Logistic Regression

Logistic regression is a widely used method to model categorical response data, and maximum likelihood (ML) estimation has widespread use in logistic regression. Although ML method is the most used method to estimate the regression coefficients in logistic regression model, multicollinearity seriously affects the ML estimator. To remedy the undesirable effects of multicollinearity, estimators alternative to ML are proposed. Drawing on the similarities between the multiple linear and logistic regressions, ridge, Liu and two parameter estimators are proposed which are based on the ML estimator. On the other hand, first-order approximated ridge estimator is proposed for use in logistic regression. This study will present further solutions to the problem in the form of alternative estimators which reduce the effect of collinearity. Owing to this, first-order approximated Liu, iterative Liu and iterative two parameter estimators are proposed. A simulation study as well as real life application are carried out to ascertain the effect of sample size and degree of multicollinearity, in which the ML based, first-order approximated and iterative biased estimators are compared. Graphical representations are presented which support the effect of the shrinkage parameter on the mean square error and prediction mean square error of the biased estimators.

Background: Depression and obesity are widespread and closely linked. Brain-derived neurotrophic factor (BDNF) and vitamin D are both assumed to be associated with depression and obesity. Little is known about the interplay between vitamin D and BDNF. We explored the putative associations and interactions between serum BDNF and vitamin D levels with depressive symptoms and abdominal obesity in a large population-based cohort. Methods: Data were obtained from the population-based Study of Health in Pomerania (SHIP)-Trend (n = 3,926). The associations of serum BDNF and vitamin D levels with depressive symptoms (measured using the Patient Health Questionnaire) were assessed with binary and multinomial logistic regression models. The associations of serum BDNF and vitamin D levels with obesity (measured by the waist-to-hip ratio [WHR]) were assessed with binary logistic and linear regression models with restricted cubic splines. Results: Logistic regression models revealed inverse associations of vitamin D with depression (OR = 0.966; 95% CI 0.951–0.981) and obesity (OR = 0.976; 95% CI 0.967–0.985). No linear association of serum BDNF with depression or obesity was found. However, linear regression models revealed a U-shaped association of BDNF with WHR (p < 0.001). Conclusion: Vitamin D was inversely associated with depression and obesity. BDNF was associated with abdominal obesity, but not with depression. At the population level, our results support the relevant roles of vitamin D and BDNF in mental and physical health-related outcomes.

Wastewater utilities are aiming to implement asset management strategies to minimize costly emergency repairs, to justify expenditures, and to optimize future renewal actions. Consequently, development of deterioration models that explain the behavior of wastewater lines and provide predictions regarding potential future condition levels is gaining importance. In this paper, deterioration models are generated to estimate the probability of failure values for sewer sections. A set of variables was obtained by examining the inventory and inspection databases of a sewer network. Three statistical methods (ordinal regression, multinomial logistic regression, and binary logistic regression) were employed in successive steps. Proportionality of odds assumption was tested for ordinal regression models, and suitability of this particular method was discussed. Estimated condition ratings were compared with observed data, and the binary logistic regression model was found to be more suitable for predicting probability of failure than the multinomial logistic regression model. The models presented in this paper are expected to assist wastewater utilities in developing section-level risk assessment models to identify pipe sections that require immediate attention and close monitoring.

ObjectiveThis study aimed to systematically identify risk factors for urinary catheter-related hematuria in patients with acute myocardial infarction (AMI). By integrating logistic regression and decision tree models, we sought to develop actionable strategies for risk stratification and complication prevention.MethodsA retrospective analysis of 209 AMI patients was conducted to evaluate predictors of hematuria, including demographics, coagulation indices (INR, platelets), and procedural variables. Logistic regression and decision tree (CART algorithm) models were employed to identify risk factors and their interactions. Model performance was assessed using ROC-AUC, sensitivity, and specificity.ResultsThe incidence of catheter-related hematuria was 32.5%. Both models identified persistent agitation during catheter indwelling and PLT ≤ 246 as common predictors. The logistic regression model specifically identified Gender (OR = 0.202), patient awareness of catheter purpose and precautions (OR = 0.470), and emergency catheter placement (OR = 2.257) as significant factors. The decision tree model uniquely identified INR > 0.955 and repeated complaints of urethral pain as predictors.ConclusionHematuria in AMI patients results from coagulation dysfunction, procedural trauma, and behavioral factors. The combined use of logistic regression and decision trees enhances risk stratification. Clinical strategies should prioritize gentle catheterization, dynamic coagulation monitoring, and patient education to reduce complications.

