I am monitoring tree death caused by insects and potential impact of human treatment on yearly amount of tree mortality in areas with and without human intervention. My data are recorded by remote sensing, thus my results represents the area of trees killed per year.

Please, is there a way how to evaluate the effect of human intervention? My data contain one observation per year per category intervention/non-intervention. Is this the case of dynamic regression?

Dataset: two areas, differing by management or non-management approaches - one without chemical treatment (A), another with chemical treatment (B). Both contain the area of killed trees in yearly time step.

How can I decide if these two types of management differs, or if one potentially leads to decreased tree mortality? Is there a way how can I include in my analysis the amount of treatment applied each year and its impact in subsequent year? The insects develop within a year, and the treatment is applied by aerial treatment, not on specific tree thus I don't observe the immediate effect on chemical on the insect individual, as the treatment can stay on leafs of bark.

Thank you a lot for your suggestions !

enter image description here

sample data:


df<-data.frame(year = c(2001:2010),
               A = floor(runif(10, min=0, max=200)),
               B = floor(runif(10, min=0, max=60)))

a<- ggplot(df, aes(factor(year), y = A)) + ggtitle("Non Management") +
geom_bar(stat = "identity") + ylim(0,200) + ylab("area in ha") +
theme_classic() + theme(axis.text.x = element_text(angle = 90))

b <- ggplot(df, aes(factor(year), y =B)) + ggtitle("Management") +
  geom_bar(stat = "identity") + ylim(0,200) + ylab("area in ha") +
  theme_classic() + theme(axis.text.x = element_text(angle = 90))

grid.arrange(a,b, ncol = 2)
  • $\begingroup$ Is there a denominator? Maybe the non-management area is just larger? $\endgroup$
    – Bill
    May 17, 2016 at 18:54
  • $\begingroup$ no, actually, the non-intervention area is smaller $\endgroup$
    – maycca
    May 17, 2016 at 20:18
  • $\begingroup$ OK, then you definitely want to divide each of management and non-management by their respective areas. After that, it seems to me that you just want a Wilcoxon signed rank test. $\endgroup$
    – Bill
    May 17, 2016 at 21:49
  • $\begingroup$ ok, thanks @Bill, I'll try it and I'll let you know ! ;) $\endgroup$
    – maycca
    May 17, 2016 at 21:55

2 Answers 2


The short answer is your data is too small to capture any dynamic relationship. From your example it appears you only have 20 observations which makes any type of statistical analysis difficult. This is especially true for model that include lags since the inclusion of a lag in a model requires the first observation of data to be drop making your already small data set even smaller.

Can you obtain data at a more disaggregated level? For example, assume that the unit of observation in your data was a hectare in a given year. For each hectare-year you have data containing the number of trees that have died and whether or not they received the treatment. Given this data set you could use a auto-regressive distributed lag (ARDL) model.

$$Morality_{i,t} = \alpha + \gamma Morality_{i,t-1} + \beta_0 T_{i,t} + \beta_1 T_{i,t-1} + \epsilon_{i,t}$$

Where $T_{i,t}$ is an indicator variable that takes on a value of 1 if the $i^{th}$ hectare in year $t$ received the treatment. You may want to consider interacting the treatment indicator with the auto-regressive terms as well. This will further help you answer the question, how does treatment affect the dynamics of morality.

That all being said, you may be facing a much more fundamental problem. Is the treatment randomly assigned to the trees? If your answer is either no or I don't know then you're potentially in a bit of trouble. For example, in your example, imagine that the park ranger first identifies those trees which are most vulnerable to insects and applies chemicals to those trees. If this is the case, then comparing mortality rates between treated and untreated trees is fundamentally flawed. As a result estimate of the any treatment effect will under estimate the true treatment effect.

The good news is that there are work arounds for this problem. A natural solution to your application would be a panel estimator which only utilizes the variation within treatment groups. This approach is not with out flaws. Specifically, this approach requires that the asymmetries between groups are time invariant, which may not be true in your case.

