MVME5500 automatic spare parts card module
Technical data of product parameters
Since crashes are fortunately rare events, it is not uncommon to find situations where some roadway
sections or intersections may have very few crashes, with many sites having zero crashes (i.e., with low
sample mean). These types of data may cause problems in estimation and some models may not
converge. In addition, Lord (2006) found that the overdispersion parameter that is estimated as part of
a negative binomial model can be biased when the sample mean is very low. At this time, there are few
solutions to this problem, except for a method suggested by ElvikMVME5500that involves “selecting a
subsample with even lower mean value than the full sample and estimate model coefficients for the
subsample” to see if the parameter estimates and the overdispersion parameter are stable.
Bias due to aggregation, averaging, or incompleteness in data
It is common that prediction models are based on summary data based on annual or monthly totals (i.e.,
aggregated data). Elvik indicates that the “use of data that are aggregated, averaged, or incomplete can
MVME5500Final Report – Recommended Protocols for Developing Crash Modification Factors 18
lead to biased estimates or model coefficients” (Elvik, 2011a, p. 256). One solution to this problem is to
use disaggregate data, such as hourly volumes instead of AADT, but that could require the analysis to
not only address the problems due to low sample mean (discussed earlier) and temporal correlation
(discussed below), but also to find a source for hourly volumes. For example, Lord et alMVME5500
data on hour traffic volume from freeway sections in Montreal, Quebec, to examine the relationship
between crashes, traffic flow, density, and v/c ratio. Lord et al., (2005) used the generalized estimating
equationsMVME5500 approach to address temporal correlation. Hierarchical Bayes models can also lead to
more stable parameter estimates and more accurate models with respect to both individual- and
aggregate-level performance (Orme, 2000).
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