Assumptions Of Linear Regression Research Articles

Water quality predictions through linear regression - A brute force algorithm approach

Linear regression is one of the oldest statistical modeling approaches. Still, it is a valuable tool, particularly when it is necessary to create forecast models with low sample sizes. When researchers use this method and have numerous potential regressors, choosing the group of regressors for a model that fulfills all the required assumptions can be challenging. In this sense, the authors developed an open-source Python script that automatically tests all the combinations of regressors under a brute-force approach. The output displays the best linear regression models, regarding the thresholds set by users for the required assumptions: statistical significance of the estimations, multicollinearity, error normality, and homoscedasticity. Further, the script allows the selection of linear regressions with regression coefficients according to the user’s expectations. This script was tested with an environmental dataset to predict surface water quality parameters based on landscape metrics and contaminant loads. Among millions of possible combinations, less than 0.1 % of the regressor combinations fulfilled the requirements. The resulting combinations were also tested in geographically weighted regression, with similar results to linear regression. The model's performance was higher for pH and total nitrate and lower for total alkalinity and electrical conductivity.•A Python script was developed to find the best linear regressions within a dataset.•Output regressions are automatically selected based on regression coefficient expectations set by the user and the linear regression assumptions.•The algorithm was successfully validated through an environmental dataset.

A pilot study of HEXACO dimensions and therapeutic change as potential predictors of negative effects of psychotherapy

Objectives. The aim of this study was to explore possible relationships between the HEXACO personality traits (i.e., Extraversion, Emotionality, Honesty-Humility, Agreeableness, Conscientiousness, Openness to experience) and the negative effects of psychotherapy.Sample and settings. A total of 148 respondents answered an online survey. Descriptive and multivariate regression analyses were performed.Hypotheses. Clients’ personality traits were expected to predict the negative effects of psychotherapy.Results. Extraversion was the strongest negative predictor of negative effects, serving as a protective factor against the worsening of symptoms, hopelessness, and stigma. Furthermore, Emotionality was related to a lower perceived quality of psychotherapy, Conscientiousness was related to hopelessness, and Openness to experience served as a protector against dependency. Limitations. The findings are based on a one-time retrospective measurement and a convenience sample. The results must be interpreted with caution because the assumptions of linear regression were not fulfilled.

Impact of Temperature and Population Size on the Spread of COVID-19 in Nigeria: A Robust Regression Approach

Background: COVID-19, a global pandemic ravaging many countries, shares some semblances with influenza, whose transmission can be affected by many factors. Atmospheric temperature and population density have been identified as two key factors influencing the spread of viruses. Nigerian states with different weather patterns and varying populations across her states have recorded about 173,908 COVID-19 cumulative confirmed cases between March 2020 and July 2021. Methods: Data sets of confirmed Covid-19 cases, average monthly temperature and population of each State, and Nigeria’s Federal Capital Territory were obtained. A test of assumptions of linear regression was carried out and there is the presence of outliers in the dataset. M-estimator as an alternative to Ordinary Least Square (O.L.S.) estimator for regression analysis was used to investigate the impacts of each State’s population size and atmospheric temperature on the rate of COVID-19 cases confirmed. The spearman rank correlation coefficient was also used to investigate the strength of the relationship be-tween the confirmed cases, the population and temperature. Results: Results show no multicollinearity (VIF=1.041) between the independent variables, and there is no autocorrelation as the Durbin-Watson test value gives 2.113 (approximately 2). There is a weak positive correlation between cumulative confirmed cases and population (r = 0.281), but a weak negative correlation exists between COVID-19 cumulative confirmed cases and atmospheric temperature (r = -0.341). For OLS estimation method, only population is significant (β1= 0.002, p < 0.002) but the population (β1= 0.0006, p < 0.05) and the atmospheric temperature ( β2= -683, p < 0.05) are both significant when M-estimation method was applied. Conclusion: The findings in this study show that population size and temperature are important factors in the spread of Covid-19. The spread of the pandemic may be partially suppressed with higher temperatures but increases with an increased population.