  • $\begingroup$ thank you @JacobH, you really let me think... thus, B is correct: I don't think that my treatement is randomly applied because it could be applied in specifid distance from previously founded infested tree. however, this can be applied everywhere within the management zone, thus it happens on multiple locations within a year and my results are the summary of all of these. do you think that I can use this partial polygons to increase the N size? or do you think that split my zones into multiple parts and recalculate my rate of damage as you proposed would be better? $\endgroup$
    – maycca
    May 18, 2016 at 6:25
  • $\begingroup$ You're comments are a little unclear. However, it appears that you can disaggregate data which is good! Cutting the data into smaller zones sounds like a good start. However, it is really up to you to use your expert knowledge in the field to determine what the correct unit of observation should be. $\endgroup$
    – Jacob H
    May 18, 2016 at 21:40
  • $\begingroup$ The fact that chemicals are applied to areas after an infestation is found is very problematic. The treatment is clearly not randomized. The treatment arm is more likely to be infested than control group and therefore are not directly comparable. Therefore any traditional estimates of the treatment effect will likely be bias. $\endgroup$
    – Jacob H
    May 18, 2016 at 21:43
  • $\begingroup$ Said another way, the trees in your control group are unlikely to be affected by an infestation because the treatment is applied to those trees in which an infestation is found. So you comparing infested trees to non-infested trees. This is like running a cancer drug trial in which you give treatment to the people with cancer and compare them to people without cancer. Comparing the mortality rates across these two groups simply does not make sense. $\endgroup$
    – Jacob H
    May 18, 2016 at 21:52
  • $\begingroup$ You need to find trees that were likely to be infested but were not treated and use them to comprise the control group. Do you have information on infestation levels? $\endgroup$
    – Jacob H
    May 18, 2016 at 21:53

This would be pretty simple to do IF (and this is a big "if") you've got data for how many trees lived, too. The other assumption, which appears to not be the case here, is that your groups are assigned randomly, ie. this area of trees is randomly selected for treatment, leaving this other group to be non-treated.

Let's pretend that you do. Let's pretend that your data looks like this:

|  Area                |  TreeID     |  Died  |
|  Intervention        |  A1         |  FALSE |
|  Intervention        |  A2         |  FALSE |
|  Intervention        |  A3         |  TRUE  |
|  NonIntervention     |  B1         |  FALSE |
|  NonIntervention     |  B2         |  TRUE  |
|  NonIntervention     |  B3         |  TRUE  |
|  NonIntervention     |  B4         |  FALSE |

At that point, it's just:

intervention     <- alldata %>% filter(Area == "Intervention")
nonintervention  <- alldata %>% filter(Area == "NonIntervention")

results          <- t.test(intervention$Died, nonintervention$Died)

And then take a look at the new results object and see if the means are significantly different than each other.

  • $\begingroup$ thank you @crazybilly. do you think that it doesn't matter the influence of time, and that the application of treatment can have impact on insect mortality next year? I feel you compare two samples, but neglect the time effect? $\endgroup$
    – maycca
    May 23, 2016 at 18:38
  • $\begingroup$ Ok I see, the filter is used to time series. These are my results: p-value = 5.473e-14 alternative hypothesis: true difference in means is not equal to 0 thus I can conclude that there is some effect on forest management on tree morality due to beetles? thank you again ! $\endgroup$
    – maycca
    May 23, 2016 at 18:52
  • $\begingroup$ also, I my example data, I've uses only yearly values on data - thus per each year I have N of dead and alive trees. in my real data, I have several polygons of both types - thus have higher N. Please, how can I answer this? $\endgroup$
    – maycca
    May 23, 2016 at 18:57
  • 1
    $\begingroup$ maycca and @crazybilly, this approach does not work. maycaa has mentioned several times that those trees are treated only after an infestation is discovered. Comparing a treatment of unhealthy trees to a control of healthy trees DOES NOT MAKE ANY SENSE. In the context of OLS you are validating the fundamental assumption known as the strict exogenity assumption and your results will be biased! This is not a controlled experiment, and therefore simple t.test are not going to cut it. $\endgroup$
    – Jacob H
    May 24, 2016 at 21:16
  • 1
    $\begingroup$ good point @JacobH - I missed that in the original question. I edited my answer to include a caveat that random selection is required. $\endgroup$
    – crazybilly
    May 25, 2016 at 20:00

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