Mark Tygert, Rachel Ward
Explicitly accounting for all applicable independent variables, even when the model being tested does not, is critical in testing goodness-of-fit for logistic regression. This can increase statistical power by orders of magnitude.
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We propose a goodness-of-fit test for the distribution of errors from a multivariate indirect regression model. The test statistic is based on the Khmaladze transformation of the empirical process of standardized residuals. This goodness-of-fit test is consistent at the root-n rate of convergence, and the test can maintain power against local alternatives converging to the null at a root-n rate.
Logistic regression is a natural and simple tool to understand how covariates contribute to explain the topology of a binary network. Once the model fitted, the practitioner is interested in the goodness-of-fit of the regression in order to check if the covariates are sufficient to explain the whole topology of the network and, if they are not, to analyze the residual structure. To address this problem, we introduce a generic model that combines logistic regression with a network-oriented residual term. This residual term takes the form of the graphon function of a W-graph. Using a variational…
In this article, the parameters of a hybrid log-linear model (log-Poisson) are estimated using the fuzzy least-squares (FLS) procedures (Celmiņš, 987a,b, D'Urso and Gastaldi, 2000, DUrso and Gastaldi, 2001). A goodness of fit have been derived in order to assess and compare this new model and the classical log-Poisson regression in loss reserving framework (Mack, 1991). Both the hybrid model and its goodness of fit are performed on a loss reserving data.
A goodness-of-fit test for the logistic propensity score model under nonignorable missing data
本文提出了一种在非忽略缺失数据下用于逻辑倾向评分模型的拟合优度检验方法，通过构建未加权残差平方和并考虑结果的不完全可观测性，建立了检验统计量的渐近分布，并通过Bootstrap方法验证其有效性。
A goodness-of-fit test for regression models with spatially correlated errors
针对空间相关误差下的参数回归模型评估问题，提出基于$L_2$距离的拟合优度检验，推导渐近性质并设计bootstrap校准程序，通过模拟和真实数据验证了性能与适用性。
Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are based on a circular distance comparing a (non-smoothed or smoothed) parametric circular estimator and a nonparametric one. Properly designed bootstrap procedures for calibrating the tests in practice are also presented. Finite sample performance of the tests in different scenarios with independent and spatially correlated samples, is analyzed by simulations…
A Goodness-of-Fit Test for Mixed-Effects Logistic Regression
本文提出一种针对混合效应逻辑回归模型的拟合优度检验方法，通过分组Wald检验检测固定效应的不规范性，适用于稀疏聚类数据，且在小样本情况下表现良好。
A New Bootstrap Goodness-of-Fit Test for Normal Linear Regression Models
本文通过分析似然信息准则中拟合优度项的分布性质，提出了一种基于非参数自助法的正态线性回归模型拟合优度检验，并通过模拟研究验证了其相对于现有方法的优势。
Bahadur efficiency for certain goodness--of--fit tests based on the empirical characteristic function
本文研究基于经验特征函数的加权L2型拟合优度检验的Bahadur效率，覆盖正态性、指数性及logistic分布检验，首次为logistic分布复合检验计算效率，并为BHEP和energy检验提供新的多元效率结果。
We propose an optimal estimating equation for logistic regression with linked data while accounting for false positives. It builds on a previous solution but estimates the regression coefficients with a smaller variance, in large samples.
This paper infers a single parameter in non-sparse logistic regression models. By transforming the null hypothesis into a moment condition, we construct the test statistic and obtain the asymptotic null distribution. Numerical experiments show that our method performs well.