Trade Credit Uncertainty and Financial Performance of Manufacturing Firms in Kenya

The main objective of this study was to find out if uncertainty in trade credit of manufacturing firm in Kenya affects their financial performance. Manufacturing firms in Kenya have not been performing to their expectation. They are expected to contribute to economic growth of the country through GDP increment, market share, attract largest strategic investments in Key processing industry, increase sales both locally and international and employ at least 20% of Kenya Population. It was noted that the manufacturing firms have been facing various challenges both financial and non-financial. Contribution to GDP has staggered at an average of 10%, profit and sales have been declining and some firms have completely moved out of market. Many factors have been cited to be contributing below expectation performance. However, the influence of trade credit uncertainty on financial performance of manufacturing firms in Kenya is not conclusive. Hence, necessitating the current study to examine the influence of trade credit uncertainty on financial performance of manufacturing firms in Kenya. The study anchored its variable on credit risk theory. Indicators of trade credit uncertainty were credit exposure rate and default rate, and proxy of performance were ROS and ROE. The study adopted positivism Philosophy and correlation design. Target population was 856 manufacturing firms registered with KAM. A sample of 90 firms was selected using Stratified random sampling technique for 14 sectors and each sample picked by random sampling. The study covered a period of 12 years starting from 2009 to 2020 all years inclusive. Panel data was collected from audited financial statements and annual reports published using data collection instrument. Pre and post diagnostic tests were carried out on collect data to test assumption of linear regression using E-view 11.8. Tests done were Normality test, Hausman test, Unit root test, Heteroskedastic test, autocorrelation, and multicollinearity test. Results showed that trade credit uncertainty had positive and significant impact on financial performance of manufacturing firms in Kenya. The study recommends having credit policy in place that will help to reduce losses because of high exposure rate. Keywords: Trade credit uncertainty, credit exposure rate, default rate and Financial Performance. DOI: 10.7176/RJFA/13-10-08 Publication date: May 31 st 2022

Effect of Electronic and Non-Electronic Fraud on Performance of Deposit Money Banks in Nigeria

Fraud in the Nigerian payments system and globally has been on the increase over the past few years as technological advancement impact on the way we pay. The objectives of the study are to examine the effect of electronic and non-electronic fraud on profit before tax, return on assets and return on equity of deposit money banks in Nigeria. The study obtained data from Nigeria Interbank Settlement System Plc (NIBSS) reports. Ordinary least square diagnostic test was done through serial correlation, heteroskedasticity and Ramsey RESET Test specification to ensure that variables are in line with classical linear regression assumptions. The result of the findings among others shows a negative relationship between electronic and non-electronic fraud on profit before tax of deposit money banks in Nigeria. The study recommends that financial institutions must thoroughly report all frauds recorded so as to curb the rising trend.

Explaining Neighbourhood Disparities in Cardiovascular Disease in Hamilton, Ontario, Canada

