I am doing some forest disturbance research, in which the aim is to predict the probabilities of wind damage occurrence in forest stands of different site (altitude, slope steepness) and stand properties (age, timber volume). I am using a logistic regression (because of the binomial response variable: 0-1) with the R package "lme4".
My data set looks like this (several thousand forest stands in the full data set):
stand_id year damage altitude slope age volume occurrence
123 2001 0 900 15 100 235 0
123 2002 0 900 15 101 242 0
123 2003 0 900 15 102 249 0
123 2004 3.6 900 15 103 256 1
123 2005 0 900 15 104 259.4 0
123 2006 2.1 900 15 105 266.4 1
123 2007 1.8 900 15 106 271.3 1
123 2008 0 900 15 107 276.5 0
123 2009 0 900 15 108 283.5 0
123 2010 0 900 15 109 290.5 0
124 2001 0 1100 10 80 172 0
124 2002 0 1100 10 81 181 0
124 2003 6.2 1100 10 82 190 1
124 2004 8.9 1100 10 83 192.8 1
124 2005 2.4 1100 10 84 192.9 1
124 2006 0 1100 10 85 199.5 0
124 2007 0 1100 10 86 208.5 0
124 2008 5.5 1100 10 87 217.5 1
124 2009 2.4 1100 10 88 221 1
124 2010 0 1100 10 89 227.6 0
. . .
If damage is bigger than 0, the response variable (occurrence) has a value of 1, otherwise 0. The model would be: occurrence ~ altitude + slope + age + volume
As you can see, there are measurements in all years for a 10-year period in all of the stands. Since we have more than one measurements for the same forest stand, a random effect (of forest stand) has to be added to the model, which will be the factor "stand_id". Regard to my understanding of Statistics, spatial autocorrelation is not a problem anymore, but temporal autocorrelation of the (residuals of the) response variable is still something needs to be dealt with. I have checked the autocorrelation function (acf) of it, and it is apparent in the first following year (acf value is ~ 0.1), then it dies off.
Many experts advise to model the temporal autocorrelation structure and use it as a correction for the previously fitted (logistic regression) model. I find this a bit tedious and overcomplicated (also cannot do simply in lme4), therefore my question would be:
Is it a valid alternative if I make a new predictor variable that is the damage of the previous year (because of the acf) and use it in the model, as well? To make it more clear, here is the new data set (last column is added):
stand_id year damage altitude slope age volume occurrence dmg_prev
123 2001 0 900 15 100 235 0 0
123 2002 0 900 15 101 242 0 0
123 2003 0 900 15 102 249 0 0
123 2004 3.6 900 15 103 256 1 0
123 2005 0 900 15 104 259.4 0 3.6
123 2006 2.1 900 15 105 266.4 1 0
123 2007 1.8 900 15 106 271.3 1 2.1
123 2008 0 900 15 107 276.5 0 1.8
123 2009 0 900 15 108 283.5 0 0
123 2010 0 900 15 109 290.5 0 0
124 2001 0 1100 10 80 172 0 0
124 2002 0 1100 10 81 181 0 0
124 2003 6.2 1100 10 82 190 1 0
124 2004 8.9 1100 10 83 192.8 1 6.2
124 2005 2.4 1100 10 84 192.9 1 8.9
124 2006 0 1100 10 85 199.5 0 2.4
124 2007 0 1100 10 86 208.5 0 0
124 2008 5.5 1100 10 87 217.5 1 0
124 2009 2.4 1100 10 88 221 1 5.5
124 2010 0 1100 10 89 227.6 0 2.4
. . .
Running the model with this new variable (dmg_prev), it also turns out to be significant, and if I am right, it carries the information on the temporal autocorrelation, as well. So no additional correction is needed anymore. Could someone verify this?
Thank you very much for your help in advance!
