Regression Model Forecasting: Weighted By Gustafson-Kessel Algorithm

Regression analysis is one of the well-known methods of multivariate analysis and it is efficiently used in many research fields, especially forecasting problems. In order for the results of regression analysis to be effective, some assumptions must be valid. One of these assumptions is the heterogeneity problem. One of the methods used to solve this problem is the weighted regression method. Weighted regression is a method that you can use when the least squares assumption of constant variance in the residuals is violated (heteroscedasticity). With the correct weight, this procedure minimizes the sum of weighted squared residuals to produce residuals with a constant variance (homoscedasticity). In this study, Gustafson-Kessel(GK) method is used to determine weights for weighted regression analysis. GK method is based on the minimization of the sum of weighted squared distances between the data points and the cluster centers. With the fuzzy clustering method, each observation value is bound to the specified clusters in a specific order of membership. These membership degrees will be calculated as weights in the weighted regression analysis and estimation work will be done. In application, 5 simulated and 1 real time data was estimated by the proposed method. The results were interpreted by comparing with Robust Methods (M and S estimator) and Weighted with FCM Regression analysis.

Generalized kernel-based inverse regression methods for sufficient dimension reduction

The linearity condition and the constant conditional variance assumption popularly used in sufficient dimension reduction are respectively close to elliptical symmetry and normality. However, it is always the concern about their restrictiveness. In this article, we give systematic studies to provide insight into the reasons why the popularly used sliced inverse regression and sliced average variance estimation need these conditions. Then we propose a new framework to relax these conditions and suggest generalized kernel-based inverse regression methods to handle a class of mixture multivariate unified skew-elliptical distributions.

Time Series Analysis of Monthly Average Temperature and Rainfall Using Seasonal ARIMA Model (in Case of Ambo Area, Ethiopia)

Forecasting mean temperature and rainfall is an important for planning and formulating agricultural strategies. Thus, this paper, try to analyze and forecast monthly mean temperature and rainfall in Ambo area on the data from January 2012 to March 2019. From graphical analysis on time plot and ACF, the series seems to have a seasonal component. For that purpose, a Seasonal Autoregressive Integrated Moving Average (SARIMA) models were used to estimate and forecast the average monthly temperature and rainfall in the Ambo area, Ethiopia. Among the competitive tentative model, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 model are the best time series model for fitting and forecasting mean temperature and rainfall, respectively. Moreover, the model diagnostic test on the residuals of SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 on mean temperature and rainfall satisfies the randomness, independency, normality and constant variance (homoscedasticity) assumptions. Finally, SARIMA (2, 0, 1) (2, 0, 1) 12 and SARIMA (1, 0, 1) (1, 0, 1) 12 were used to forecast mean of monthly temperature and rainfall from the period April 2019 to March 2023.

Error Models for the Kinetic Evaluation of Chemical Degradation Data

In the kinetic evaluation of chemical degradation data, degradation models are fitted to the data by varying degradation model parameters to obtain the best possible fit. Today, constant variance of the deviations of the observed data from the model is frequently assumed (error model “constant variance”). Allowing for a different variance for each observed variable (“variance by variable”) has been shown to be a useful refinement. On the other hand, experience gained in analytical chemistry shows that the absolute magnitude of the analytical error often increases with the magnitude of the observed value, which can be explained by an error component which is proportional to the true value. Therefore, kinetic evaluations of chemical degradation data using a two-component error model with a constant component (absolute error) and a component increasing with the observed values (relative error) are newly proposed here as a third possibility. In order to check which of the three error models is most adequate, they have been used in the evaluation of datasets obtained from pesticide evaluation dossiers published by the European Food Safety Authority (EFSA). For quantitative comparisons of the fits, the Akaike information criterion (AIC) was used, as the commonly used error level defined by the FOrum for the Coordination of pesticide fate models and their USe(FOCUS) is based on the assumption of constant variance. A set of fitting routines was developed within the mkin software package that allow for robust fitting of all three error models. Comparisons using parent only degradation datasets, as well as datasets with the formation and decline of transformation products showed that in many cases, the two-component error model proposed here provides the most adequate description of the error structure. While it was confirmed that the variance by variable error model often provides an improved representation of the error structure in kinetic fits with metabolites, it could be shown that in many cases, the two-component error model leads to a further improvement. In addition, it can be applied to parent only fits, potentially improving the accuracy of the fit towards the end of the decline curve, where concentration levels are lower.

Analyzing pre-post designs using the analysis of covariance models with and without the interaction term in a heterogeneous study population.

Pre-post parallel group randomized designs have been frequently used to compare the effectiveness of competing treatment strategies and the ordinary least squares (OLS)-based analysis of covariance model (ANCOVA) is a routine analytic approach. In many scenarios, the associations between the baseline and the post-randomization scores could differ between the treatment and control arms, which justifies the inclusion of the treatment by baseline score interaction in ANCOVA. This heterogeneity may also cause heteroscedastic errors in ANCOVA. In this study, we compared the performances of the ANCOVA models with and without the interaction term in estimating the marginal treatment effect in a heterogeneous two-arm pre-post design. We explored the relationship between the two nested ANCOVA models from the perspective of an omitted variable bias problem and further revealed the reasons why the usual ANCOVA may fail in heterogeneous scenario through the discussion of the three types of variances associated with the ANCOVA estimators of the marginal treatment effect: the target unconditional variance, the conditional variance allowing unequal error variances, and the OLS conditional variance derived under the assumption of constant error variance. We demonstrated analytically and with simulations that the proposed heteroscadastic-consistent variance estimators provide valid unconditional inference for ANCOVA, and the ANCOVA interaction model is more powerful than the ANCOVA main effect model when a design is unbalanced.

A residual-based multivariate constant correlation test

We propose a new multivariate constant correlation test based on residuals. This test takes into account the whole correlation matrix instead of the considering merely marginal correlations between bivariate data series. In financial markets, it is unrealistic to assume that the marginal variances are constant. This motivates us to develop a constant correlation test which allows for non-constant marginal variances in multivariate time series. However, when the assumption of constant marginal variances is relaxed, it can be shown that the residual effect leads to nonstandard limit distributions of the test statistics based on residual terms. The critical values of the test statistics are not directly available and we use a bootstrap approximation to obtain the corresponding critical values for the test. We also derive the limit distribution of the test statistics based on residuals under the null hypothesis. Monte Carlo simulations show that the test has appealing size and power properties in finite samples. We also apply our test to the stock returns in Euro Stoxx 50 and integrate the test into a binary segmentation algorithm to detect multiple break points.