Comparison of Multivariate Matching Methods: Structures,Distances, and Algorithms

Abstract

A comparison and evaluation is made of recent proposals for multivariate matched sampling in observational studies, where the following three questions are answered: (1) Algorithms: In current statistical practice, matched samples are formed using “nearest available” matching, a greedy algorithm. Greedy matching does not minimize the total distance within matched pairs, though good algorithms exist for optimal matching that do minimize the total distance. How much better is optimal matching than greedy matching? We find that optimal matching is sometimes noticeably better than greedy matching in the sense of producing closely matched pairs, sometimes only marginally better, but it is no better than greedy matching in the sense of producing balanced matched samples. (2) Structures: In common practice, treated units are matched to one control, called pair matching or 1–1 matching, or treated units are matched to two controls, called 1–2 matching, and so on. It is known, however, that the optimal structure is a full matching in which a treated unit may have one or more controls or a control may have one or more treated units. Optimal 1 — k matching is compared to optimal full matching, finding that optimal full matching is often much better. (3) Distances: Matching involves defining a distance between covariate vectors, and several such distances exist. Three recent proposals are compared. Practical advice is summarized in a final section.     

The Interaction of Benzyl Alcohol with Trimethoxyboroxine : Amine Adducts of Triarylboroxines as Model Compounds

The interaction of benzyl alcohol with trimethoxyboroxine has been investigated by hydrogen-1 and carbon-13 NMR and IR spectroscopy. These techniques indicate formation of a weak Lewis acid/base adduct, additionally stabilized by a hydrogen-bonding interaction, which undergoes rapid ligand exchange at room temperature. The system has been modelled by the synthesis and characterization of a series of amine-triarylboroxine adducts. These adducts rapidly undergo ligand dissociation-recombination in solution with ΔG⁺ of ca. 40-50 kJ/mol.     

Stable,High‐Molecular‐Weight Poly(phthalaldehyde)

Low ceiling temperature, thermodynamically unstable polymers have been troublesome to synthesize and keep stable during storage. In this study, stable poly(phthalaldehyde) has been synthesized with BF₃‐OEt₂ catalyst. The role of BF₃ in the polymerization is described. The interaction of BF₃ with the monomer is described and used to maximize the yield and molecular weight of poly(phthalaldehyde). Various Lewis acids were used to investigate the effect of catalyst acidity on poly(phthalaldehyde) chain growth. In situ nuclear magnetic resonance was used to identify possible interactions formed between BF₃ and phthalaldehyde monomer and polymer. The molecular weight of the polymer tracks with polymerization yield. The ambient temperature stability of poly(phthalaldehyde) was investigated and the storage life of the polymer has been improved. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 55, 1166–1172     

A model of product line design and introduction sequence with reservation utility

Cannibalization is a major concern for a firm when designing a product line. In addition, external options from outside the firm’s product line may also play a significant role. In this paper, we investigate the impact of external options, represented by reservation utility, on product line design and introduction sequence. We find that: (a) heterogeneous reservation utility defines the relative attractiveness of segments and corresponding product line; (b) reservation utility makes it more favorable to introduce products sequentially rather than simultaneously; (c) aggregating segments is an effective way to mitigate cannibalization when it becomes too difficult to manage with different values of reservation utility across multiple segments; and (d) introducing products in a non-monotone order of quality can improve profit from simultaneous introduction when the value of reservation utility of a middle segment is particularly high.     

Computationally Efficient Changepoint Detection for a Range of Penalties

In the multiple changepoint setting, various search methods have been proposed, which involve optimizing either a constrained or penalized cost function over possible numbers and locations of changepoints using dynamic programming. Recent work in the penalized optimization setting has focused on developing an exact pruning-based approach that, under certain conditions, is linear in the number of data points. Such an approach naturally requires the specification of a penalty to avoid under/over-fitting. Work has been undertaken to identify the appropriate penalty choice for data-generating processes with known distributional form, but in many applications the model assumed for the data is not correct and these penalty choices are not always appropriate. To this end, we present a method that enables us to find the solution path for all choices of penalty values across a continuous range. This permits an evaluation of the various segmentations to identify a suitable penalty choice. The computational complexity of this approach can be linear in the number of data points and linear in the difference between the number of changepoints in the optimal segmentations for the smallest and largest penalty values. Supplementary materials for this article are available online.