Repeated measures field experiment: statistical design

Question

In a study on a bird, breeding territories were mapped in 1990 and controlled in 2017. Each territory is one sample with the dependent variable territory abandoned (possible values: "yes" and "no"). I also sampled temperature, precipitation and forest cover both in 1990 and in 2017 and I want to find out if these have a effect on territory abandonment.

So, I'd like to carry out a multivariate analysis like GLMM (the territories were mapped in several patches) to analyse the effect of absolute veriable values as well as variable changes over time on territory abandonment. However, I am quite unsure about the statistical design I should be using. Any help?

I have attached some example data to illustrate the issue.

> Example.Data
1  ID abandoned temp.1990 temp.2017 prec.1990 prec.2017 forest.1990 forest.2017
2   1         n       3.4      5.97      1754      1611          33          61
3   2         n       3.5      6.08      1632      1699          56          66
4   3         n       6.1      8.71      1890      1610          46          49
5   4         n       4.5      6.33      1662      1894          32          48
6   5         n       5.5      8.18      1638      1716          60          67
7   6         n       5.2      7.16      1765      1660          50          54
8   7         n       3.6      5.78      1745      1674          54          42
9   8         n       4.3      7.22      1806      1727          65          52
10  9         n       4.1      6.11      1733      1618          48          61
11 10         n       4.8      6.34      1756      1665          43          52
12 11         n       5.1      7.96      1741      1788          39          66
13 12         n       3.9      5.60      1878      1613          52          64
14 13         n       4.2      5.91      1814      1692          70          67
15 14         n       3.5      5.38      1805      1798          61          61
16 15         n       3.6      5.58      1955      1641          45          56
17 16         n       4.5      5.83      1757      1815          31          43
18 17         n       5.6      6.98      1910      1649          65          41
19 18         n       5.1      7.66      1924      1714          52          62
20 19         n       2.9      5.85      1960      1736          55          58
21 20         n       3.8      6.79      1747      1594          49          56
22 21         n       5.7      7.59      1602      1689          43          62
23 22         n       4.7      7.24      1976      1565          34          66
24 23         n       3.5      5.08      1684      1648          38          66
25 24         n       3.7      5.29      1778      1700          52          44
26 25         y       3.7      6.59      1746      1694          50          35
27 26         y       6.3      8.52      1681      1634          52          97
28 27         y       4.4      8.12      1762      1740          35          54
29 28         y         6     10.30      1962      1584          45          96
30 29         y       6.3      9.82      1811      1709          36          77
31 30         y       5.4      8.27      1666      1727          49          95
32 31         y         5      6.45      1779      1720          61          78
33 32         y       6.3      9.22      1804      1587          59          91
34 33         y       6.5      9.33      1727      1673          58          56
35 34         y       6.3      9.42      1822      1693          33          59
36 35         y         5      6.55      1887      1562          65          91
37 36         y       4.1      7.71      1727      1618          49          81
38 37         y       4.9      6.15      1896      1691          60          82
39 38         y         5      6.45      1837      1592          39          78
40 39         y       3.8      7.99      1788      1745          66          38
41 40         y       5.3      7.57      1964      1606          35          97

Answer 1

If your question is whether territory abandonment is associated with any of the environmental variables then a sensible starting point would be to carry out a logistic regression.

Use "abandoned" as your response variable (but changing "n" to 0 and "y" to 1) and the environmental variables as your predictors. Because there is only one dependent variable ("abandoned") this is a univariate analysis, not a mutlivariate analysis.

The repeated measures aspect of your question doesn't really apply. In order to ask if there is abandonment of territories then you must have measured the same territory more than once. But it isn't necessary to account for this in the model structure because you aren't including the occupancy status of the territories in 1990 and 2017, only whether the occupancy has changed.

You might also want to add some other predictors: the difference in temperature, precipitation and forest cover between the two time points. This will allow you to look at whether changes in these values are more important than the values themselves.

You should carry out some preliminary data exploration and regression diagnostics to see whether the results are driven by extreme values or whether polynomial terms should be included (or the use of smoothing functions). I have provided links to some useful resources in another answer - Proportion / Percentage Regression Analysis methods

Reply to further comments

I think there are a couple of ways of looking at this problem.

Firstly, you could treat "abandoned" as a predictor (an independent variable) and then say you have measured a number of attributes of each territory (temperature, precipitation, forest cover), these being the response variables (which would be linked because they are being measured in the same territory - that is, they are repeated measures).

Then you could do a multivariate analysis to see whether the territories, when mapped in multivariate space, group separately depending on whether they are abandoned or not. One way to do this is to normalise the environmental variables, calculate euclidean distances, map out with non-metric multidimensional scaling (nMDS) and then determine whether the points map out in different parts of the multidimensional space using an ANOSIM test.

However, it is stated in the comments that that territory is the dependent variable (i.e. the response that is of interest to you), and the question asks about GLMM which is an extension of GLM (and therefore logistic regression), and also asks about providing an explanation of the response in terms of the different environmental variables (they are acting as predictors). So, from this viewpoint I thought starting with a logistic regression seemed the most appropriate.