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have a set of data as follows where we measured the change in aluminium or copper according to time, concentration of sediment, temperature and the site the water was taken from.

Here is a sample of the data

Id Temp Time Site Al    Cu    Alch  CuCh
1   1   0   1   0.1402  0.0008  0   0
2   1   0   2   0.3554  0.0095  0   0
3   1   0   3   7.4977  0.1851  0   0
4   1   0   4   0.0214  0.0009  0   0
5   2   0   1   0.047   0.0001  0   0
6   2   0   2   0.111   0.0044  0   0
7   2   0   3   15.2199 0.3317  0   0
8   2   0   4   0.041   0.001   0   0
9   1   1   1   0.1271  0.0022  -0.0131 0.0014
10  1   1   1   0.1145  0.0024  -0.0257 0.0016
11  1   1   1   0.1413  0.0025  0.0011  0.0017
12  1   1   1   0.1521  0.0026  0.0119  0.0018
13  1   1   2   0.2140  0.0061  -0.1414 -0.0034
14  1   1   2   0.2259  0.0061  -0.1295 -0.0034
15  1   1   2   0.0024  0.001172698 -0.3530 -0.0083
16  1   1   2   0.216372    0.005144016 -0.1390 -0.0044
17  1   1   3   5.817103    0.140388    -1.6806 -0.0447
18  1   1   3   5.475608    0.132562    -2.0221 -0.0525
19  1   1   3   5.639903    0.1373  -1.8578 -0.0478
20  1   1   3   5.6843  0.1351  -1.8134 -0.0500
21  1   1   4   0.0113  0.0016  -0.0101 0.0007
22  1   1   4   0.0163  0.0033  -0.0051 0.0024
23  1   1   4   0.0122  0.0016  -0.0092 0.0007
24  1   1   4   0.0134  0.0014  -0.0080 0.0005

I wanted to see the effect of temperature, time, site, and sediment concentration on AlCh or CuCh- e.e. is there a significant difference? I have 2 temps, 4 times, 4 sites and 4 sediment concentrations. As I have multiple predictors should I do a MANCOVA to estimate for covariates? The data is not normal on a q q plot.

LucySHE
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1 Answers1

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Since you have repeated measures on each site, your errors will not be independent. This violates the assumptions of ANOVA, ANCOVA, regression....

There are various ways to deal with this. One common one that looks applicable to your data is a multilevel model.

Peter Flom
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  • yes I've found a model for a three level model with multiple predictors in SPSS but was unsure that was the way to go. Do you know how I could do this in R or do you know of any good references I could look at? – LucySHE Aug 08 '17 at 13:33
  • Multilevel models have been extensively discussed here on CrossValidated. There are lots of good book on them, too. In the R area, Pinheiro and Bates wrote a book that is sort of seminal. – Peter Flom Aug 08 '17 at 14:03