I'm running an ANOVA on some data for respiration in a forest. I am having a problem with my degrees of freedom. For one of my variables I get one fewer degrees of freedom than I should. I have 12 plots and I therefore expected 11 degrees of freedom, but instead I got 10. Any ideas? I have some code and output below:> class(Combined.Plot)[1] "character"> levels(as.factor(Combined.Plot))[1] "60m" "A1" "B1" "B3" "B4" "C5" "C9" "D2" "D9" "F60m" "F8" "Q7"> nlevels(as.factor(Combined.Plot))[1] 12> Anova.Trt.D.M.T.Pr.Model <- aov(Combined.Rs~Combined.Trt + > as.factor(Combined.Plot) + as.factor(Combined.Day) + > Combined.Trt*as.factor(Combined.Day) + > Combined.Plot*as.factor(Combined.Day))Warning message: In model.matrix.default(mt, mf, contrasts) : variable 'Combined.Plot' converted to a factor> summary(Anova.Trt.D.M.T.Pr.Model)Df Sum Sq Mean Sq F value Pr(>F) Combined.Trt 1 52.80 52.805 2.0186e+30 < 2.2e-16 *** as.factor(Combined.Plot) 10 677.69 67.769 2.5907e+30 < 2.2e-16 *** as.factor(Combined.Day) 16 2817.47 176.092 6.7317e+30 < 2.2e-16 *** Combined.Trt:as.factor(Combined.Day) 16 47.82 2.989 1.1426e+29 < 2.2e-16 *** as.factor(Combined.Day):Combined.Plot 160 611.21 3.820 1.4604e+29 < 2.2e-16 *** Residuals 204 0.00 0.000 --- Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 -- View this message in context: http://r.789695.n4.nabble.com/ANOVA-1-too-few-degrees-of-freedom-tp3493349p3493349.html Sent from the R help mailing list archive at Nabble.com.
Most likely your combined.trt is linearly dependent on the combined.plot factor. Try Anova.Trt.D.M.T.Pr.Model <- aov(Combined.Rs ~ as.factor(Combined.Plot) ..... and see if combined.plot now has the 11 df you are anticipating. Rich On Tue, May 3, 2011 at 3:37 PM, Rovinpiper <david.j.meehan@gmail.com> wrote:> I'm running an ANOVA on some data for respiration in a forest. I am having > a > problem with my degrees of freedom. For one of my variables I get one fewer > degrees of freedom than I should. > > I have 12 plots and I therefore expected 11 degrees of freedom, but instead > I got 10. > > Any ideas? > > I have some code and output below: > > > > class(Combined.Plot) > [1] "character" > > > levels(as.factor(Combined.Plot)) > [1] "60m" "A1" "B1" "B3" "B4" "C5" "C9" "D2" "D9" "F60m" > "F8" "Q7" > > > nlevels(as.factor(Combined.Plot)) > [1] 12 > > > Anova.Trt.D.M.T.Pr.Model <- aov(Combined.Rs~Combined.Trt + > > as.factor(Combined.Plot) + as.factor(Combined.Day) + > > Combined.Trt*as.factor(Combined.Day) + > > Combined.Plot*as.factor(Combined.Day)) > > Warning message: > In model.matrix.default(mt, mf, contrasts) : > variable 'Combined.Plot' converted to a factor > > > summary(Anova.Trt.D.M.T.Pr.Model) > Df Sum Sq > Mean Sq F value Pr(>F) > > Combined.Trt 1 52.80 > 52.805 2.0186e+30 < 2.2e-16 *** > as.factor(Combined.Plot) 10 677.69 67.769 > 2.5907e+30 < 2.2e-16 *** > as.factor(Combined.Day) 16 2817.47 176.092 > 6.7317e+30 < 2.2e-16 *** > Combined.Trt:as.factor(Combined.Day) 16 47.82 2.989 > 1.1426e+29 < 2.2e-16 *** > as.factor(Combined.Day):Combined.Plot 160 611.21 3.820 1.4604e+29 < > 2.2e-16 *** > > Residuals 204 0.00 > 0.000 > > --- > > Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > > -- > View this message in context: > http://r.789695.n4.nabble.com/ANOVA-1-too-few-degrees-of-freedom-tp3493349p3493349.html > Sent from the R help mailing list archive at Nabble.com. > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >[[alternative HTML version deleted]]
Hi Richard, Thanks for your advice. I think that your suggestion is that I run the ANOVA with Combined.Plot as a factor. I have tried that does not alleviate the problem. Did I understand you properly? Do you have another idea? Thanks, David -- View this message in context: http://r.789695.n4.nabble.com/ANOVA-1-too-few-degrees-of-freedom-tp3493349p3493632.html Sent from the R help mailing list archive at Nabble.com.