The logistic regression and statistical index models are applied and verified for landslide susceptibility mapping in Daguan County, Yunnan Province, China, by means of the geographic information system (GIS). A detailed landslide inventory map was prepared by literatures, aerial photographs, and supported by field works. Fifteen landslide-conditioning factors were considered: slope angle, slope aspect, curvature, plan curvature, profile curvature, altitude, STI, SPI, and TWI were derived from digital elevation model; NDVI was extracted from Landsat ETM7; rainfall was obtained from local rainfall data; distance to faults, distance to roads, and distance to rivers were created from a 1:25,000 scale topographic map; the lithology was extracted from geological map. Using these factors, the landslide susceptibility maps were prepared by LR and SI models. The accuracy of the results was verified by using existing landslide locations. The statistical index model had a predictive rate of 81.02%, which is more accurate prediction in comparison with logistic regression model (80.29%). The models can be used to land-use planning in the study area.

The recent incident, the gang rape and murder of a 19-year-old woman in Hathras, a small village in Uttar Pradesh of India, once again sparks a debate on links between sexual violence and castes in India. This article aims to examine the links between sexual violence and castes in India. This study utilizes the national representative National Family Health Survey 4 (NFHS-4, 2015–16) data. A bivariate analysis was carried out to analyse the data. A binary logistic regression model was applied to predict the effect of explanatory variables, viz. type of place of residence, years of schooling complete, economic status in terms of wealth index and finally castes on predicted variable, i.e. sexual violence. The binary regression model indicates that there were links between sexual violence and castes. For secured and dignified life of women, caste-based sexual violence must be annihilated.

Binary logistic semiparametric regression analysis is a commonly used statistical technique when the dependent variable is dichotomous or binary. In this analysis, the relationship between the success probability and certain explanatory variables is assumed to have a linear form, while the relationship to other variables is unknown. Multicollinearity is a serious problem that arises when explanatory variables in logistic semiparametric regression are highly correlated. It is well known that the variance of the maximum likelihood estimator is inflated due to multicollinearity in the semiparametric logistic regression model. Therefore, a novel stochastic restricted iterative weighted ridge estimator for logistic semiparametric regression is introduced, and its statistical properties are extracted asymptotically. Moreover, an extension of the generalized cross validation (GCV) function is introduced and applied for choosing the best values of the ridge parameter and the bandwidth of the kernel smoother. Additionally, some theorems are developed to illustrate the convergence of the GCV mean. Ultimately, the Monte-Carlo simulation studies and an actual real-life data set are conducted to support our theoretical discussion, and the findings indicated that the new estimator outperformed the other estimators under consideration.

Clinical prediction rules could help identify children at risk of slowed growth after an episode of diarrheal illness, and these rules may be generalizable to all children, regardless of diarrhea status.

Forest cover dynamics (1998 to 2019) and prediction of deforestation probability using binary logistic regression (BLR) model of Silabati watershed, India

A cost-minimizing diagnostic methodology for discrimination between neoplastic and non-neoplastic brain lesions: utilizing a genetic algorithm 1 scientific reports

