Many statisticians have had the experience of fitting a linear model with uncorrelated errors, then adding a spatially-correlated error term (random effect) and finding that the estimates of the fi...

Since quantile regression curves are estimated individually, the quantile curves can cross, leading to an invalid distribution for the response. A simple constrained version of quantile regression is proposed to avoid the crossing problem for both linear and nonparametric quantile curves. A simulation study and a reanalysis of tropical cyclone intensity data shows the usefulness of the procedure. Asymptotic properties of the estimator are equivalent to the typical approach under standard conditions, and the proposed estimator reduces to the classical one if there is no crossing. The performance of the constrained estimator has shown significant improvement by adding smoothing and stability across the quantile levels.

With the advance of methods for estimating species distribution models has come an interest in how to best combine datasets to improve estimates of species distributions. This has spurred the development of data integration methods that simultaneously harness information from multiple datasets while dealing with the specific strengths and weaknesses of each dataset. We outline the general principles that have guided data integration methods and review recent developments in the field. We then outline key areas that allow for a more general framework for integrating data and provide suggestions for improving sampling design and validation for integrated models. Key to recent advances has been using point‐process thinking to combine estimators developed for different data types. Extending this framework to new data types will further improve our inferences, as well as relaxing assumptions about how parameters are jointly estimated. These along with the better use of information regarding sampling effort and spatial autocorrelation will further improve our inferences. Recent developments form a strong foundation for implementation of data integration models. Wider adoption can improve our inferences about species distributions and the dynamic processes that lead to distributional shifts.

The last decade has seen a dramatic increase in the use of species distribution models (SDMs) to characterize patterns of species’ occurrence and abundance. Efforts to parameterize SDMs often create a tension between the quality and quantity of data available to fit models. Estimation methods that integrate both standardized and non‐standardized data types offer a potential solution to the tradeoff between data quality and quantity. Recently several authors have developed approaches for jointly modeling two sources of data (one of high quality and one of lesser quality). We extend their work by allowing for explicit spatial autocorrelation in occurrence and detection error using a Multivariate Conditional Autoregressive (MVCAR) model and develop three models that share information in a less direct manner resulting in more robust performance when the auxiliary data is of lesser quality. We describe these three new approaches (“Shared,” “Correlation,” “Covariates”) for combining data sources and show their use in a case study of the Brown‐headed Nuthatch in the Southeastern U.S. and through simulations. All three of the approaches which used the second data source improved out‐of‐sample predictions relative to a single data source (“Single”). When information in the second data source is of high quality, the Shared model performs the best, but the Correlation and Covariates model also perform well. When the information quality in the second data source is of lesser quality, the Correlation and Covariates model performed better suggesting they are robust alternatives when little is known about auxiliary data collected opportunistically or through citizen scientists. Methods that allow for both data types to be used will maximize the useful information available for estimating species distributions.