>>> Rovinpiper <david.j.meehan at gmail.com> 04/05/2011 22:43 >>> >So this seems to indicate that I have what I want. I have two >respiration data points at each plot on each day.Yes; if you had only Plot+Day you'd have a completely balanced full factorial ... for Plot and Day. But I think I now see an answer to your puzzlement. Your original ANOVA table was Df Sum Sq Mean Sq F value Pr(>F) Combined.Trt 1 52.80 52.805 2.0186e+30 < 2.2e-16 *** as.factor(Combined.Plot) 10 677.69 67.769 2.5907e+30 < 2.2e-16 *** as.factor(Combined.Day) 16 2817.47 176.092 6.7317e+30 < 2.2e-16 *** Combined.Trt:as.factor(Combined.Day) 16 47.82 2.989 1.1426e+29 < 2.2e-16 *** as.factor(Combined.Day):Combined.Plot 160 611.21 3.820 1.4604e+29 < 2.2e-16 *** Residuals 204 0.00 0.000 Now, your Day:Plot combination has 17*12=204 combinations. And you are showing 204 residual DOF, which is exactly right for two observations per group and 204 groups. That's exactly right for the model Day+Plot+Day:Plot. But you have Trt in the model as well. Where are the Treatment DoF coming from? Clearly, the treatment DoF has not come out of the residual term. That means the treatment DoF must have come from somewhere else. Since you've lost 2 instead of 1 DoF from Plot and kept your n[Day]-1 degrees of freedom for Day, I would guess that Plot is nested in Trt. If that is the case, you'd 'obviously' expect n[Plot]-2 dof for Plot. And indeed i could replicate your ANOVA table DoF with Trt<-gl(2,204) Plot<-gl(12,34) #Note that Plot is NOT fully crossed with Trt; each Trt has only 6 Plots Day <- gl(17,2,408) y<-rnorm(408) anova(lm(y~Trt+Plot+Day+Trt:Day+Day:Plot)) So that would be one data structure that would explain your DoF. But if that is indeed the structure, there are other concerns that you may need to look out for. First, compare the two models anova(lm(y~Trt+Plot+Day+Trt:Day+Day:Plot)) #and anova(lm(y~Trt+Plot+Day+Day:Plot+Trt:Day)) Same terms in the model specification, but different DoF and Trt:Day has completely vanished from the second ANOVA table. Something is clearly either aliased, unbalanced or incorrectly specified. In my presumed version of events, because the Plot is nested in Trt, Day:Plot is also nested in Trt. To get _consistent_ results independent of model order you would need to reflect that additional nesting in the model: anova(lm(y~Trt+Plot+Day+Trt:Day:Plot+Trt:Day)) #vs anova(lm(y~Trt+Plot+Day+Trt:Day+Trt:Day:Plot)) and this time, the two models give identical results for all rows in the table. Somewhat reassuringly anova(lm(y~Day+Trt/Plot+Trt:Day+Trt:Day:Plot)) and even more reassuringly car's Anova does too. But there's another more fundamental thing that may suggest this is still not quite the right thing to do. If Plot is nested in Trt, it matters whether plot is random or fixed when asking about the treatment effect. I'd guess Plot is random. If plot is random and nested in Trt it would not be appropriate to simply compare any calculated Trt MS with the residual MS. Rather, one would compare the Trt MS with the Trt:Plot interaction. Or perhaps resort to a mixed effects model using lme (if Plot is the only random term) or lmer if Plot and Day are both random. ******************************************************************* This email and any attachments are confidential. Any use...{{dropped:8}}