# Statistical modeling of land use - 3 types of variables

I am struggling at the moment with how to determine links between different sets of variables. I have data on land use/cover changes in a number of regions in a period of 20 years. They are all expressed in percentages of area surface changed. I have data on so called drivers of change (population change, employment levels, education structure changes, slope, altitude etc) also expressed in percentages or indices. I have a third type of variables - a questionnaire survey.

Basically what I did was multiple regression analysis on each independent variable (land cover change - forest change, grassland expansion or reduction, arable land expansion or reduction etc.) with all of the drivers of change. So I would get R for the connection between e.g. deforestation on one side and population change and altitude on the other (other drivers were eliminated through backward stepwise regression).

So after I would determine that forest cover change is affected by changes in population number or altitude, I would use data from the questionnaire survey to interpret the reasons for such connection.

Is there any better way to model these variables? I am dabbling into canonical correlation - could it be useful? Land cover variables on one side, and the drivers on the other? And could I include the data from the questionnaire survey in the canonical correlation in any way? Thank you very much for your help.

A few points:

1. If you have the same regions for multiple years then your data are not independent, thus violating one assumption of regression. There are different ways to deal with this; the one I am most familiar with is mixed models (aka multilevel models and a variety of other terms) but you do have to deal with it. Another method is generalized estimating equations (GEE).

2. You have multiple independent variables; so, you can include more than one in a regression. There is a whole art to model building, extensively discussed here and in books.

3. Since your dependent variable is a percentage, you may need a nonlinear model. If all the percentages are near the middle, then you might not, but you probably should use one anyway.

So, you have a fairly complex problem.

On a much less complex level, you can (and should) make lots of graphs of the variables against each other.

• Actually, I have data for 1991 and 2011, and every variable is just a difference between the first and the last year in the period. it's just one region. I also excluded highly correlated variables (e.g. population density and aging population) before multiple regression. I was hoping that canonical correlation could solve my problems, because it works with two sets of variables, and that's exactly what I have. – Miren Sanov Feb 15 '14 at 22:19
• OK, canonical correlation might work for that. You might also want to look into multivariate regression (more than one DV) – Peter Flom - Reinstate Monica Feb 15 '14 at 22:30