Introduction: In 2010, Hamilton’s local newspaper published a series of articles highlighting the inequities in numerous health outcomes across the city, with cardiovascular disease (CVD) Emergency Room (ER) visits among them (DeLuca et al., 2012). In Canada CVD is the second leading cause of death and the leading cause of hospitalizations, however, previous research has demonstrated that CVD risk may vary geographically (Chu et al., 2019). Furthermore, health analyses are rarely conducted in ways accessible to non-scientific communities. Given inequities in the distribution of COVID-19 across Hamilton communities, the need for population level analysis of comorbidities and risk factors is of heightened importance. The aim of this study is to identify the underlying factors that explain neighbourhood differences in the rate of CVD across Hamilton, Ontario. Methods: Census Tract (CT) aggregated Ontario Marginalization (ON-Marg) values and health data from Cancer Care Ontario were used. The material deprivation dimension of ON-Marg includes information on income, employment, education, and lone parent households, which have previously been linked to increased CVD risk, while the dependency dimension represents those who do not have income from employment which captures older age and disability (Matheson & van Ingen, 2018). Factor analysis was performed to identify underlying factors that account for common variance. Spatial associations were analyzed using choropleth maps as well as measures of both global spatial autocorrelation (i.e., global Moran’s I) and local indicators of association (i.e., local Moran’s I). Contiguity was based on rook-weights (sharing a common boundary). Exploratory ordinary least squares (OLS) regression was performed to understand which indicators may explain geographic variation in CVD ER visits. Linear regression assumptions were assessed by testing the residuals for heteroskedasticity using the Koenker test, spatial autocorrelation using Global Moran’s I, and normality using the Kolmogorov-Smirnov test. Results: Initial analysis from 2016 and 2017 revealed that the rate of CVD ER visits in Hamilton is spatially autocorrelated (global Moran’s I score of 0.516 (p<0.001) and ranged from less than 3 in 1000 to over 30 in 1000 people per year. For regression analysis, factor scores for material deprivation and dependency domains of the well validated ON-Marg Index were used together with the percentage of patients with no family physician. OLS regression using the four regressors resulted in a statistically significant model (F=65.94, p<0.001) that explains about 65% of the variability in CVD ER visits in Hamilton (R2 = 0.653). Residuals were tested for heteroscedasticity (Koenker = 4.33, p=0.363), autocorrelation (global Moran’s I = 0.042, p = 0.367) and normality (Kolmogorov-Smirnov = 0.072, p = 0.079). Discussion: This information can help inform neighbourhood-level public health interventions and broader policy decisions to help address local CVD disparities. Patterns of high CVD and poorer socioeconomic conditions also correspond with COVID-19 disparities and support the need for greater neighbourhood-level research of both infectious and chronic conditions. Furthermore, geographic outputs of this work also provide visual and interactive neighbourhood-level health information accessible to non-scientific audiences that may support community-centred health and social action.

Influence of Risk Analysis as a Risk Management Practice on Project Performance in Kenya Commercial Banks

Undertaking an information technology project in a banking environment is a complex task. Studies globally and locally indicate a high failure rate of information technology projects. Standish group report 2019 states that 83.9 percent of information technology projects partially or completely fail. The majority of projects 52 percent were over budget, overdue, or lacked promised functionality. Previous studies indicate information technology projects in commercial Banks in Kenya experience the same project performance variations, as projects are either delayed, over budget or have issues with functionality. Risk is a factor that challenges project performance. Project risk management includes risk identification, analysis, response, and monitoring and control of risk in a project. The overall goal of this study was to examine the relationship of risk management and information technology project performance in Kenyan commercial banks, taking into account the moderating effect of project complexity and the mediating effect of risk culture, both of which had been largely overlooked in previous research hence filling a research vacuum. The target population was forty projects in Kenyan commercial banks in Kenya which made the unit of analysis. Stratified and simple random sampling technique was used. Stratified and simple random sampling technique was used. Questionnaires were used to collect the data from the targeted one hundred and eight respondents. The instrument was tested for reliability by use of Cronbach's alpha coefficient of internal consistency test and validity by use of selected information technology project professionals' review. Drop and pick method of administering questionnaires was used so as to allow respondents enough time to go through the questionnaires and give their responses. An option of online questionnaires was also available to respondents. Based on a survey, the research used both descriptive and explanatory analysis designs. The association between risk analysis and performance of information technology projects in Kenyan commercial banks was investigated using multiple regression. Quantitative data was analyzed using multiple regression analysis model software tool SPSS Version 25. The study adopted empirical model of least squares method while testing the hypotheses. The researcher conducted diagnostic tests of Normality, Linearity, Homoscedasticity and Multicollinearity to see if the data conforms to the basic assumptions of linear regression. The findings were presented using statistical parameter estimates. Tables and figures were used to present data, and supported by explanatory annotations. The results indicated that risk analysis had significant effects on the performance of information technology projects in the banking sector. The study recommends that banks should consider implementing and fully operationalize risk analysis in information technology projects. The Central Bank of Kenya should also consider putting in place an information technology projects risk policy framework to aid the banks in project undertakings. The finding in this research will aid project managers and different stakeholders in the banking and related sectors in managing information technology projects risks and hence increase the success rate of the projects. The knowledge gap is also addressed by scholarly work that has resulted from this research by providing statistical data analysis and explanations on the IT project performance in relation to risk analysis influence in commercial banks in Kenya.

