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European R&D networks: a snapshot from the 7th EU Framework Programme
Published in Cristiano Antonelli, Albert N. Link, Assessing Technology and Innovation Policies, 2020
Sara Amoroso, Alex Coad, Nicola Grassano
As we are dealing with overly dispersed count data, ordinary least squares estimation approach is not appropriate (Silva and Tenreyro 2006). Most often, a Poisson model specification is applied (Scherngell and Barber 2009; Hoekman et al. 2013). However, many regions did not collaborate and the amount of zeros in the dependent variable is larger than assumed for a Poisson distribution. As a result, the conditional variance may be higher than the conditional mean, Var[Yij|.] = exp(α)E[Yij|.], which violates the equidispersion property of the Poisson distribution. A common approach to deal with overdispersed data is the negative binomial regression model. Note that, when α=0 the data is equidispersed and a Poisson model is more adequate. We test the hypothesis α=0 using a likelihood ratio test.
God Spiked the Integers
Published in Richard McElreath, Statistical Rethinking, 2020
We will engineer complete examples of the two most common types of count model. Binomial regression is the name we’ll use for a family of related procedures that all model a binary classification—alive/dead, accept/reject, left/right—for which the total of both categories is known. This is like the marble and globe tossing examples from Chapter 2. But now you get to incorporate predictor variables. Poisson regression is a GLM that models a count with an unknown maximum—number of elephants in Kenya, number of applications to a PhD program, number of significance tests in an issue of Psychological Science. As described in Chapter 10, the Poisson model is a special case of binomial. At the end, the chapter describes some other count regressions.
Investigation of the effect of tourism on road crashes
Published in Journal of Transportation Safety & Security, 2020
Vasileios Bellos, Apostolos Ziakopoulos, George Yannis
A study in an island environment comparable to the Greek islands, namely, the Balearic Islands, has been conducted in Spain (Rosselló & Saenz-de-Miera, 2011). This study obtained data from different databases for day-to-day vehicle collisions in the islands. Several statistical methods were considered for the analyses. The presence of overdispersion led to the rejection of the Poisson regression model and the use of the negative binomial regression model. The results showed that tourism can be associated with a significant proportion of road traffic crashes in the Balearic Islands, as the study provided empirical evidence to show that, in fact, the presence of tourists leads to an increase in the number of road traffic crashes. Specifically, by quantifying the relationship between tourism and road traffic crashes, it was concluded that population growth due to the presence of tourists leads to an increase in road traffic crashes.
Model justification and stratification for confounding of Chlamydia trachomatis disease
Published in Letters in Biomathematics, 2019
The logistic model (or logit model) is a statistical model which is usually taken to apply on a binary dependent variable. The logistic regression is the most important model for ordered categorical response data (Anderson, 1984; McCullagh, 1980). It is used increasingly in a wide variety of applications. It is not only used in biomedical studies but also rapidly used in social science research and marketing in the past 20 years. Apart from this, another area of increasing application is genetics. In statistics, binomial regression is a technique in which the response (often referred to as Y) is the result of a series of Bernoulli trials or a series of one of two possible disjoint outcomes (traditionally denoted as ‘success’ or 1, and ‘failure’ or 0). The log-binomial model is simply a binomial generalized linear model (GLM) with a log link function. It is particularly useful (or, popular) in biostatistical and epidemiological applications as an alternative to logistic regression.
How do users’ feedback influence creators’ contributions: an empirical study of an online music community
Published in Behaviour & Information Technology, 2023
As our dependent variables are count variables, we build a Negative Binomial regression model in Stata 14 to analyze creators’ content-contributions behaviors in UGC communities. The Negative Binomial regression model is mainly used to deal with count data, and our data is the amounts of content created by a creator per week. Besides, it deals with more variation than expected if the process were Poisson (Hoef and Boveng 2007). Considering the characteristics of our dataset, we use random effects to capture the unobserved traits of creators. As is shown in Table 1, the unconditional means of the independent variable of quantity is much lower than its variance, which suggests that overdispersion is present and that a Negative Binomial regression would be appropriate.