# Confused about textbook example of OLS with count data as dependent variable

As a student if traffic engineering/planning I'm a little confused about the use of OLS on count data. I'm currently reading Ortuzar and Willumson's book - Modelling Transport.

We've been assigned to build an OLS model with dependent/independent variables of our choice. In Ortuzar and Willumson's book, an OLS is discussed as one model to infer trip generation from geographical zones or households.

From my education, I find this problematic as the dependent variable is count data. I've read that OLS should have a truly continuous dependent variable (neg infinity to pos infinity). This cannot exist for number of trips per zone. The authors do discuss the use of a logit model, but im confused on why an OLS is included.

Is an OLS correct to use in calculating trip generation? Is there some law I'm missing?

Im interested in cycling and therefore would like to model bike trip generation. My plan was to build a model with origin destination cycling (strava) data by assigning number of commute trips from zones as dependent variable, and income, population density, land value as independent variables.

Any guidance on building an OLS to understand the first step in a 4 step model, trip generation would be highly appreciated.

• It would be germane to tell us the sizes of the counts in the data. The reason is that in practice there is no such thing as a "truly continuous" variable: continuity is a model that idealizes what really happens. (For instance, a computer using double-precision floats can represent at most $2^{64}$ values which, because they are finite in number, must have a discrete distribution.) Consequently, the question comes down to whether modeling the count responses with a continuous distribution will be sufficiently accurate for your needs. – whuber Feb 18 '17 at 14:20
• My answer here is relevant: stats.stackexchange.com/questions/142338/… – kjetil b halvorsen Feb 19 '17 at 18:08

It is perfectly true that any variable which is bounded above or below cannot have a normal distribution which conditional on the covariates is implied here by the OLS model since, as you hint, the normal has its support on the whole real line. In practice though we are willing to take a view on this for practical purposes. We might consider human height to have a normal distribution with mean 160 and standard deviation 10 (numbers made up). We know that (a) it is only measured to a finite precision as @whuber comments, and (b) this distribution gives us a positive probability of negative height people (which is absurd) and we know that Attack of the 50 foot woman is just a film.

In your case I would be more concerned about whether modelling trips on a linear scale makes sense. If you modified the conditions would you expect to generate 3 more trips per area or would you expect to see a 3% increase? If the latter you are implicitly modelling on a log scale. You might consider a Poisson model. If your areas vary in size you way want to consider using an offset for area size.