Confidence Intervals For Coefficients Research Articles

Bootstrapping the coefficients of multiple logistic regression model in medicine data

Bootstrap is becoming a useful and very popular tool for obtaining estimations and confidence intervals for coefficients in many researches in different scientific fields without making assumptions about the population. Our goal is to apply bootstrap technique in parameter estimation and confidence intervals for the coefficients in Multiple Logistic Regression model in a study using medical records. We will use R programming language and SPSS software to obtain the coefficients of the model and the estimations using non-parametric bootstrap and we will also make a comparison of the results emphasizing the importance of using resampling methods even in a study with real data.

Adding Measurement Error to Location Data to Protect Subject Confidentiality While Allowing for Consistent Estimation of Exposure Effects

Summary In public use data sets, it is desirable not to report a respondent's location precisely to protect subject confidentiality. However, the direct use of perturbed location data to construct explanatory exposure variables for regression models will generally make naive estimates of all parameters biased and inconsistent. We propose an approach where a perturbation vector, consisting of a random distance at a random angle, is added to a respondent's reported geographic co-ordinates. We show that, as long as the distribution of the perturbation is public and there is an underlying prior population density map, external researchers can construct unbiased and consistent estimates of location-dependent exposure effects by using numerical integration techniques over all possible actual locations, although coefficient confidence intervals are wider than if the true location data were known. We examine our method by using a Monte Carlo simulation exercise and apply it to a real world example using data on perceived and actual distance to a health facility in Tanzania.

Selective inference with unknown variance via the square-root lasso

SummaryThere has been much recent work on inference after model selection in situations where the noise level is known. However, the error variance is rarely known in practice and its estimation is difficult in high-dimensional settings. In this work we propose using the square-root lasso, also known as the scaled lasso, to perform inference for selected coefficients and the noise level simultaneously. The square-root lasso has the property that the choice of a reasonable tuning parameter does not depend on the noise level in the data. We provide valid $p$-values and confidence intervals for coefficients after variable selection and estimates for the model-specific variance. Our estimators perform better in simulations than other estimators of the noise variance. These results make inference after model selection significantly more applicable.

Fighting Collinearity in QSPR Equations for Solution Kinetics with the Monte Carlo Method and Total Weighting

A Monte Carlo method is used in addition to functional and individual weighting to overcome multicollinearity problems in multiple linear regression equations applied as quantitative-structure-property-relationships, allowing the estimation of correct coefficient confidence intervals. The method was applied to rate constants for the Menschutkin reaction between Et3N and EtI in mono- and di-alcohols, at 25.00 oC. Results show that the use of our methodology produces a significant improvement upon confidence interval estimates regardless of the level of collinearity present. Addition of weighting shows additional advantages, increasing the overall consistency of the regression process.

SAS Code for Calculating Intraclass Correlation Coefficients and Effect Size Benchmarks for Site-Randomized Education Experiments

When evaluators plan site-randomized experiments, they must conduct the appropriate statistical power analyses. These analyses are most likely to be valid when they are based on data from the jurisdictions in which the studies are to be conducted. In this method note, we provide software code, in the form of a SAS macro, for producing statistical power analyses using such data. The macro is designed to estimate statistical parameters for multiple school subjects and multiple grades in a single computer run. Among other convenient features, the macro calculates intraclass correlation coefficient confidence intervals, which are essential for planning studies conservatively. We also provide a SAS macro for calculating benchmarks–again, using locally-based–data for interpreting the feasibility of achieving the minimum detectable effect sizes that are calculated in statistical power analyses. The benchmarks are potentially useful for interpreting the meaning of the effect sizes that are achieved in completed studies, as well. We describe the macros, describe how we verified their accuracy, show how they can be useful to education evaluators, and give examples of their use with statewide educational assessment data. It is our hope that the macros will help evaluators use local data when conducting group-randomized studies.

Reporting quality of multivariable logistic regression in selected Indian medical journals

Use of multivariable logistic regression (MLR) modeling has steeply increased in the medical literature over the past few years. Testing of model assumptions and adequate reporting of MLR allow the reader to interpret results more accurately. To review the fulfillment of assumptions and reporting quality of MLR in selected Indian medical journals using established criteria. Analysis of published literature. Medknow.com publishes 68 Indian medical journals with open access. Eight of these journals had at least five articles using MLR between the years 1994 to 2008. Articles from each of these journals were evaluated according to the previously established 10-point quality criteria for reporting and to test the MLR model assumptions. SPSS 17 software and non-parametric test (Kruskal-Wallis H, Mann Whitney U, Spearman Correlation). One hundred and nine articles were finally found using MLR for analyzing the data in the selected eight journals. The number of such articles gradually increased after year 2003, but quality score remained almost similar over time. P value, odds ratio, and 95% confidence interval for coefficients in MLR was reported in 75.2% and sufficient cases (>10) per covariate of limiting sample size were reported in the 58.7% of the articles. No article reported the test for conformity of linear gradient for continuous covariates. Total score was not significantly different across the journals. However, involvement of statistician or epidemiologist as a co-author improved the average quality score significantly (P=0.014). Reporting of MLR in many Indian journals is incomplete. Only one article managed to score 8 out of 10 among 109 articles under review. All others scored less. Appropriate guidelines in instructions to authors, and pre-publication review of articles using MLR by a qualified statistician may improve quality of reporting.

On the Distribution of two Alternative StructuraltStatistics

Abstract Two alternative structural t statistics for simultaneous equation models are derived. The statistics could be used to test hypotheses or construct confidence intervals for coefficients in econometric models. It is demonstrated that the exact distribution functions converge to Student's t-distribution function as the concentration parameter increases. Computations of the variance of the t-statistics indicate the degree of approximation afforded by the limiting distribution functions.