Dear mixed-modelers,
I have built a mixed model and I'm having serious trouble with interpreting
the output.
I want to test differences in the coefficient of variation (CV) of light
across 3 tree crown exposures (Depth). I have measured direct and diffuse
radiation (RF) and I want to test for differences for each kind of radiation
between crown exposures, as well as differences between radiation fractions
at each crown exposure. I have sampled 5 individuals (Ind) at each of 2
populations (Pop), thus individual is nested in population. I have repeated
the experiment at 2 periods of day and 2 seasons.
I have allowed for different variances at each level of the fixed factors
"Depth" and "RF", denoted in the model by weights=vf3.
The model is:
> lmeF2 <- lme(CV ~ Depth * RF * Season/Period, random = ~ 1 | Pop/Ind,
> method = "REML", data = trf, weights=vf3)
> Anova(lmeF2, type="III")
Analysis of Deviance Table (Type III tests)
Response: CV1
Chisq Df Pr(>Chisq)
(Intercept) 2.7866 1 0.0950585 .
Depth 24.0113 2 6.110e-06 ***
RF 23.3307 1 1.364e-06 ***
Season 1.4841 1 0.2231326
Depth:RF 73.0870 2 < 2.2e-16 ***
Depth:Season 37.8293 2 6.102e-09 ***
RF:Season 11.6653 1 0.0006368 ***
Depth:RF:Season 4.4843 2 0.1062273
Depth:RF:Season:Period 101.9454 12 2.313e-16 ***
I'm not interested in main effects, because only the interaction Depth*RF
(and hence multiple interactions involving this one) give relevant
biological information. I feel I need post hoc tests, but after a lot of
searching and asking without getting a satisfactory solution, I feel I have
reached a dead end.
So my first question is: Does anybody know how to perform post-hoc tests
(such as Tukey HSD) to this kind of model?
However, I've tried to explain (for myself) these anova results through
model summary :
> summary(lmeF2)
Linear mixed-effects model fit by REML
Data: trf
AIC BIC logLik
-622.2264 -514.2175 343.1132
Random effects:
Formula: ~1 | Pop
(Intercept)
StdDev: 3.36984e-07
Formula: ~1 | Ind %in% Pop
(Intercept) Residual
StdDev: 0.00140597 0.006489656
Variance function:
Structure: Different standard deviations per stratum
Formula: ~1 | RF * Depth
Parameter estimates:
Direct*1F Direct*2M Direct*3D Diffuse*1F Diffuse*2M Diffuse*3D
1.0 40.0268548 51.7503905 0.8484995 6.3698389 7.7130822
2.0
Fixed effects: CV1 ~ Depth * RF * Season/Period
Value Std.Error DF t-value
p-value
(Intercept) 0.003 0.00179716 207 1.669297
0.0966
Depth2M 0.031 0.01318771 207 2.350674
0.0197
Depth3D 0.069 0.01592435 207 4.332987
0.0000
RFDirect 0.013 0.00269141 207 4.830183
0.0000
SeasonWinter -0.003 0.00246257 207 -1.218240
0.2245
Depth2M:RFDirect 0.563 0.08322066 207 6.765147
0.0000
Depth3D:RFDirect 0.562 0.10740948 207 5.232313
0.0000
Depth2M:SeasonWinter 0.111 0.01865024 207 5.951667
0.0000
Depth3D:SeasonWinter -0.033 0.02252043 207 -1.465336
0.1443
RFDirect:SeasonWinter -0.013 0.00380623 207 -3.415455
0.0008
Depth2M:RFDirect:SeasonWinter -0.249 0.11769179 207 -2.115696
0.0356
Depth3D:RFDirect:SeasonWinter -0.014 0.15189994 207 -0.092166
0.9267
Depth1F:RFDiffuse:SeasonSummer:PeriodMm -0.002 0.00246257 207 -0.812160
0.4176
Depth2M:RFDiffuse:SeasonSummer:PeriodMm 0.006 0.01848694 207 0.324553
0.7458
Depth3D:RFDiffuse:SeasonSummer:PeriodMm -0.021 0.02238539 207 -0.938112
0.3493
Depth1F:RFDirect:SeasonSummer:PeriodMm -0.014 0.00290226 207 -4.823823
0.0000
Depth2M:RFDirect:SeasonSummer:PeriodMm 0.095 0.11616843 207 0.817778
0.4144
Depth3D:RFDirect:SeasonSummer:PeriodMm 0.131 0.15019320 207 0.872210
0.3841
Depth1F:RFDiffuse:SeasonWinter:PeriodMm 0.005 0.00246257 207 2.030401
0.0436
Depth2M:RFDiffuse:SeasonWinter:PeriodMm -0.114 0.01848694 207 -6.166514
0.0000
Depth3D:RFDiffuse:SeasonWinter:PeriodMm -0.005 0.02238539 207 -0.223360
0.8235
Depth1F:RFDirect:SeasonWinter:PeriodMm 0.010 0.00290226 207 3.445588
0.0007
Depth2M:RFDirect:SeasonWinter:PeriodMm 0.393 0.11616843 207 3.383019
0.0009
Depth3D:RFDirect:SeasonWinter:PeriodMm 0.477 0.15019320 207 3.175909
0.0017
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.40565911 -0.49125600 -0.07135492 0.27988944 4.73995350
Number of Observations: 240
Number of Groups:
Pop Ind %in% Pop
2 10
#But I have serious problems when interpreting this.
For instance, from this summary we have:
Depth2M:RFDirect p<0.000
Does this mean that CV of direct radiation differs from that of diffuse at
Depth2M, or that CV of direct radiation at Depth2M differs from that at
reference Depth1F?
Is there any book or guide for learning to understand this?
Thank you very much in advance!
A. Lesp
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