# Measuring distance to roads using raster data in ArcMap?

I am using ArcMap 10.1 on a Windows x64 system.

I am trying to analyse the driving force of urban land use land cover changes. I have 7 raster files represents distance to roads, distance to river, slope, elevation, population density, precipitation, and land use map within my area. I have been using the “combine” in Arcmap 10.1 to merge multiple raster layers into a new single one, and I have been exporting the attribute table to SPSS to do the binary logistic regression.

In binary logistic regression model, the built-up land is a binary dependent variable, while the slope, the elevation etc. are independent variables. See logistic regression result below: the coefficient (B) of the distance to river is 0, which means there is no relationship between the built-up land changes and the distance to river. Also, the distance to roads got the same result. I don't feel right the regression result, because generally the coefficient of distance from the roads should be negative, which means that the probability of built-up land increases near the roads than away from the roads. I crated these two distance maps from the roads and the river polyline datasets, respectively, using Eculidean distance in arcmap 10.01, and then doing the regression. See the processing and the results below: Is there something wrong with my method to calculate the distance to river and roads?

All maps are the same projection and cell size.

• Just so I understand your methodology: are you assigning a distance measurement to a location and then doing the regression? – Wes Aug 6 '15 at 19:29
• @Wes, thanks for the comment. Yes, I crated these two distance maps from the roads and the river polyline dataset, and then doing the regression. I don't feel right the regression result, because generally the coefficient of distance from the roads should be negative, which means that the probability of built-up land increases near the roads than away from the roads. – user121 Aug 6 '15 at 20:40
• To provide any requested clarifications it is usually best to use the edit button beneath your question to revise it. There is no guarantee that potential answerers will read the comment trail. – PolyGeo Aug 7 '15 at 0:05
• I'd normalise independent variables first, using for example (x-xMin)/(xMax-xMin) – FelixIP Aug 10 '15 at 2:21
• @FelixIP, thank you. my regression result looks logical after doing normalization. – user121 Aug 10 '15 at 19:31

On second thought I decided to post my answer.

Normalising variables, which solved an issue is not exactly GIS thing, however careful spatial variables selection for regression analysis is.

I'd suggest caution with that many independent variables, because some of them aren't really independent, e.g. distance from 'river' and terrain slope.

I've made a quick check for terrain and 'rivers' shown below:

Random sampling (200 points) of Euclidian distance and slope shown no correlation between two. However when I reclassified distance into 5 classes and derived average slope per class result was very telling: I also suggest to exclude precipitation from your analysis, unless it is a continental scale study. Even if it is, altitude will do better, because humans don't last long with a lack of oxygen

Thanks again @FelixIP, and I'd like to post my new answer

Here, the independent variables include slope, elevation, precipitation,distance to roads, and distance to river, and all values are 0 to 100 after doing normalization.

For normalization all the values to a range of 0 to 100, I used the Raster calculator tool in ArcMap 10.1 with this equation:

("my_raster" - "my_raster".minimum) / ("my_raster".maximum - "my_raster".minimum) * 100

Slope, as a dummy variable in binary logistic regression, is divided into three groups (I = the value is between 0 and 10, II = the value is between 10 and 25, and III = the value is more than 25).

The built-up land is a binary dependent variable. When other land cover types are converted from non-built-up land to built-up land, the value is set as Y=1; otherwise, Y=0.

See my new result below: As you mentioned, ''I also suggest to exclude precipitation from your analysis, unless it is a continental scale study.'' The coefficient of precipitation is o, which means there is no relationship between these two variables.

Among the continuous variables, the coefficient of distance from roads is -0.013, which means that the probability of built-up land increases near the roads than away from the roads. The categorical variables, slope I and slope II, have positive association with built-up land changes. It means that the probability of built-up land increase with the slope between 0 and 25°.