A Compound Logistic Regression Model for Binary Responses
本文提出复合逻辑回归模型，用于处理二元响应中的相关性与协变量，扩展了传统逻辑回归的应用范围。
A New Look at the Odds Ratio in Logistic Regression
针对逻辑回归标准比值比仅限单个变量的局限，推导出适用于所有解释变量及其组合的多变量比值比。
In several FICO studies logistic regression has been shown to be a very competitive technology for developing unrestricted scoring models, especially for performance metrics like ROC area. Application of logistic regression has been hampered by the lack of software to handle complex score engineering such as shape and pattern constraints. The purpose of this paper is to develop a sequential quadratic programming algorithm for score engineered logistic regression. This approach is based on a simple Taylor series expansion of minus log likelihood, which is locally quadratic. and fits in with the…
Logistic Regression Model for Differentially-Private Matrix Masked Data
本文提出了一种在差分隐私矩阵掩码数据下有效进行逻辑回归统计分析的方法，通过理论分析和实验验证其有效性。
A sizable amount of goodness-of-fit tests involving functional data have appeared in the last decade. We provide a relatively compact revision of most of these contributions, within the independent and identically distributed framework, by reviewing goodness-of-fit tests for distribution and regression models with functional predictor and either scalar or functional response.
The Zenga (1984) inequality curve is constant in p for Type I Pareto distributions. This characterizing behavior will be exploited to obtain graphical and analytical tools for tail analysis and goodness of fit tests. A testing procedure for Pareto-type behavior based on a regression of technique will be introduced.
In this paper we propose a principal component Liu-type logistic estimator by combining the principal component logistic regression estimator and Liu-type logistic estimator to overcome the multicollinearity problem. The superiority of the new estimator over some related estimators are studied under the asymptotic mean squared error matrix. A Monte Carlo simulation experiment is designed to compare the performances of the estimators using mean squared error criterion. Finally, a conclusion section is presented.
Rejoinder to "Multivariate Bayesian Logistic Regression for Analysis of Clinical Trial Safety Issues" by W. DuMouchel [arXiv:1210.0385].
Benchmarking Goodness-of-Fit and Calibration Algorithms for Logistic Regression Classifiers: A Large-Scale Simulation Study under Sparse Data
研究逻辑回归分类器拟合优度和校准算法，通过开源R包实现二十多种测试，在多种场景下评估，发现紧凑核心测试平衡最佳且比Hosmer-Lemeshow测试更强大，为评估逻辑回归拟合提供实用指南。
Discussion of "Multivariate Bayesian Logistic Regression for Analysis of Clinical Trial Safety Issues" by W. DuMouchel [arXiv:1210.0385].
Discussion of "Multivariate Bayesian Logistic Regression for Analysis of Clinical Trial Safety Issues" by W. DuMouchel [arXiv:1210.0385].
Goodness-of-Fit Tests and Calibration Machine-Learning Algorithms for Logistic Regression with Sparse Data
本论文针对稀疏数据下的逻辑回归，比较约30种统计检验与机器学习校准算法，发现多种检验需结合可视化检查，才能有效评估模型拟合优度。
This article develops the theoretical framework needed to study the multinomial logistic regression model for complex sample design with pseudo minimum phi-divergence estimators. Through a numerical example and simulation study new estimators are proposed for the parameter of the logistic regression model with overdispersed multinomial distributions for the response variables, the pseudo minimum Cressie-Read divergence estimators, as well as new estimators for the intra-cluster correlation coefficient. The results show that the Binder's method for the intra-cluster correlation coefficient exhi…
We obtain new mathematical properties of the exponentiated odd log-logistic family of distributions, and of its special case named the exponentiated odd log-logistic Weibull, and its log transformed. A new location and scale regression model is constructed, and some simulations are carried out to verify the behavior of the maximum likelihood estimators, and of the modified deviance-based residuals. The methodology is applied to the Japanese-Brazilian emigration data.
This paper looks at effects, due to the boundary, on inference in logistic regression. It shows that first -- and, indeed, higher -- order asymptotic results are not uniform across the model. Near the boundary, effects such as high skewness, discreteness and collinearity dominate, any of which could render inference based on asymptotic normality suspect. A highly interpretable diagnostic tool is proposed allowing the analyst to check if the boundary is going to have an appreciable effect on standard inferential techniques.