Health care manager commitment towards implementation of citizen charter standards and associated factors in public hospitals of Jimma zone, Southwest Ethiopia

BackgroundManagerial commitment is important for effective design and implementation of citizen charter to assure the quality of health service delivery as per the standards depicted in the document. Hence the objective of this study is to assess the level of managerial commitment towards implementation of the citizen charter standards and associated factor in Jimma zone public hospitals.MethodsA Facility based cross-sectional study design was employed in Jimma zone public hospitals from March 14 to May 16, 2019 and 422 health managers who were currently working at all levels of management were participated in the study. After checking its completeness, the data was entered into EPI data version 3.1 and exported to SPSS version 20 for statistical analysis. Factor analysis was conducted. Simple and multiple linear regression were done using 95%CI and significance was declared at P < 0.05. All assumptions of linear regression and principal component analysis were checked.ResultsThe percentages mean score of managerial commitment for health managers working in jimma zone public hospitals was 58%. Perceived value and care for managers (β = .329,95% CI,.245,.413, p-value<.001), Interaction between staff and managers’ (β = 0.077,95%CI,.032,.122, p-value< 001),involvement during implementation of citizen charter(β = 0.061,95%CI,.010,.112,p-value = 018) and positional level(β = − 122,95%CI,-.242,-.002,p-value = .046) as predictors of managerial commitment towards implementation of citizen charter standards.ConclusionsIn this study, the percentage mean score of managerial commitment for health care managers working in Jimma zone public hospitals was medium. Hence, all levels of managers to consider and maintain factors identified in this study in their management practice to foster a higher level of managerial commitment towards implementation of citizen charter standards in jimma zone public hospitals.

A boundary finding-based spatiotemporal fusion model for vegetation index

ABSTRACT The spatiotemporal image fusion technique is regarded as an effective and efficient remedy to blend two or more geometrically registered remote sensing images of the same scene acquired from different sensors into a single image with both high temporal and high spatial resolutions. A number of existing fusion methods developed for generating Landsat-like images from the Moderate Resolution Imaging Spectroradiometer (MODIS) have successfully solved limitations on vegetation dynamics monitoring. However, these methods either treat the weighting parameters as constants or adopt insufficient linear regression coefficients (considering only spatial, temporal or spectral weights), which may contribute to blocky artefacts and dissimilar pixels in the predicted image. In this study, a boundary finding-based vegetation index spatiotemporal fusion model (BESFM) is newly proposed to generate high spatial and high temporal resolutions Enhanced Vegetation Index (EVI) images in homogeneous and heterogeneous regions with rapid vegetation changes. The cloud-free Landsat-8 Operational Land Imager (OLI) and the MODIS (MOD09GA) data acquired from two study sites, located in Queensland and New South Wales and Australia, were selected to evaluate the performance of the proposed method. Compared with the enhanced spatial and temporal adaptive reflectance fusion model (ESTARFM) and flexible spatiotemporal data fusion (FSDAF), the BESFM outperforms in both visible image quality (reducing the spatial distortion and blocky artefacts in prediction caused by abrupt land cover changes) and quantitative indices (with RSME minimum to 0.011 and R2 maximum to 0.956). Since the BESFM method not only uses adjustable linear regression assumptions for heterogeneous and homogeneous regions differently but also implements boundary detection-based spatial weight with temporal and spectral weights together to enhance the predicted spatial details, it has the potential to increase the availability of fine spatial resolution data.

