A test for the slope in the functional measurement error model

Recognition that measurement error in the independent (predictor) variable of data used for regression modeling necessitates special methods of model fitting dates back to the late 1800s. In the ensuing 100 years attention was devoted almost entirely to measurement error in linear regression models, at which time advances in computing opened the door to the nonlinear statistical modeling generally, and to the study of measurement error in nonlinear regression modeling in particular. This article contains an introduction to the problem of measurement error in regression using linear regression measurement error models to illustrate key ideas. It includes a discussion of the types of measurement error commonly studied (classical and Berkson, differential and nondifferential) and how those types arise in practice. A summary of the consequences of ignoring measurement error when analyzing data measured with error is presented, with detailed results given for simple and multiple linear measurement error models. Pointers to the literature on both linear and nonlinear measurement error models are provided.

This study applies quantile regression to model the Body Mass Index (BMI) of 152 students from Delta State Polytechnic in Delta State, Nigeria. The BMI serves as the response variable, while skin fold (SK), feeding habit (FH), feeding frequency (FF), and frequency of exercising (FE) are considered as explanatory variables. A comparison is made between the results obtained from the classical linear regression model and quantile regression models at different quantiles (p = 0.1, 0.25, 0.5, 0.75, and 0.9) to examine the impact of the variables on the students' BMI and assess if the relationships differ across quantiles. The findings reveal significant differences between the classical linear regression and quantile regression models, emphasizing the importance of quantile regression in capturing the nuances of the relationship between variables at different points of the BMI distribution. The study highlights the limitations of the classical linear regression model in providing a comprehensive understanding of the data and underscores the value of quantile regression in enhancing our insights into the relationship between BMI and the considered factors. This research contributes to the broader literature on quantile regression and its applications in exploring BMI and related health issues among students

The effect of population model choice and network topologies on extinction time patterns in dendritic ecological networks

Analyses of variables measured with error are often flawed when measurement error is ignored. An extensive literature on linear measurement error models is available by [1], and more recently, for non-linear measurement error models by [2] and [3]. We investigate problems encountered in the analysis of longitudinal change, where the difference in some outcome variable is modeled on a set of regressor variables in a linear regression model. This type of analysis has become quite popular in biomedical research, and the results are often biased when the outcome variable is measured with error and its observed baseline value is included as a covariate in the fitted model. [4] demonstrated the effects of measurement error in the analysis of change in wall thickness of the common carotid artery. They showed the naive analysis led to erroneous findings due to the measurement error bias, even when the regressor variables were assumed to be measured precisely. In this paper, we present a method-of-moments correction for measurement error bias, provided the measurement error variance is known or can be estimated. This work extends the work of [4] to include regressor variables that are measured with error.

In this chapter, we discuss constrained ordination and related approaches: stepwise selection of a set of explanatory variables, Monte Carlo permutation tests and variance partitioning procedure.

IntroductionThe length of hospital stay (LOHS) caused by COVID-19 has imposed a financial burden, and cost on the healthcare service system and a high psychological burden on patients and health workers. The purpose of this study is to adopt the Bayesian model averaging (BMA) based on linear regression models and to determine the predictors of the LOHS of COVID-19.MethodsIn this historical cohort study, from 5100 COVID-19 patients who had registered in the hospital database, 4996 patients were eligible to enter the study. The data included demographic, clinical, biomarkers, and LOHS. Factors affecting the LOHS were fitted in six models, including the stepwise method, AIC, BIC in classical linear regression models, two BMA using Occam's Window and Markov Chain Monte Carlo (MCMC) methods, and GBDT algorithm, a new method of machine learning.ResultsThe average length of hospitalization was 6.7 ± 5.7 days. In fitting classical linear models, both stepwise and AIC methods (R2 = 0.168 and adjusted R2 = 0.165) performed better than BIC (R2 = 0.160 and adjusted = 0.158). In fitting the BMA, Occam's Window model has performed better than MCMC with R2 = 0.174. The GBDT method with the value of R2 = 0.64, has performed worse than the BMA in the testing dataset but not in the training dataset. Based on the six fitted models, hospitalized in ICU, respiratory distress, age, diabetes, CRP, PO2, WBC, AST, BUN, and NLR were associated significantly with predicting LOHS of COVID-19.ConclusionThe BMA with Occam's Window method has a better fit and better performance in predicting affecting factors on the LOHS in the testing dataset than other models.

We present three different methods based on the conditional mean imputation when binary explanatory variables are incomplete. Apart from the single imputation and multiple imputation especially the so-called pi imputation is presented as a new procedure. Seven procedures are compared in a simulation experiment when missing data are confined to one independent binary variable: complete case analysis, zero order regression, categorical zero order regression, pi imputation, single imputation, multiple imputation, modified first order regression. After a brief theoretical description of the simulation experiment, MSE-ratio, variance and bias are used to illustrate differences within and between the approaches.

Finding a new drug which is both safe and efficient is an expensive and time-consuming endeavour. In particular, establishing the ‘dose-effect relationship’ – how beneficial a drug is at different dosages – can be challenging. Predicting this curve requires gathering experimental data by exposing and recording how cells respond to various levels of the drug. However, extreme values are often observed at low and high dosages, potentially introducing errors that are hard to correct in the prediction process. Yet, these extreme observations are sometimes genuine so researchers cannot just ignore them. To improve dose-effect estimation, Zhou, Liu, Fang et al. developed a new general-purpose approach. It uses advanced statistical modelling to account for extremes in lab data. This strategy outperformed other methods when dealing with these observations while also providing higher efficiency in data analysis with more uniform data in experiments. To facilitate implementation, Zhou, Liu, Fang et al. set up a user-friendly tool baptized ‘REAP’; this free online resource allows scientists without advanced statistical experience to harness the new approach and to perform dose-effect analysis more easily and accurately. This could boost research across many different disciplines that examine the effects of chemicals on cells.