A penalized logistic generalized regression estimator
本文在模型辅助框架下提出一种惩罚逻辑广义回归估计量，结合Lasso或Ridge惩罚控制辅助变量影响，经模拟和实例验证可提高稀疏模型下估计效率，适用于含多辅助变量的复杂调查数据场景。
In order to overcome multicollinearity, we propose a stochastic restricted Liu-type max- imum likelihood estimator by incorporating Liu-type maximum likelihood estimator (Inan and Erdo- gan, 2013) to the logistic regression model when the linear restrictions are stochastic. We also discuss the properties of the new estimator. Moreover, we give a method to choose the biasing parameter in the new estimator. Finally, a simulation study is given to show the performance of the new estimator.
We consider Bayesian logistic regression models with group-structured covariates. In high-dimensional settings, it is often assumed that only small portion of groups are significant, thus consistent group selection is of significant importance. While consistent frequentist group selection methods have been proposed, theoretical properties of Bayesian group selection methods for logistic regression models have not been investigated yet. In this paper, we consider a hierarchical group spike and slab prior for logistic regression models in high-dimensional settings. Under mild conditions, we esta…
Consider a set of categorical variables $\mathcal{P}$ where at least one, denoted by $Y$, is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the binary variable as the outcome. Extending results in Christensen (1997), by also considering the case where factors present in the contingency table disappear from the logistic regression model, we prove that the Maximum Likelihood Estimate (MLE) for the parameters of the logistic regression equals the MLE for the corresponding parameters of the log-linear mod…
One Goodness-of-Fit Test Is Not Enough: Error-Controlled Localization of Misfit in Logistic Risk Models
该研究针对逻辑风险模型，提出将拟合不足拆分为四个正交部分，通过闭合检验实现误差控制的错误定位，外部验证可检测全部部分，模拟及重症监护数据验证了方法的有效性。
Objective: To investigate the impact of different logistic regression estimators applied to RDS samples obtained by simulation and real data. Methods: Four simulated populations were created combining different connectivity models, levels of clusterization and infection processes. Each subject in the population received two attributes, only one of them related to the infection process. From each population, RDS samples with different sizes were obtained. Similarly, RDS samples were obtained from a real-world dataset. Three logistic regression estimators were applied to assess the association b…
Consider a set of categorical variables where at least one of them is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the binary variable as the outcome. Within the Bayesian framework, the $g$-prior and mixtures of $g$-priors are commonly assigned to the parameters of a generalized linear model. We prove that assigning a $g$-prior (or a mixture of $g$-priors) to the parameters of a certain log-linear model designates a $g$-prior (or a mixture of $g$-priors) on the parameters of the corresponding logist…
A new family of minimum distance estimators for binary logistic regression models based on $ϕ$-divergence measures is introduced. The so called "pseudo minimum phi-divergence estimator"(PM$ϕ$E) family is presented as an extension of "minimum phi-divergence estimator" (M$ϕ$E) for general sample survey designs and contains, as a particular case, the pseudo maximum likelihood estimator (PMLE) considered in Roberts et al. \cite{r}. Through a simulation study it is shown that some PM$ϕ$Es have a better behaviour, in terms of efficiency, than the PMLE.