Tissue‐Specific Differences in Myocardial and Coronary Vascular ACE2 and TMPRSS2 mRNA Levels are Dependent Upon Sex, Comorbidities, Pressure‐Overload, and Pig Species

SARS‐COV‐2, or COVID‐19, is a respiratory virus infecting over 86 million people worldwide. In addition to respiratory infections, SARS‐COV‐2 has been shown to include cardiovascular (CV) complications, including myocarditis and acute coronary syndrome. Risk of severe complications from SARS‐COV‐2 in individuals with existing CV and metabolic disease has been shown to be increased. Evidence indicates SARS‐COV‐2 enters tissues via the angiotensin‐converting enzyme 2 (ACE2) receptor and that the virus is primed and activated by transmembrane protease, serine 2 (TMPRSS2). The goal of this study was to determine ACE2 and TMPRSS2 mRNA levels in pre‐clinical swine models of heart failure (HF). We hypothesized sex, pressure‐overload, and comorbidities would increase ACE2 and TMPRSS2 mRNA levels. A retrospective analysis was conducted in previously completed studies in our lab including: 1) Female, intact Ossabaw swine that were either lean control or western diet‐fed aortic‐banded (N=4‐5/group); 2) Female Yucatan mini‐swine subject to ovariectomy and/or aortic banding (N=5‐8/group); and 3) Sedentary and exercise trained male, intact Yucatan mini‐swine that were aortic banded. ACE2 and TMPRSS2 mRNA levels were evaluated in the left ventricle (LV), right ventricle (RV), and coronary vasculature using qRT‐PCR. Linear regression analysis was used to determine differences between the following variables: pig species, sex hormones, aortic banding, comorbidities, exercise training, and tissue. Data was log‐transformed to meet linear regression assumptions. ACE2 and TMPRSS2 mRNA levels were significantly influenced by sex, comorbidity, and tissue type. TMPRSS2 mRNA levels were also influenced by species and disease status. Specifically, ACE2 mRNA levels decreased 57.1% in the LV and increased 169.9% in the RV of males compared to coronary vessels in intact females. TMPRSS2 mRNA levels increased in the LV and RV of males (1,218.6% and 5,479.8%, respectively) compared to coronary vessels in intact females. ACE2 and TMPRSS2 mRNA levels increased 344% and 453.4%, respectively, in the LV of Ossabaw swine fed a Western Diet compared to coronary vessels from Yucatan and Ossabaw swine without comorbidities. Species differences indicated TMPRSS2 mRNA levels increased 449.2% in the RV and 498.6% in the LV in Yucatan mini‐swine compared to coronary vessels in Ossabaw swine. A 107.3% increase in TMPRSS2 mRNA level was observed in male swine without HF compared to female intact swine with HF highlighting the importance of sex and disease state. Exercise training did not impact ACE2 or TMPRSS2 mRNA levels irrespective of tissue. In conclusion, these results suggest differences in RV, LV and coronary mRNA levels of ACE2 and TMPRSS2 are dependent upon sex and comorbidities. TMPRSS2 levels are additionally influenced by pig species and pressure‐overload. These results provide insight into how ACE2 and TMPRSS2 mRNA levels may influence the cardiovascular involvement of SARS‐COV‐2 infection in an experimental setting of pre‐clinical HF incorporating different swine species, sex, and comorbidities.

