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I'm trying to measure the biological impacts of an industrial development using a Before-After-Gradient approach. I am using a linear mixed model approach in R, and am having trouble specifying an appropriate model, especially the random effects. I've spent a lot of time researching this, but so far haven't come up with a clear solution--at least not one that I understand. I am new to LMM (and R for that matter) so would welcome any advice.

The response variables (for example, changes in abundance of key species) will be measured as a function of distance from the edge of impact, using plots established at fixed distances along multiple transects ("gradients") radiating out from the edge of the disturbance. Ideally, each plot would be sampled at multiple times both before and after the impact; however, for simplicity I'm starting by assuming the simplest case, where each plot is sampled once before and once after the impact. Assume also that the individual gradients are far enough apart that they can be considered spatially independent.

First, some simulated data. The effect here is linear instead of curvilinear, but you get the idea.

> str(bag)
'data.frame':   30 obs. of  5 variables:
 $ Plot    : Factor w/ 15 levels "G1-D0","G1-D100",..: 1 2 4 5 3 6 7 9 10 8 ...
 $ Gradient: Factor w/ 3 levels "1","2","3": 1 1 1 1 1 2 2 2 2 2 ...
 $ Distance: Factor w/ 5 levels "0","100","300",..: 1 2 3 4 5 1 2 3 4 5 ...
 $ Period  : Factor w/ 2 levels "After","Before": 2 2 2 2 2 2 2 2 2 2 ...
 $ response: num  0.633 0.864 0.703 0.911 0.676 ...
> bag
       Plot Gradient Distance Period   response
1     G1-D0        1        0 Before 0.63258749
2   G1-D100        1      100 Before 0.86422356
3   G1-D300        1      300 Before 0.70262745
4   G1-D700        1      700 Before 0.91056851
5  G1-D1500        1     1500 Before 0.67637353
6     G2-D0        2        0 Before 0.75879579
7   G2-D100        2      100 Before 0.77981992
8   G2-D300        2      300 Before 0.87714158
9   G2-D700        2      700 Before 0.62888739
10 G2-D1500        2     1500 Before 0.83217617
11    G3-D0        3        0 Before 0.87931801
12  G3-D100        3      100 Before 0.81931761
13  G3-D300        3      300 Before 0.74489963
14  G3-D700        3      700 Before 0.68984485
15 G3-D1500        3     1500 Before 0.94942006
16    G1-D0        1        0  After 0.00010000
17  G1-D100        1      100  After 0.05338171
18  G1-D300        1      300  After 0.15846741
19  G1-D700        1      700  After 0.34909588
20 G1-D1500        1     1500  After 0.77138824
21    G2-D0        2        0  After 0.00010000
22  G2-D100        2      100  After 0.05801157
23  G2-D300        2      300  After 0.11422562
24  G2-D700        2      700  After 0.34208601
25 G2-D1500        2     1500  After 0.52606733
26    G3-D0        3        0  After 0.00010000
27  G3-D100        3      100  After 0.05418663
28  G3-D300        3      300  After 0.19295391
29  G3-D700        3      700  After 0.46279103
30 G3-D1500        3     1500  After 0.58556186

As far as I can tell, the fixed effects should be Period (Before,After) and Distance, treating distance as continuous (not a factor) so we can estimate the slope. The interaction between Period and Distance (equivalent to the difference in slopes, before vs. after) measures the impact. I'm still scratching my head over how to specify the random effects. I assume I should control for variation among gradients, as follows:

result <- lme(response ~ Distance + Period + Distance:Period, random=~ 1 | Gradient, data=bag)

However, I suspect I may be missing some source of variation. For example, I'm not sure the above model controls for the re-sampling of individual plots before and after. Any suggestions?

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正如您所拥有的，使用一个样本/渐变，无需指定随机效果或有关渐变的任何内容。您可以使用直接多元回归来做到这一点。一旦您在每个渐变中有多个度量，您就可以使用您指定的模型。也就是说，梯度对模型的截距有预期的主要影响，但距离、周期及其相互作用的影响（斜率）应该是固定的。

如果您预计其他预测变量的梯度之间存在可观的可变性，则可以指定额外的随机效应。我不确定你是如何做到的lme，或者即使你可以做到，但在lmer一个例子中可能是：

lmer(response ~ Distance * Distance:Period + (1 + Distance | Gradient), data=bag)

这将允许距离斜率具有固定的效果分量和随梯度变化的分量。您可以查看随机效应的进一步规范，但希望您能看到总体思路，然后您可以决定制作模型的复杂程度。

于 2013-09-07T23:46:25.317 回答