Rusdi -

You asked about "...total of crashes (by consider total length and AADT)...." Does that mean that you do not actually have the number of accidents by segment? If you have to estimate number of accidents for each segment, then a separate estimate of total accidents in a given period each can give you a different estimate if you total those, than if you do a combined estimate to begin with, I think, depending upon how you do it. But I would think you would have access to the actual number of accidents in each segment in the given (annual?) period. Then adding the number of accidents in each segment for a given road is the same number as the total number of accidents on that road.

Do your segments each have their own entrance and exit points, so that the overall AADT will be different for each, or for at least some segments of A, than for A overall, and similarly for B? If so, then it seems very important to look at each segment.

Are you looking to compare A and B overall as alternate routes between the same two destinations? If so, and you have total accidents (in the year?) for each segment of A and total accidents (same period) for each segment of B, then you can compare apparent safety of the two routes by looking at road totals for accidents. (Of course this may vary each year.)

If you are looking at accidents per mile or kilometer, it seems you would still be interested in each segment.

It would also seem interesting, though you have very little data here, to compare accidents per kilometer (y-value) to AADT per kilometer (x-value) for the nine data points you have. If the segments vary somewhat in length, then a slight improvement might be obtained by weighting these points in a regression, but I would be more concerned with the heteroscedasticity and its impact on regression weight. But here you only have nine distinct data points, four for one road and five for the other, so you hardly have enough even to determine if the relationship between traffic volume as predictor for accidents is linear or nonlinear. I suspect it is nonlinear, but if linear 'enough,' it would seem that the slope, telling you accidents per traffic volume unit, would be interesting. There are a lot of other predictors (regressors) involved in determining accidents. So this would only give rough ideas for further study. But you could do a scatterplot of y and x (as noted above), with the points for the two roads color coded, just to see what the scatterplot looks like. But remember that you have very little data, and missing regressors that add to the residuals, so this will not be conclusive. (You might call it 'exploratory.') The attached spreadsheet and info in the RG 'abstract' may be of interest to such a study.

Also, how much measurement error do you have? That is, do you think you have high quality data?

You asked this: "Should I compare the total of crashes (by consider total length and AADT) for both roads or doing separately by segments and after that compare the average?"

To more directly answer this, I'd say you probably want to look at each segment.

Best wishes - Jim

Data CRE Prediction 'Bounds' and Graphs Example for Section 4 of ...

Dear Eng Rusdi Rusli,

Road safety today is about the fatal and serious injury crashes and how to prevent them in spite of human fallibility. This enables a simple model for comparison, even without crash statistics, and improved comparison is possible where crash statistics are available.

Best practice road safety can reduce today's road infrastructure costs because the old approach delivers straighter, wider and flatter roads, which is contrary to the latest human factor research and the energy transfer physics associated with barriers.

There is a Safe System Review and Action Plan process that can help any road infrastructure practitioner to achieve true safety.

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Refer to the Highway safety manual there is a chapter related to how to estimate the expected number of crashes (chapter 10 for rural two lane , Ch 11 for rural multilane and Ch 12 for Urban highways) this will help you to consider the expected number of crashes, to compare them you should have the observed number of crashes over period of years, check the calibration factor to change from one site to the other site 

Best Regards

You plan to make a comparison between the 2 locations, and each location has its own road segments, for a total of 9 segments. The number of crashes that you have recorded could of course be normalised by AADT and by length of segment.

However, before proceeding with any analysis, it is important to know:

1) How many pieces of data you have. Do you have just one piece of data for each segment, that is the total number of accidents for the whole year, making up for a total of 9 numbers? If not, what detail do you have?

2) What crash information per record you have. Do you have information about the severity of crashes so that we can perform classification?

If you answer these 2 questions, it will be easier to discuss further.

Best

Yorgos

Hi James,

Sorry took long time to answer this questions.

I have crashes record for the 5 years period for every segments. These segments are not connected each others. I just identify road segments with the same geographical condition and put either as a A and B.

Yes, every segments have different entrance and exit points, AADT and length different each others.

I try to compare the crash characteristics such as crash type, vehicle type etc between these two location, A and B.

AADT and length are different between each segments. Right now, we used kilometer post as the indicator for crash location.

Regards

Rusdi

Hi Fatemeh,

Not at all at this stage. This study only to identify different crash characteristics at A and B. There have different geographical conditions as well as AADT and Speed Limit.

Hi Brendan,

Maybe at next stage we be looking for this thing.

Rusdi

Hi Muath,

We have crash data for all these segments for 5 years as well as AADT and length.

Hi Yorgos,

That's correct.