Robustness of model averaging methods for the violation of standard linear regression assumptions

Robustness of model averaging methods for the violation of standard linear regression assumptions

Gaussian Kernel Methods for Seismic Fragility and Risk Assessment of Mid-Rise Buildings

Seismic fragility functions can be evaluated using the cloud analysis method with linear regression which makes three fundamental assumptions about the relation between structural response and seismic intensity: log-linear median relationship, constant standard deviation, and Gaussian distributed errors. While cloud analysis with linear regression is a popular method, the degree to which these individual and compounded assumptions affect the fragility and the risk of mid-rise buildings needs to be systematically studied. This paper conducts such a study considering three building archetypes that make up a bulk of the building stock: RC moment frame, steel moment frame, and wood shear wall. Gaussian kernel methods are employed to capture the data-driven variations in the median structural response and standard deviation and the distributions of residuals with the intensity level. With reference to the Gaussian kernels approach, it is found that while the linear regression assumptions may not affect the fragility functions of lower damage states, this conclusion does not hold for the higher damage states (such as the Complete state). In addition, the effects of linear regression assumptions on the seismic risk are evaluated. For predicting the demand hazard, it is found that the linear regression assumptions can impact the computed risk for larger structural response values. However, for predicting the loss hazard with downtime as the decision variable, linear regression can be considered adequate for all practical purposes.

Neural Networks to Estimate Generalized Propensity Scores for Continuous Treatment Doses.

The generalized propensity score (GPS) addresses selection bias due to observed confounding variables and provides a means to demonstrate causality of continuous treatment doses with propensity score analyses. Estimating the GPS with parametric models obliges researchers to meet improbable conditions such as correct model specification, normal distribution of variables, and large sample sizes. The purpose of this Monte Carlo simulation study is to examine the performance of neural networks as compared to full factorial regression models to estimate GPS in the presence of Gaussian and skewed treatment doses and small to moderate sample sizes. A detailed conceptual introduction of neural networks is provided, as well as an illustration of selection of hyperparameters to estimate GPS. An example from public health and nutrition literature uses residential distance as a treatment variable to illustrate how neural networks can be used in a propensity score analysis to estimate a dose-response function of grocery spending behaviors. We found substantially higher correlations and lower mean squared error values after comparing true GPS with the scores estimated by neural networks. The implication is that more selection bias was removed using GPS estimated with neural networks than using GPS estimated with classical regression. This study proposes a new methodological procedure, neural networks, to estimate GPS. Neural networks are not sensitive to the assumptions of linear regression and other parametric models and have been shown to be a contender against parametric approaches to estimate propensity scores for continuous treatments.

Automating Data Analysis Methods in Epidemiology

Technological advances in software development effectively handled technical details that made life easier for data analysts, but also allowed for nonexperts in statistics and computer science to analyze data. As a result, medical research suffers from statistical errors that could be otherwise prevented such as errors in choosing a hypothesis test and assumption checking of models. Our objective is to create an automated data analysis software package that can help practitioners run non-subjective, fast, accurate and easily interpretable analyses. We used machine learning to predict the normality of a distribution as an alternative to normality tests and graphical methods to avoid their downsides. We implemented methods for detecting outliers, imputing missing values, and choosing a threshold for cutting numerical variables to correct for non-linearity before running a linear regression. We showed that data analysis can be automated. Our normality prediction algorithm outperformed the Shapiro-Wilk test in small samples with Matthews correlation coefficient of 0.5 vs. 0.16. The biggest drawback was that we did not find alternatives for statistical tests to test linear regression assumptions which are problematic in large datasets. We also applied our work to a dataset about smoking in teenagers. Because of the opensource nature of our work, these algorithms can be used in future research and projects.

Estimation Modeling of Abutment Volume with Variations of Bridge Span, Abutment Height, and Seismic Zone

The initial cost estimate for a bridge project using an estimation model can be done based on the dimensions, type, and material of the bridge. Research that has included bridge location as a determinant variable for initial bridge cost estimation has not been carried out much. The different locations of the bridge project will have different seismic accelerations and seismic load analysis. This study aims to create a model used to calculate the quantity needed for the construction of abutment in various locations with a PCI-Girder superstructure. The data used for the quantity estimation model was derived from the abutment design results. The data obtained from the calculation of concrete and reinforcing steel quantities from the abutment design with variations in bridge span i.e. 20 m; 25 m; 30 m; 35 m; and 40 m, abutment height i.e. 4 m; 6 m; and 8 m, and seismic zone 1, 2, 3, and 4. Volume estimation models are obtained by multiple linear regression analysis. The results show a very strong correlation between the span of the bridge and the height of abutment with the dependent variables. While the seismic zone has a strong correlation with the dependent variables. However, the seismic zone in this study did not meet the linear regression assumptions. This study developed 8 models to estimate abutment volumes. The R2 values of these models are 0.983 – 0.997. These showed that the models are properly made to be used to estimate abutment volumes with a PCI-Girder superstructure.

