
Dear R-sig-ecology users,

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 m3/ha, the response variable (occurrence) has a value of 1, otherwise 0.
The model should 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!

Ferenc Pasztor
PhD student
Institute of Silviculture (Institut für Waldbau)
Department of Forest- and Soil Sciences
BOKU - University of Natural Resources and Life Sciences, Vienna 		 	   		  
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