It is quite common to encounter compositional data in a regression framework in data analysis. When both responses and predictors are compositional, most existing models rely on a family of log-ratio based transformations to move the analysis from the simplex to the reals. This often makes the interpretation of the model more complex. A transformation-free regression model was recently developed, but it only allows for a single compositional predictor. However, many datasets include multiple compositional predictors of interest. Motivated by an application to hydrothermal liquefaction (HTL) data, a novel extension of this transformation-free regression model is provided that allows for two (or more) compositional predictors to be used via a latent variable mixture. A modified expectation-maximization algorithm is proposed to estimate model parameters, which are shown to have natural interpretations. Conformal inference is used to obtain prediction limits on the compositional response. The resulting methodology is applied to the HTL dataset. Extensions to multiple predictors are discussed.

In an Order‐of‐Addition (OofA) problem, a response depends on the order in which several components are added to a system. This is critical for many modern applications, such as combinatorial drug therapy for cancer patients, chemical engineering, and NP‐hard optimization problems. If the number of components is large, it is impossible to check all possible orders. This motivates the use of Design of Experiments (DOE) to select an optimal and affordable subset of orders for an experiment. In the past few years alone, over 30 statistical publications have emerged that deal with design and modeling for OofA experiments. This large body of literature is difficult for new practitioners to navigate. The main goals of this article are to provide a comprehensive overview of the main models for OofA experiments, to introduce theoretical and algorithmic methods for constructing optimal OofA experiments, and to describe how to analyze the experimental results so that an optimal order‐of‐addition can be obtained. We provide recommendations for using a model‐free approach for solving OofA problems, as well as recommendations for using OofA models that incorporate the effects of other covariates. We also provide some novel discussion for designing experiments in the case where constraints on the pairwise order of components exist. Recent developments in OofA experiments will greatly impact research in pharmaceutical industries, biomedical science, chemical engineering, and computer science, as they allow researchers to efficiently construct designs for larger numbers of components than before. This article reviews the wide variety of approaches for constructing designs and models for OofA experiments, which is critical for continued innovation in this field.

Observational data with massive sample sizes are often distributed on many local machines. From an experimental design perspective, investigators often desire to identify the effect of new treatments (even ML algorithms) on many blocks of experimental data. With time requirements or budget constraints, assigning all treatments to each block is not always feasible. This creates incomplete responses with respect to a randomized complete block design (RCBD). These incomplete responses are missing by design. However, whether they can be estimated with missing imputation methods is not well understood. Thus, it is challenging to correctly identify the treatment effects with missing data. To this end, this paper provides a method for imputation and analysis of the responses with missing data. The proposed method consists of three steps: Reconstruction, Imputation, and ‘Complete’-data Analysis (RICA). The incomplete responses are imputed with the expectation-maximization (EM) algorithm. The RCBD model is then fitted by the resulting dataset. The identifiability result suggests that the missing may be nonignorable for each block, but the whole data of an incomplete design are missing by design when the design is balanced. Theoretical results on relative efficiency also inform us when the missingness should be imputed for incomplete designs with the role of balanced variance. Applications on real-world data verify the efficacy of this method.

Many experiments require modeling a non-Normal response. In particular, count responses and binary responses are quite common. The relationship between predictors and the responses are typically modeled via a Generalized Linear Model (GLM). Finding D-optimal designs for GLMs, which reduce the generalized variance of the model coefficients, is desired. A common approach to finding optimal designs for GLMs is to use a local design, but local designs are vulnerableto parameter misspecification. The focus of this paper is to provide designs for GLMs that are robust to parameter misspecification. This is done by applying a bagging procedure to pilot data, where the results of many locally optimal designsare aggregated to produce an approximate design that reflects the uncertainty in the model coefficients. Results show that the proposed bagging procedure is robust to changes in the underlying model parameters. Furthermore, the proposed designs are shown to be preferable to traditional methods, which may be over-conservative.

In recent years, the size of datasets has dramatically increased. This has encouraged the use of subsampling, where only a subset of the full dataset is used to fit a model in a more computationally efficient manner. Existing methods do not provide much guidance on how to find optimal subsamples for a linear model when the variance of the errors depends on the model covariates through an unknown function. This paper presents three main contributions that aid in finding optimal subsamples in the case of heteroscedastic errors. First, a kernel-based method is proposed for estimating the error variances in the full dataset based on a Latin Hypercube subsample. Second, a generalized version of the Information-Based Optimal Subdata Selection (IBOSS) algorithm is introduced that uses the variance estimates to find subsamples with high D−efficiency. Third, an Approximate Nearest Neighbor Simulated Annealing (ANNSA) algorithm is used to find subsamples that are efficient under the I−optimality criterion, which seeks to minimize integrated prediction error variance. Simulations show that the proposed subsampling algorithms have better D− and I−efficiencies than existing methods. The subsampling methods are used to analyze an airline dataset with over 7 million rows.