Answer:

Q1) We have every single crash data with 90 variables such as crash type, vehicle type etc. for each segments.

Q2) Yes, we also have personal record for each victim involved in all the crashes such as severity, sex, gender etc.

Regards,

Rusdi

Thanks all for contribution..

Rusdi -

It seems you have a great many variables, and relatively little data. As Fatemeh noted, it would be helpful when investigating the impact of one characteristic, to be able to hold the others constant. However, that would appear to leave little data for each such test. Multiple regression comes to mind, but that can get rather difficult to assess, and the scarcity of data would probably tend to push you to overfit the models, meaning the model would not hold up with new data.

It sounds like data must be taken at the segment level, but overall conclusions may be more at the road location level.

Perhaps you should pick variables you want to compare, two at a time, and plot them on a scatterplot. No regression lines to start with, just data points. You could look at a number of these scatterplots to try to get an idea as to any patterns that might emerge. You could take similar data, say the same x,y paired data for some comparison in a given year, for example, but then include the same data from the other years, color-coding the different years. By including similar - but different - data, color- and/or shape-coded points on a scatterplot, you may discover other relationships.

One possibility would be that you could have various x-y relationships that may be linear regressions through the origin. For each of those you would have a slope estimate, b, that relates y as predicted by x, an estimated standard error of b, and you could estimate the "variance of the prediction error" for given predicted y-values. You could compare b estimates for pairs of segments or compare b for the two roads by looking at the difference between the two b's and estimating the standard error around that difference. If a reasonable (%) confidence interval around the difference in b estimates does not include zero, then maybe you found a substantial difference. I would look at confidence intervals, rather than p-values, as a p-value is a function of sample size and does not stand alone well without a specific power analysis or other sensitivity analysis. Confidence intervals would be more practical.

You could amass descriptive statistics - means and standard errors of means, etc - for the lowest level groups and some more aggregate level groups.

It sounds like you have a lot of exploring to do. But with relatively scarce data with so many variables, it will be difficult to avoid overstating results that may not hold up in a second study later. So caution is required.

Starting with scatterplots and other graphics, to look for patterns and to become familiar with the data, may be a good beginning.

By the way, for a difference between two b's or for a difference between two means of randomly drawn data, if they are for independently drawn data, the variance of the difference is the variance of one (b or mean or total) plus the variance of the other one. For dependent samples, there is -2 times the covariance to include, but I don't see that happening here. I could be wrong.

So, graphics and descriptive tables to begin with - remembering standard deviations and standard errors; some confidence intervals; maybe some regressions. Those might be helpful, I think.

Cheers - Jim 

Hi James,

Thanks for your advice. I used descriptive analysis for those variables in getting clear view about all of them. Until today, I found a few significant variables for further study.

Regards,

Rusdi

Sounds good. Hope you find some interesting, useful information. 

This is great question as the first step into the world of statistical analysis of traffic safety :-) Snce crash data are count (discrete), non-negative, not normally distributed, common regression techniques cannot be used here - generalized linear regression is usually used. Explanatory variables are the ones you mention - AADT, length, etc.

Rusdi -  Ah!  Jiri noted your data are discrete.  Yes, my experience was in continuous data. Good point. It appears that Jiri has some papers available through his ResearchGate page that may be very useful for you.  - Best wishes. - Jim  

Since you have a lot of data, it would be useful to classify them in terms of certain strong variables, such as crash type and severity. After this, you can select the largest class and study that class. This should give a better chance of proposing statistically-significant relationships that will be applicable to that class.

Hi Jiri,

Thanks for your answer. I will try to use Negative Binomial model and Random Effect Negative Binomial model to relate explanatory variables with crash count. Do you have any recommendations to other models?

Hi James,

Yes. Crash data is discrete. I will learn more from you all.

Hi Yorgos,

After my first study, only used decriptive analysis, I found a few of strong variables such as run-off crash, speeding, single crashes and four wheel drive (pick up).

Hi Rusdi, I am also dealing with the issues that you mention. There are lots of details to be considered: how should roads be segmented, which variables to use, which function forms, which kind of model, how to check its quality, how to determine safety estimate, etc. It is impossible to write it all here... or maybe I am only lazy :-) All in all, I would recommend to read some example papers where authors did exactly the same what you aim to do. I personally did some studies, but there are certainly better papers. Among all I would recommend Ezra Hauer - he is maybe the most renowned person in this area. Check his ResearchGate profile or alternatively this website - https://ezrahauer.wordpress.com/ I wish you success!

Thanks Jiri..I will check his ResearchGate profile.

I recommend the following website; it is helpful.

https://ezrahauer.wordpress.com/