Most of this book concerns the interpretation of regression models, with the understanding that they can be fit to data fairly automatically using R and Bugs. However, it can be useful to understand some of the theory behind the model fitting, partly to connect to the usual presentation of these models in statistics and econometrics. This chapter outlines some of the basic ideas of likelihood and Bayesian inference and computation, focusing on their application to multilevel regression. One point of this material is to connect multilevel modeling to classical regression; another is to give enough insight into the computation to allow you to understand some of the practical computational tips presented in the next chapter. Least squares and maximum likelihood estimation We first present the algebra for classical regression inference, which is then generalized when moving to multilevel modeling. We present the formulas here without derivation; see the references listed at the end of the chapter for more. Least squares The classical linear regression model is y i = X i β + ∊ i , where y and ∊ are (column) vectors of length n , X is a n × k matrix, and β is a vector of length k . The vector β of coefficients is estimated so as to minimize the errors ∊ i .

This paper studies the large-eddy simulation (LES) of isothermal turbulent channel flows. We investigate zero-equation algebraic models without wall function or wall model: functional models, structural models, and mixed models. In addition to models from the literature, new models are proposed and their relevance is examined. Dynamic versions of each type of model are also analyzed. The performance of the subgrid-scale models is assessed using the same finite difference numerical method and physical configuration. The friction Reynolds number of the simulations is 180. Three different mesh resolutions are used. The predictions of large-eddy simulations are compared to those of a direct numerical simulation filtered at the resolution of the LES meshes. The results are more accurate than those of a simulation without model. The predictions of functional eddy-viscosity models can be improved using constant-parameter or dynamic tensorial methods.

Checking the adequacy of functional linear quantile regression model

Here I propose a fundamentally new flexible model to reveal the association between a trait and a set of genetic variants in a genomic region/gene. This model was developed for the situation when original individual-level phenotype and genotype data are not available, but the researcher possesses the results of statistical analyses conducted on these data (namely, SNP-level summary Z score statistics and SNP-by-SNP correlations). The new model was analytically derived from the classical multiple linear regression model applied for the region-based association analysis of individual-level phenotype and genotype data by using the linear compression of data, where the SNP-by-SNP correlations are among the explanatory variables, and the summary Z score statistics are categorized as the response variables. I analytically show that the regional association analysis methods developed within the framework of the classical multiple linear regression model with additive effects of genetic variants can be reformulated in terms of the new model without the loss of information. The results obtained from the regional association analysis utilizing the classical model and those derived using the proposed model are identical when SNP-by-SNP correlations and SNP-level statistics are estimated from the same genetic data.

Count Data in Medical Research: Poisson Regression and Negative Binomial Regression

The profitability of insurance companies has been the focus of several studies within the rise of economies across the countries worldwide. This study aimed to identify determinants of profitability of insurance companies in Ethiopian. The study used nine insurance companies selected by purposive sampling technique among the total 17 insurance companies in Ethiopia from period of 2011 to 2020 based on their establishment. Descriptive, causal research design and quantitative research approach were adopted in carrying out this study. Classical linear regression model under estimation of ordinary least square was employed to identify the determinants of profitability of insurance companies in Ethiopia at 5% level of significance. The classical linear regression model revealed that variable age of the company, tangibility of an asset, size of the company, managerial efficiency, leverage ratio, premium growth and GDP have a positive coefficient relationship with return on asset while loss ratio and inflation have a negative coefficient relationship with return on asset. On the other hand, age of the company size, managerial efficiency, leverage ratio, liquidity ration inflation and premium growth have statistically significant at 5% confidence interval level, whereas the other variables such tangibility of asset and GDP have no statistical significance at 5% confidence interval level. The insurance companies’ previous profit, age of the company, company size, managerial efficiency, leverage ratio, liquidity ratio, loss ratio, premium growth and inflation rate variables are significant key drivers of profitability of Ethiopian insurance companies. Giving due attention to the sector in line with key factors affecting the profitability will improve the overall performance of the insurance companies in Ethiopia.

Beta regression model is used for modeling proportions measured on a continuous scale; its parameters are estimated with the maximum likelihood method. Classical regression models, such as linear regression model and nonlinear regression models like logistic regression are not suitable for such situations. As in linear regression model, the independent variables are assumed to be uncorrelated if this assumption is not met, then the multicollinearity appears. Multicollinearity problem means that there is a near dependency between the independent variables. Biased estimators are commonly used for correcting the multicollinearity problem. In this study, we propose a generalized biased estimator for correcting multicollinearity in beta regression that is generalize beta ridge regression estimator (GBRRE). The performance of the proposed generalized biased estimator is evaluated theoretically via the matrix mean squared errors and the scalar mean squared errors; and practically using a Monte Carlo simulation study. The simulation results show that the optimal shrinkage estimator is K1 and the worst one is K2. Also, the proposed generalized estimator is applied to a real data set of pre-university education students in Egypt during the academic year (2018/2019) and we found the application results agree with the simulation results. Finally based on the results of the simulation study and the application the performance of the suggested generalized biased estimator is better than maximum likelihood estimators.