I have only a very basic background in statistics, and I have a possibly simple question, but I'm having a bit of trouble with my model. I suppose this is also an R question, but also statistical!
I'm looking for some advice concerning the interpretation my
I am modelling photosynthesis-irradiance -relationship and have fitted a nonlinear mixed model in
nlme such as this with 3 parameters to estimate:
nlme(Foto~picurve(PAR, Amax, Aqe, LCP), fixed = list(Amax ~ Place, Aqe + LCP ~ 1), random = pdDiag(Amax ~ 1), weight = varPower(), correlation = corARMA(p = 1, q = 1), method = "ML", start = rep(c(15, 0.0054, 20), 2), data = data1)
The summary is as follows
... Fixed effects: list(Amax ~ Place, Aqe + LCP ~ 1) Value Std.Error DF t-value p-value Amax.(Intercept) 16.427779 0.6567488 959 25.01380 0.0000 Amax.Place 2 -1.328056 0.9169505 959 -1.44834 0.1478 Amax.Place 3 -1.063690 0.8996467 959 -1.18234 0.2374 Amax.Place 4 -3.207345 0.9171032 959 -3.49726 0.0005 Aqe 0.057579 0.0015047 959 38.26518 0.0000 LCP 21.388703 0.7486608 959 28.56928 0.0000 ...
I need to make inference on the fixed effects at the 4 places. Each place contains 3 genotypes, and each genotype contain several individuals, but they're not modelled here. Some genotypes contain more individuals than others (unbalanced?), and some individuals may have a few more measurements in them than the others. But I suppose that's beyond the point.
Now my questions is, what is the current recommended way of making inferences about the fixed effects parameter estimates? If I understood correctly, MCMCs etc. are the "most correct" approach, but they are probably beyond my comprehension at the moment and probably not what my superiors would want anyway. I know I can obtain the conditional F-test statistics and compare the places with
anova(), even if that probably is a bad approach due to the denominator df problems I've been hearing about. But other than that, I don't know any way of doing this (recommendations are welcome).
Next, and more importantly, how does one make pairwise/multiple comparisons between the fixed effects? I need to compare all places to each others, as so:
Place 1 - Place 2 Place 1 - Place 3 Place 1 - Place 4 Place 2 - Place 3 ...
Now, again, MCMCs might not be my cup of tea here. The conditional t-test values from the summary can probably be used, at least in some (balanced?) instances, but would still leave me wanting to compare other groups besides the first.
What I would have to do, if I am correct (am I?), is set my contrasts so that I can compare the other groups as well. I tried approaching this with the
summary(glht(psn7, linfct = matrix(c(0, 0, 1, -1, 0, 0), 1))) Linear Hypotheses: Estimate Std. Error z value Pr(>|z|) 1 == 0 2.1437 0.8862 2.419 0.0156 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Adjusted p values reported -- single-step method)
This is where the troubles begin.
1) Is glht unsuited for nlme? It reports z-values (df problems?) - I thought it always reported t-values...
2) I still cannot compare the first group and the others, do I need to manipulate the order of my data or is there a more elegant way of getting all the comparisons?
I know this a very simple question, and I apologize. I'm quite new to this all...
p.s. also, bonus question, how about likelihood ratio tests? Can they be used for inference about fixed effects?