Double-slicing assisted sufficient dimension reduction for high-dimensional censored data

This paper provides a unified framework and an efficient algorithm for analyzing high-dimensional survival data under weak modeling assumptions. In particular, it imposes neither parametric distributional assumption nor linear regression assumption. It only assumes that the survival time $T$ depends on a high-dimensional covariate vector $\mathbf{X}$ through low-dimensional linear combinations of covariates $\Gamma ^{T}\mathbf{X}$. The censoring time is allowed to be conditionally independent of the survival time given the covariates. This general framework includes many popular parametric and semiparametric survival regression models as special cases. The proposed algorithm produces a number of practically useful outputs with theoretical guarantees, including a consistent estimate of the sufficient dimension reduction subspace of $T\mid \mathbf{X}$, a uniformly consistent Kaplan–Meier-type estimator of the conditional distribution function of $T$ and a consistent estimator of the conditional quantile survival time. Our asymptotic results significantly extend the classical theory of sufficient dimension reduction for censored data (particularly that of Li, Wang and Chen in Ann. Statist. 27 (1999) 1–23) and the celebrated nonparametric Kaplan–Meier estimator to the setting where the number of covariates $p$ diverges exponentially fast with the sample size $n$. We demonstrate the promising performance of the proposed new estimators through simulations and a real data example.

Investigating the effect of dependence between conditions with Bayesian Linear Mixed Models for motif activity analysis.

Cellular identity and behavior is controlled by complex gene regulatory networks. Transcription factors (TFs) bind to specific DNA sequences to regulate the transcription of their target genes. On the basis of these TF motifs in cis-regulatory elements we can model the influence of TFs on gene expression. In such models of TF motif activity the data is usually modeled assuming a linear relationship between the motif activity and the gene expression level. A commonly used method to model motif influence is based on Ridge Regression. One important assumption of linear regression is the independence between samples. However, if samples are generated from the same cell line, tissue, or other biological source, this assumption may be invalid. This same assumption of independence is also applied to different yet similar experimental conditions, which may also be inappropriate. In theory, the independence assumption between samples could lead to loss in signal detection. Here we investigate whether a Bayesian model that allows for correlations results in more accurate inference of motif activities. We extend the Ridge Regression to a Bayesian Linear Mixed Model, which allows us to model dependence between different samples. In a simulation study, we investigate the differences between the two model assumptions. We show that our Bayesian Linear Mixed Model implementation outperforms Ridge Regression in a simulation scenario where the noise, which is the signal that can not be explained by TF motifs, is uncorrelated. However, we demonstrate that there is no such gain in performance if the noise has a similar covariance structure over samples as the signal that can be explained by motifs. We give a mathematical explanation to why this is the case. Using four representative real datasets we show that at most ∼​40% of the signal is explained by motifs using the linear model. With these data there is no advantage to using the Bayesian Linear Mixed Model, due to the similarity of the covariance structure. The project implementation is available at https://github.com/Sim19/SimGEXPwMotifs.

