Gaining a better understanding of the factors that affect the likelihood of a vehicle crash has been an area of research focus for many decades. However, in the absence of detailed driving data that would help improve the identification of cause and effect relationships with individual vehicle crashes, most researchers have addressed this problem by framing it in terms of understanding the factors that affect the frequency of crashes - the number of crashes occurring in some geographical space (usually a roadway segment or intersection) over some specified time period. This paper provides a detailed review of the key issues associated with crash-frequency data as well as the strengths and weaknesses of the various methodological approaches that researchers have used to address these problems. While the steady march of methodological innovation (including recent applications of random parameter and finite mixture models) has substantially improved our understanding of the factors that affect crash-frequencies, it is the prospect of combining evolving methodologies with far more detailed vehicle crash data that holds the greatest promise for the future.

http://ceprofs.tamu.edu/dlord/Papers/Lord-Mannering_Review.pdf

The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives

Data from 16S ribosomal RNA (rRNA) amplicon sequencing present challenges to ecological and statistical interpretation. In particular, library sizes often vary over several ranges of magnitude, and the data contains many zeros. Although we are typically interested in comparing relative abundance of taxa in the ecosystem of two or more groups, we can only measure the taxon relative abundance in specimens obtained from the ecosystems. Because the comparison of taxon relative abundance in the specimen is not equivalent to the comparison of taxon relative abundance in the ecosystems, this presents a special challenge. Second, because the relative abundance of taxa in the specimen (as well as in the ecosystem) sum to 1, these are compositional data. Because the compositional data are constrained by the simplex (sum to 1) and are not unconstrained in the Euclidean space, many standard methods of analysis are not applicable. Here, we evaluate how these challenges impact the performance of existing normalization methods and differential abundance analyses. Effects on normalization: Most normalization methods enable successful clustering of samples according to biological origin when the groups differ substantially in their overall microbial composition. Rarefying more clearly clusters samples according to biological origin than other normalization techniques do for ordination metrics based on presence or absence. Alternate normalization measures are potentially vulnerable to artifacts due to library size. Effects on differential abundance testing: We build on a previous work to evaluate seven proposed statistical methods using rarefied as well as raw data. Our simulation studies suggest that the false discovery rates of many differential abundance-testing methods are not increased by rarefying itself, although of course rarefying results in a loss of sensitivity due to elimination of a portion of available data. For groups with large (~10×) differences in the average library size, rarefying lowers the false discovery rate. DESeq2, without addition of a constant, increased sensitivity on smaller datasets ( 20 samples per group) but also critically the only method tested that has a good control of false discovery rate. These findings guide which normalization and differential abundance techniques to use based on the data characteristics of a given study.

/pdf/normalization-and-microbial-differential-abundance-4i311yp8jx.pdf

Normalization and microbial differential abundance strategies depend upon data characteristics

This article introduces the use of regression models based on the Poisson distribution as a tool for resolving common problems in analyzing aggregate crime rates. When the population size of an aggregate unit is small relative to the offense rate, crime rates must be computed from a small number of offenses. Such data are ill-suited to least-squares analysis. Poisson-based regression models of counts of offenses are preferable because they are built on assumptions about error distributions that are consistent with the nature of event counts. A simple elaboration transforms the Poisson model of offense counts to a model of per capita offense rates. To demonstrate the use and advantages of this method, this article presents analyses of juvenile arrest rates for robbery in 264 nonmetropolitan counties in four states. The negative binomial variant of Poisson regression effectively resolved difficulties that arise in ordinary least-squares analyses.

Poisson-Based Regression Analysis of Aggregate Crime Rates

http://eprints.lse.ac.uk/25506/1/Further_Simulation_Evidence_on_the_Performance_of_the_Poisson_Pseudo%2DMaximum_Likelihood_Estimator.pdf

Further simulation evidence on the performance of the Poisson pseudo-maximum likelihood estimator

Self-report is often used to estimate health care utilization. However, the accuracy of such data is of paramount concern. The authors conducted a systematic review of 42 studies that evaluated the accuracy of self-report utilization data, where utilization was defined as a visit to a clinical provider or entity. They also present a broad conceptual model that identifies major issues to consider when collecting, analyzing, and reporting such data. The results show that self-report data are of variable accuracy. Factors that affect accuracy include (1) sample population and cognitive abilities, (2) recall time frame, (3) type of utilization, (4) utilization frequency, (5) questionnaire design, (6) mode of data collection, and (7) memory aids and probes.

Self-reported utilization of health care services: improving measurement and accuracy.

Regression Analysis of Count Data: Preface

Regression Analysis of Count Data: Measurement Errors

Introduction Econometric models of durations are models of the length of time spent in a given state before transition to another state, such as duration unemployed or alive or without health insurance. In biostatistics a duration in a state is also known as lifetime and the time of transition is referred to as death ; in operations research where one often studies lifetimes of physical objects such as light bulbs and machines, the end of useful life, that is, transition to useless life, is called failure time . In econometrics a state is a classification of an individual entity at a point in time, transition is movement from one state to another, and a spell length or duration is the time spent in a given state. A typical regression example is determining the effect of higher unemployment benefit levels on the average length of an unemployment spell or the probability of transition out of unemployment. The literature on this subject can be quite daunting, for a number of reasons. First, several related distributional functions are of interest and either the duration or probability of transition may be modeled. Second, many different sampling schemes are possible and statistical inference depends on both the duration model and the sampling scheme. For example, sampling methods for data on unemployment duration include flow sampling of those entering unemployment in a given month, stock sampling of people unemployed in a given month, and population sampling of all people regardless of employment status.

Pravin K. Trivedi

Papers

Regression Analysis of Count Data: Preface

Regression Analysis of Count Data: Measurement Errors

Microeconometrics: Transition Data: Survival Analysis

Regression Analysis of Count Data: Notation and Acronyms

Microeconometrics: Binary Outcome Models