Estimation of logistic regression parameters for complex survey data: a real data based simulation study
针对复杂调查数据中逻辑回归参数估计是否使用抽样权重的问题，通过基于真实数据的模拟研究比较三种方法，结果表明加权逻辑回归模型更优，凸显了抽样权重的重要性。
We introduce Bayesian additive regression trees (BART) for log-linear models including multinomial logistic regression and count regression with zero-inflation and overdispersion. BART has been applied to nonparametric mean regression and binary classification problems in a range of settings. However, existing applications of BART have been limited to models for Gaussian "data", either observed or latent. This is primarily because efficient MCMC algorithms are available for Gaussian likelihoods. But while many useful models are naturally cast in terms of latent Gaussian variables, many others …
Mastering Rare Event Analysis: Optimal Subsample Size in Logistic and Cox Regressions
针对现有最优子采样方法缺乏最优子样本量选择工具的问题，本研究提出了适配稀有事件Cox回归、平衡与不平衡数据logistic回归的样本量选择工具及不平衡数据logistic回归的新型子采样流程，并通过模拟与真实数据集分析验证了有效性。
This paper derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald-type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the l…
Data generation for the logistic regression model under controlled conditions
针对受控条件下逻辑回归模型数据生成的难题，提出集成迭代二分算法，可确定截距与回归系数以生成指定患病率和预测准确率的数据，经模拟验证性能，且需考虑参数选择与预测准确率的关系用于模型评估数据生成。
Recently, graph (network) data is an emerging research area in artificial intelligence, machine learning and statistics. In this work, we are interested in whether node's labels (people's responses) are affected by their neighbor's features (friends' characteristics). We propose a novel latent logistic regression model to describe the network dependence with binary responses. The key advantage of our proposed model is that a latent binary indicator is introduced to indicate whether a node is susceptible to the influence of its neighbour. A score-type test is proposed to diagnose the existence …
Logistic regression models for binomial responses are routinely used in statistical practice. However, the maximum likelihood estimate may not exist due to data separability. We address this issue by considering a conjugate prior penalty which always produces finite estimates. Such a specification has a clear Bayesian interpretation and enjoys several invariance properties, making it an appealing prior choice. We show that the proposed method leads to an accurate approximation of the reduced-bias approach of Firth (1993), resulting in estimators with smaller asymptotic bias than the maximum-li…
Shrinkage invalidates the Hosmer-Lemeshow test: goodness of fit for penalized logistic regression, with an application to glaucoma diagnosis
惩罚逻辑回归下Hosmer-Lemeshow检验因收缩失效，提出收缩校正版本，并在青光眼诊断中显示模型需重新校准而非重建。
Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets only. It is shown how outlier-free subsets can be identified efficiently, and how appropriate tuning parameters for the elastic net penalties can be selected. A final reweighting step improves the efficiency of the estimators. Simulation studies compare with non-robust and other competing robust estimators and reveal the superiority of the newly proposed met…
Firth-type logistic regression has become a standard approach for the analysis of binary outcomes with small samples. Whereas it reduces the bias in maximum likelihood estimates of coefficients, bias towards 1/2 is introduced in the predicted probabilities. The stronger the imbalance of the outcome, the more severe is the bias in the predicted probabilities. We propose two simple modifications of Firth-type logistic regression resulting in unbiased predicted probabilities. The first corrects the predicted probabilities by a post-hoc adjustment of the intercept. The other is based on an alterna…
An accurately identified maximum tolerated dose (MTD) serves as the cornerstone of successful subsequent phases in oncology drug development. Bayesian logistic regression model (BLRM) is a popular and versatile model-based dose-finding design. However, BLRM with original overdose control strategy has been reported to be safe but "excessively conservative". In this manuscript, we investigate the reason for conservativeness and point out that a major reason could be the lack of appropriate underdose control. We propose designs that balance overdose and underdose control to improve the performanc…
This paper describes a method for a model-based analysis of clinical safety data called multivariate Bayesian logistic regression (MBLR). Parallel logistic regression models are fit to a set of medically related issues, or response variables, and MBLR allows information from the different issues to "borrow strength" from each other. The method is especially suited to sparse response data, as often occurs when fine-grained adverse events are collected from subjects in studies sized more for efficacy than for safety investigations. A combined analysis of data from multiple studies can be perform…
This is a note on logistic regression models and logistic kernel machine models. It contains derivations to some of the expressions in a paper -- SNP Set Analysis for Detecting Disease Association Using Exon Sequence Data -- submitted to BMC proceedings by these authors.
[DeepGOF] Where Does a Logistic Risk Model Fail? An Audited Neural Goodness-of-Fit Test for Model Development and External Validation
针对逻辑回归拟合优度检验在小样本下水平漂移的问题，提出基于预训练卷积网络的检验方法，利用自助法校准保证水平精确性，并提供可计算的一致性证书，在基准上表现稳定且功效优越。
This study aims to show the fundamental difference between logistic regression and Bayesian classifiers in the case of exponential and unexponential families of distributions, yielding the following findings. First, the logistic regression is a less general representation of a Bayesian classifier. Second, one should suppose distributions of classes for the correct specification of logistic regression equations. Third, in specific cases, there is no difference between predicted probabilities from correctly specified generative Bayesian classifier and discriminative logistic regression.
