Parametric modal regression with varying precision

In this paper, we propose a simple parametric modal linear regression model where the response variable is gamma distributed using a new parameterization of this distribution that is indexed by mode and precision parameters, that is, in this new regression model, the modal and precision responses are related to a linear predictor through a link function and the linear predictor involves covariates and unknown regression parameters. The main advantage of our new parameterization is the straightforward interpretation of the regression coefficients in terms of the mode of the positive response variable, as is usual in the context of generalized linear models, and direct inference in parametric mode regression based on the likelihood paradigm. Furthermore, we discuss residuals and influence diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. Finally, we illustrate the usefulness of the new model by two applications, to biology and demography.     

Some Improved Regression Estimators of Heritability

Three new improved regression estimators of heritability viz. modified range restricted estimator, minimum quadratic loss estimator and minimax linear restricted estimator are proposed. In addition, these estimators are illustrated and compared numerically with the existing restricted estimator based on linear stochastic constraint.     

Long-Term Ecological Research on Chlorophyll Cycling in the Yuanyang Lake Nature Preserve I. The Grey Prediction Models on Chlorophyll Degradation of Chamaecyparis var. Formosana Leaf

We applied the grey system theory to evaluation of chlorophyll (Chl) degradation in Chamaecyparis Sieb. & Zucc. var. formosana (Hayata) Rehder needle-leaf in the Yuanyang Lake Nature Preserve of northern Taiwan. Pigment analysis was finished within 12 h after collecting the samples. Four grey prediction models for the degradation of Chl a, Chl b, and for the change of Chl a/b ratio and water content were established and compared with the results of linear and exponential regression analysis. The residual error and accuracy range show that the grey prediction process is much better than regression analysis. The degradation of Chl a and b contains two phases, one being fast and the other slow.     

Estimation of regression models under linear restrictions

The variance-covariance matrices of restricted regression and mixed regression estimators are compared and the consequences of introducing variability in the restrictions are examined.     

Discretizing a Normal Prior for Change Point Estimation in Switching Regressions

Bayes decision procedures are considered for change point estimation in the simple bilinear segmented model. A discretized normal prior density is employed as the prior distribution for the change point index. Posterior probability functions are developed for this index under a vague prior formulation on the regression parameters. The procedure is applied to an example involving mercury toxicity data.     

When is Piece-Wise Regression Really Necessary?

Results are obtained showing that when a response surface can be modelled as a single function, then a single regressor is more efficient and less biased than a segmented regression. However, if the surface is segmented, a segmented regressor is less biased than a single regressor. Areas of application are indicated.     

Comparability of segmented line regression models

Segmented line regression models, which are composed of continuous linear phases, have been applied to describe changes in rate trend patterns. In this article, we propose a procedure to compare two segmented line regression functions, specifically to test (i) whether the two segmented line regression functions are identical or (ii) whether the two mean functions are parallel allowing different intercepts. A general form of the test statistic is described and then the permutation procedure is proposed to estimate the p-value of the test. The permutation test is compared to an approximate F-test in terms of the p-value estimation and the performance of the permutation test is studied via simulations. The tests are applied to compare female lung cancer mortality rates between two registry areas and also to compare female breast cancer mortality rates between two states.     

Fair regression for health care spending

The distribution of health care payments to insurance plans has substantial consequences for social policy. Risk adjustment formulas predict spending in health insurance markets in order to provide fair benefits and health care coverage for all enrollees, regardless of their health status. Unfortunately, current risk adjustment formulas are known to underpredict spending for specific groups of enrollees leading to undercompensated payments to health insurers. This incentivizes insurers to design their plans such that individuals in undercompensated groups will be less likely to enroll, impacting access to health care for these groups. To improve risk adjustment formulas for undercompensated groups, we expand on concepts from the statistics, computer science, and health economics literature to develop new fair regression methods for continuous outcomes by building fairness considerations directly into the objective function. We additionally propose a novel measure of fairness while asserting that a suite of metrics is necessary in order to evaluate risk adjustment formulas more fully. Our data application using the IBM MarketScan Research Databases and simulation studies demonstrates that these new fair regression methods may lead to massive improvements in group fairness (eg, 98%) with only small reductions in overall fit (eg, 4%).     

Bias correction of bounded location error in binary data

Binary regression models for spatial data are commonly used in disciplines such as epidemiology and ecology. Many spatially referenced binary data sets suffer from location error, which occurs when the recorded location of an observation differs from its true location. When location error occurs, values of the covariates associated with the true spatial locations of the observations cannot be obtained. We show how a change of support (COS) can be applied to regression models for binary data to provide coefficient estimates when the true values of the covariates are unavailable, but the unknown location of the observations are contained within nonoverlapping arbitrarily shaped polygons. The COS accommodates spatial and nonspatial covariates and preserves the convenient interpretation of methods such as logistic and probit regression. Using a simulation experiment, we compare binary regression models with a COS to naive approaches that ignore location error. We illustrate the flexibility of the COS by modeling individual-level disease risk in a population using a binary data set where the locations of the observations are unknown but contained within administrative units. Our simulation experiment and data illustration corroborate that conventional regression models for binary data that ignore location error are unreliable, but that the COS can be used to eliminate bias while preserving model choice.     

Deep transformation models for functional outcome prediction after acute ischemic stroke

In many medical applications, interpretable models with high prediction performance are sought. Often, those models are required to handle semistructured data like tabular and image data. We show how to apply deep transformation models (DTMs) for distributional regression that fulfill these requirements. DTMs allow the data analyst to specify (deep) neural networks for different input modalities making them applicable to various research questions. Like statistical models, DTMs can provide interpretable effect estimates while achieving the state-of-the-art prediction performance of deep neural networks. In addition, the construction of ensembles of DTMs that retain model structure and interpretability allows quantifying epistemic and aleatoric uncertainty. In this study, we compare several DTMs, including baseline-adjusted models, trained on a semistructured data set of 407 stroke patients with the aim to predict ordinal functional outcome three months after stroke. We follow statistical principles of model-building to achieve an adequate trade-off between interpretability and flexibility while assessing the relative importance of the involved data modalities. We evaluate the models for an ordinal and dichotomized version of the outcome as used in clinical practice. We show that both tabular clinical and brain imaging data are useful for functional outcome prediction, whereas models based on tabular data only outperform those based on imaging data only. There is no substantial evidence for improved prediction when combining both data modalities. Overall, we highlight that DTMs provide a powerful, interpretable approach to analyzing semistructured data and that they have the potential to support clinical decision-making.     

On the Estimation of Intra-Sire Regression Heritability Subject to Linear Constraint

The derivation of the restricted intra-sire regression heritability estimator is provided. Procedures for obtaining a stable estimate of residual error variance σ² are outlined. A small illustration based on live data is given.