I have 9 degradation curves which I would like to compare and would like advice as to how best to do this. My initial thoughts surrounded comparing non-linear regressions. I will first explain the question and then detail the experimental design a bit more:
My questions are:
- how can I compare the rate of degradation between my 9 groups?
- how can I determine to what extent my two primary independent variables (type of organic matter and field plot) drive the rate of degradation.
I placed 3 types of organic matter (X, Y, Z) outside in 3 field plots (A, B, C). 12 samples of each organic matter were placed in each plot (36 samples per plot, total 108 samples). I know the original organic matter (OM) (as both a total value and as percentage of dry matter) content for each sample. At 3 time points a week apart (T1, T2, T3) I removed 4 samples of each type from each plot and again measured organic matter content.
So for each of the 9 combinations (AX, AY, AZ, BX, BY, BZ, CX, CY, CZ) I have: 12 measurments of original organic matter at T0 and 4 measurements of organic matter at each of the latter 3 time points (T1, T2, T3).
I hope that I have provided enough information - please ask if I have not. I am very appreciative of any help and advice surrounding this query.
Thank you, and Merry Christmas.
Andrew.
Link to sample date: https://docs.google.com/spreadsheets/d/1a5w9BeeogprKAOwHi3WYSW7JF8EtjQOaaG9z-qzDRgw/pub?output=xlsx
Here is something quick to give you a start. Due to your few time points I would use a linear model. I assume that absolute differences of OM are sensible here, i.e., that samples are normalized in some meaningful way. You might need to work with relative values instead (and could possibly even need a GLMM in that case?).
Some people advice only fitting random effects if a larger number of groups is available, but I generally trust also models with few groups if the resulting fit seems reasonable. Of course, you shouldn't put too much trust into the variance estimate of the random effects in such a case. Alternatively, you could treat
Plot
as a fixed effects, but your model would need two more parameters then. However, usually we are not interested too much in plot differences and prefer to concentrate on treatment effects. YMMV.Apparently degradation rates before your samplings were different between sample types (see the different intercepts according to sample type), which would mean non-linear rates (as we would expect). A linear model of the differences means constant absolute degradation rates.