Maximum-likelihood regression with systematic errors for astronomy and the physical sciences: I. Methodology and goodness-of-fit statistic of Poisson data
本文提出一种准最大似然方法，将系统误差纳入泊松数据的回归分析，推广Cash统计量以处理过离散，并通过模拟和真实天文数据验证，为整数计数数据分析提供通用框架。
Liu-type Shrinkage Estimators for Mixture of Logistic Regressions: An Osteoporosis Study
针对混合逻辑回归模型中多重共线性导致最大似然估计不可靠的问题，本研究开发了岭估计器和Liu型估计器等收缩方法，数值研究及50岁及以上女性骨质疏松应用均证实该方法能提供更可靠的系数估计。
Recently, a very attractive logistic regression inference method for exponential family Gibbs spatial point processes was introduced. We combined it with the technique of quadratic tangential variational approximation and derived a new Bayesian technique for analysing spatial point patterns. The technique is described in detail, and demonstrated on numerical examples.
In this paper we discuss how to evaluate the differences between fitted logistic regression models across sub-populations. Our motivating example is in studying computerized diagnosis for learning disabilities, where sub-populations based on gender may or may not require separate models. In this context, significance tests for hypotheses of no difference between populations may provide perverse incentives, as larger variances and smaller samples increase the probability of not-rejecting the null. We argue that equivalence testing for a prespecified tolerance level on population differences inc…
Logistic regression has been widely applied in the field of biomedical research for a long time. In some applications, covariates of interest have a natural structure, such as being a matrix, at the time of collection. The rows and columns of the covariate matrix then have certain physical meanings, and they must contain useful information regarding the response. If we simply stack the covariate matrix as a vector and fit the conventional logistic regression model, relevant information can be lost, and the problem of inefficiency will arise. Motivated from these reasons, we propose in this pap…
Logistic regression is an important statistical tool for assessing the probability of an outcome based upon some predictive variables. Standard methods can only deal with precisely known data, however many datasets have uncertainties which traditional methods either reduce to a single point or completely disregarded. In this paper we show that it is possible to include these uncertainties by considering an imprecise logistic regression model using the set of possible models that can be obtained from values from within the intervals. This has the advantage of clearly expressing the epistemic un…
A Two-Step Projection-Based Goodness-of-Fit Test for Ultra-High Dimensional Sparse Regressions
本文提出了一种针对超高维稀疏回归的两步投影型适配性检验方法，通过构建投影统计量并结合p值组合程序，提高了在高维数据下的检验功效。
We propose a new algorithm called PLUTO for building logistic regression trees to binary response data. PLUTO can capture the nonlinear and interaction patterns in messy data by recursively partitioning the sample space. It fits a simple or a multiple linear logistic regression model in each partition. PLUTO employs the cyclical coordinate descent method for estimation of multiple linear logistic regression models with elastic net penalties, which allows it to deal with high-dimensional data efficiently. The tree structure comprises a graphical description of the data. Together with the logist…
In this letter, we consider the problem of field estimation using binary measurements. Previous work has formulated the problem as a parameter estimation problem, with the parameter estimation carried out in an online manner using sequential Monte Carlo techniques. In the current work, we consider an alternative approach to the parameter estimation based on online logistic regression. The developed algorithm is less computationally intensive than the sequential Monte Carlo approach, while having more reliable estimation performance.
We propose a penalized likelihood method that simultaneously fits the multinomial logistic regression model and combines subsets of the response categories. The penalty is non differentiable when pairs of columns in the optimization variable are equal. This encourages pairwise equality of these columns in the estimator, which corresponds to response category combination. We use an alternating direction method of multipliers algorithm to compute the estimator and we discuss the algorithm's convergence. Prediction and model selection are also addressed.
Robust Liu-Type Estimation for Multicollinearity in Fuzzy Logistic Regression
本文提出了一种针对模糊逻辑回归中多重共线性问题的鲁棒刘型估计方法，通过模拟和实际数据验证了FLLTPE和FLLTE在参数估计中的优越性。
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