Determinants of Capital Structure:An Empirical Study on Ethiopian Insurance Industry

The aim of this study was to examine the firm-specific, industry-specific and macro-economic determinants of Ethiopian insurance companies’ capital structure decision with the sample size of nine insurance companies, covering the period of 2005-2016.To achieve this objective quantitative research approach and quantitative data were used. The data was obtained from the annual audited financial statement of insurance companies and from NBE. In comply with this objective the study applied panel data model with fixed effect Ordinary Least Square regression. To test the hypotheses those were formulated through the review of available literature, the collected data was organized and checked for the fulfillment of OLS linear regression assumptions and then analyzed using fixed effect linear regression. The finding of the study shows that age of the firm, firm size and growth rate of real GDP have statistically significant and positive relationship with insurance company’s capital structure decision. On the other hand, variables like business risk, tangibility of asset and liquidity have a negative and statistically significant relationship with capital structure of insurance companies However, the relationship to exchange rate, profitability, growth opportunity and non-debt tax shield appear to be statistically insignificant. Depending up on the finding the study recommends that insurance companies in Ethiopia should not focus only on firm specific factors but also on macroeconomic environment so as to make an optimal capital structure decision and also the management of those insurance companies has to be focused on reducing factors that causes earning volatility to enhance earning sustainability. Finally the regulator (NBE) need to address problem of information asymmetry through setting up of rules that will ensure effective disclosures of the insurance companies audited financial statements. Keywords: Capital structure, firm specific factors, macro-economic factors, industry specific factors DOI: 10.7176/RJFA/11-9-02 Publication date: May 31 st 2020

Detection of suspicious interactions of spiking covariates in methylation data

BackgroundIn methylation analyses like epigenome-wide association studies, a high amount of biomarkers is tested for an association between the measured continuous outcome and different covariates. In the case of a continuous covariate like smoking pack years (SPY), a measure of lifetime exposure to tobacco toxins, a spike at zero can occur. Hence, all non-smokers are generating a peak at zero, while the smoking patients are distributed over the other SPY values. Additionally, the spike might also occur on the right side of the covariate distribution, if a category “heavy smoker” is designed. Here, we will focus on methylation data with a spike at the left or the right of the distribution of a continuous covariate. After the methylation data is generated, analysis is usually performed by preprocessing, quality control, and determination of differentially methylated sites, often performed in pipeline fashion. Hence, the data is processed in a string of methods, which are available in one software package. The pipelines can distinguish between categorical covariates, i.e. for group comparisons or continuous covariates, i.e. for linear regression. The differential methylation analysis is often done internally by a linear regression without checking its inherent assumptions. A spike in the continuous covariate is ignored and can cause biased results.ResultsWe have reanalysed five data sets, four freely available from ArrayExpress, including methylation data and smoking habits reported by smoking pack years. Therefore, we generated an algorithm to check for the occurrences of suspicious interactions between the values associated with the spike position and the non-spike positions of the covariate. Our algorithm helps to decide if a suspicious interaction can be found and further investigations should be carried out. This is mostly important, because the information on the differentially methylated sites will be used for post-hoc analyses like pathway analyses.ConclusionsWe help to check for the validation of the linear regression assumptions in a methylation analysis pipeline. These assumptions should also be considered for machine learning approaches. In addition, we are able to detect outliers in the continuous covariate. Therefore, more statistical robust results should be produced in methylation analysis using our algorithm as a preprocessing step.

A Machine Learning Approach to Predict Human Judgments in Compensatory and Noncompensatory Judgment Tasks

Traditionally, in judgment analysis, multiple linear regression based lens model, which assumes decision makers assess every cue, weigh, and combine them to make overall judgments, has been used to model and analyze human judgments. However, linear regression assumptions are limited in situations where logical rules for making decisions are not consistent with a weighting and summing formula. In this study, we sought to extend the body of knowledge in the judgment analysis research by adopting the rule-based lens model and using machine learning models to predict human judgments in compensatory and noncompensatory judgment tasks. Overall, the selected machine learning models outperformed the linear logistic regression (LgR) model in both compensatory and noncompensatory tasks. Our own results suggest that, at least for the present application, machine learning models may be better at predicting human judgments in compensatory and noncompensatory judgment tasks than linear multiple LgR models. We conclude that machine learning algorithms can yield useful models for training and decision support applications.