Financial institutions have a large amount of data on their borrowers, which can be used to predict the probability of borrowers defaulting their loan or not. Some of the models that have been used to predict individual loan defaults include linear discriminant analysis models and extreme value theory models. These models are parametric in nature since they assume that the response being investigated takes a particular functional form. However, there is a possibility that the functional form used to estimate the response is very different from the actual functional form of the response. The purpose of this research was to analyze individual loan defaults in Kenya using the logistic regression model. The data used in this study was obtained from equity bank of Kenya for the period between 2006 to 2016. A random sample of 1000 loan applicants whose loans had been approved by equity bank of Kenya during this period was obtained. Data obtained was on the credit history, purpose of the loan, loan amount, nature of the saving account, employment status, sex of the applicant, age of the applicant, security used when acquiring the loan and the area of residence of the applicant (rural or urban). This study employed a quantitative research design, it deals with individual loans defaults as group characteristics of a borrower. The data was pre-processed by seeding using R- Software and then split into training dataset and test data set. The train data was used to train the logistic regression model by employing Supervised machine learning approach. The R-statistical software was used for the analysis of the data. The test data set was used to do cross-validation of the developed logistic model which later was used for analysis prediction of individual loan defaults. This study focused on the analysis of individual loan defaults in Kenya using the logistic regression model in Machine learning. The logistic regression model predicted 303 defaults from train data set, 122 non-defaults and misclassified loans were 56 and 69. The model had an accuracy of 0.7727 with the train data and 0.7333 with the test data. The logistic regression model showed a precision of 0.8440 and 0.8244 with the train and test data respectively. The performance of the model with both the train and test data was illustrated using a plot of train errors and test errors against sample size on the same axes. The plot showed that the performance of the model increases with an increase in sample size. The study recommended the use of logistic regression in conjunction with supervised machine learning approach in loan default prediction in financial institutions and also more research should be carried out on ensemble methods of loan defaults prediction in order to increase the prediction accuracy.

Using Binary Logistic Regression Models for Ordinal Data with Non-proportional Odds

Climate change affects the livelihood of farmers in a variety of ways. Farmers’ indigenous knowledge influences their perception of climate-related issues. A perception-based, semi-structured questionnaire survey of 530 households was performed to gather information about the awareness of, indicators for, and determinants of climate change. The survey covered three ecological regions of Nepal. The statistical analysis was done with a chi-square (χ2) test and a binary logistic regression (BLR) model to screen farmers’ perception of climate change. This study shows that socio-economic and agricultural characteristics of the farmers directly influence their perception of climate change. Farmers have identified climate change indicators in various forms, e.g., an increase in temperature (99.2% of those surveyed), a decrease in precipitation (98.9%), and an increase in climate-induced diseases and pests (96.8%) for agricultural crops. Observed precipitation (− 16.093 mm/year; p = 0.055) and temperature (0.0539 °C/year; p = 0.007) between 2000 and 2015 are both consistent with farmers’ perception. The selected independent variables are significantly correlated with the dependent variables, as confirmed by the BLR model, where χ2 = 83 with p = 0.002. The BLR shows there is a strong relationship between farmers’ perception of climate change and the group of descriptive variables, with a coefficient of determination of 85%. The biophysical characteristics and impact variables were the most important determinants. It is important that organizations and policymakers in Nepal develop adaptation strategies that improve the livelihoods of farmers. These strategies include introducing drought-tolerant crops, developing disease- and pest-tolerant seeds, constructing irrigation systems, and building hospitals.

Uncertainties in spatially aggregated predictions from a logistic regression model

Improving health literacy has been found to play a significant role in enhancing medication adherence in patients with type 2 diabetes. The present study aims to evaluate health literacy and its association with medication adherence among diabetic patients in Jordan. This cross-sectional study included 400 diabetic patients, predominantly female (68.8%), with a median age of 58 years, attending the endocrinology outpatient clinic at Albasheer Hospital in Amman, Jordan, between August and December 2023. Patients were recruited using convenience sampling, including those aged 18 and older, literate, diagnosed with T2DM for at least one year, and on at least one medication for T2DM. Sample size was calculated based on the Events Per Variable (EPV) criterion to ensure sufficient power for logistic regression analysis. Data were collected using two validated instruments: the Jordanian Diabetic Health Literacy Questionnaire (JDHLQ), assessing health literacy, and the Medication Adherence Report Scale (MARS-5), measuring medication adherence. A binary logistic regression model was constructed to identify variables associated with adherence levels. The study enrolled 400 diabetic patients (females =68.8%). While most of the participants (70.3%) reported high adherence levels, results revealed a window for health literacy improvement as the median for the JDHLQ score was 22 (ranging from 18 to 25) out of a maximum possible score of 32. More than half of the participants replied "never" to "I forget to take my medications", followed by "I stop taking my medications for a while". The binary regression model revealed that a higher JDHLQ score significantly increased the odds of a high adherence level. The significant association between improved health literacy and medication adherence necessitates the implementation of educational campaigns for enhancing literacy and hence medication adherence among patients with type 2 diabetes.