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Suggested Citation:"Appendix A Factor analysis details." National Academies of Sciences, Engineering, and Medicine. 2019. Identification of Factors Contributing to the Decline of Traffic Fatalities in the United States from 2008 to 2012. Washington, DC: The National Academies Press. doi: 10.17226/25590.
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Page 106
Page 107
Suggested Citation:"Appendix A Factor analysis details." National Academies of Sciences, Engineering, and Medicine. 2019. Identification of Factors Contributing to the Decline of Traffic Fatalities in the United States from 2008 to 2012. Washington, DC: The National Academies Press. doi: 10.17226/25590.
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Page 107

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Page 91 Appendix A Factor analysis details Factor analysis is a method of dimension reduction based on Principal Components Analysis (PCA). The starting point is a rectangular dataset with a relatively large number of correlated variables (p) and a larger number of observations (n). The original set of variables can be thought of as dimensions in a p- dimensional space, and PCA produces a new basis for that space, where each dimension in the new space is a linear combination of the original variables. The linear combinations are selected based on variance accounted for by each dimension. The first Principal Component (PC) is the linear combination that accounts for the most total variance in all variables, followed by the PC that accounts for the most remaining variance and is orthogonal to the first PC, followed by the PC that accounts for the most remaining variance and is orthogonal to the first two PCs, and so on. Once the PCs are determined, the next step is to select a small subset of dimensions to define a new, smaller space that accounts for a large proportion of the original variance. Note that these new dimensions (PCs) are orthogonal by definition. Factor analysis takes the reduced dimensions and rotates them in the original space to better line up with the original dimensions. The goal of the rotation is to produce a reduced, but more interpretable set of dimensions. In this application, a group of variables that are all correlated with a given PC give an indication of the “meaning” of that PC. From these groups, it is generally possible to identify a process that is being captured and to select 1-2 variables from the set that will be used in analysis of fatalities to represent that process. Factor analyses for this project were run in groups of similar variables to focus the data reduction activities around each variable grouping (rather than trying to develop dimensions across all possible variables. The analysis is not prescriptive in which variables might be the best predictors, so we present the reasoning behind our selections in each section. Population Variables Population variables include overall state population for each year, as well as state population broken down by age and gender, 19 variables in total. The factor analysis resulted in only one factor, which accounted for 97.7% of the total variation in all population variables. Thus, states vary generally in population, but do not have substantially different age distributions or gender distributions. Total population will be used to represent population in analysis where appropriate. VMT Variables A series of VMT variables including overall state VMT for each year, as well as VMT broken down by rural and urban road types, were available for analysis. Three factors were identified, but the first one accounts for 63% of the total variance and the second and third account for 8% and 7% respectively. The first factor generally reflects the magnitude of VMT for each state with an emphasis on urban VMT. The second reflects rural VMT variables, and the third is specific to VMT on rural freeways and rural local roads. Thus, urban VMT and rural VMT vary somewhat differently across states, but variation by road

Page 92 type is common across states. Based on these results, we selected total VMT (to capture the overall magnitude as in Factor 1) and proportion of VMT that is rural VMT (to capture rural-specific VMT as in Factors 2 and 3). Employment/Unemployment Variables Employment and unemployment for different age and gender groups consisted of 20 different variables. Factor analysis on these variables produce two factors that captured 68% and 15% of the variance, respectively. After rotation, Factor 1 primarily reflected average employment and unemployment (where employment had negative coefficients) with a greater weight on unemployment. Factor 2 primarily reflected employment alone and especially employment of older portions of the population (who, if retired, would affect the employment statistics but not the unemployment statistics). Although older adults’ employment varies somewhat differently from employment and unemployment across the age groups, further investigation of the relationship between employment, unemployment and fatalities showed that unemployment among young people (ages 16-24) is more strongly associated with fatalities than for other age groups. Since unemployment in this group is correlated with other employment/unemployment statistics, it captures the overall magnitude as well as the specific variation in the younger population. Thus, we used only this statistic as the predictor representing employment and unemployment. Expenditures Expenditures per mile were available for the following categories: total, capital, administrative, safety, maintenance, HSIP apportioned and HSIP obligated. The factor analysis of these variables returned a single factor explaining 74% of the variance. This factor reflected the overall magnitude of spending per mile, which varies by state but is fairly consistent across all categories. Because of the safety application of this project, we used two categories—capital expenditures and total safety expenditures including HSIP—to represent expenditures in our models.

Next: Appendix B Descriptive statistics »
Identification of Factors Contributing to the Decline of Traffic Fatalities in the United States from 2008 to 2012 Get This Book
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Between 2005 and 2011, the number of traffic fatalities in the U.S. declined by 11,031, from 43,510 in 2005 to 32,479 in 2011. This decline amounted to a reduction in traffic-related deaths of 25.4 percent, by far the greatest decline over a comparable period in the last 30 years.

Historically, significant drops in traffic fatalities over a short period of time have coincided with economic recessions. Longer recessions have coincided with deeper declines in the number of traffic fatalities. This report from the National Cooperative Highway Research Program, NCHRP Research Report 928: Identification of Factors Contributing to the Decline of Traffic Fatalities in the United States from 2008 to 2012, provides an analysis that identifies the specific factors in the economic decline that affected fatal crash risk, while taking into account the long-term factors that determine the level of traffic safety.

A key insight into the analysis of the factors that produced the sharp drop in traffic fatalities was that the young contributed disproportionately to the drop-off in traffic fatalities. Of the reduction in traffic fatalities from 2007 to 2011, people 25-years-old and younger accounted for nearly 48 percent of the drop, though they were only about 28 percent of total traffic fatalities prior to the decline. Traffic deaths among people 25-years-old and younger dropped substantially more than other groups. Young drivers are known to be a high-risk group and can be readily identified in the crash data. Other high-risk groups also likely contributed to the decline but they cannot be identified as well as age can.

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