tree diameter growth
Dear Bin Yue, you've described a pretty interesting modelling effort. It's true that determining what should be a fixed and what should be a random effect is laregly up to the analyst, but different interpretations will be available from these different choices. You may find it worth reading the Hierarchical Models chapter in my icebreakeR document (freely available online), http://www.ms.unimelb.edu.au/~andrewpr/r-users/icebreakeR.pdf or Chapter 7 of "Forest Analytics in R", both of which discuss fixed and random effects fomr a forestry point of view. I would tend to think that the following model is worth trying: gr1 <- lmer(log(dbh.y)-log(dbh.x) ~ scale(log(dbh.x)) + classsizedist + (scale(log(dbh.x)) | spcode), data = livestem) My reasoning is as follows. First, the goal is to determine the effect of different size-class distributions on growth. I think that you'd probably like to be able to represent these estimates and discuss them. To me it seems natural to make them fixed effects. Second, one could argue for the species effect to be fixed or random. Increasingly I see people fitting species as a random effect, and in this case, it makes sense to me. However, note that I'm allowing for each species to have a different growth trajectory. I would suspect that there would be species-specific variation in the growth rates as a function of size; this term will allow for that contingency. I hope that these thoughts are useful to you. Andrew
On Fri, Aug 19, 2011 at 04:46:41PM +0800, Bin Yue wrote:
Dear experts in mixed-models, I am a postdoc dealing with the growth data of a 20 ha forest plot. I want to know whether the diameter growth of individuals is relatedto the size distribution types( reversed j shaped and unimiodal) of the speciesthe individuals belong to. Although I have obtained result, I am still hesitating. Because I feel that something is worong with the output. I used this command: lmer(log(dbh.y)-log(dbh.x)~scale(log(dbh.x))+(1|spcode/classsizedist),data=livestem)->gr, where the left side is the response variable : the logarithm of dbh in 2010 minus the logarithm of dbh in 2005 ( the relative diameter growth rate), the first component on the right side is the logarithm of dbh in 2005 after standardization ( each element minus the mean and devided by the sd), the second part is what makes me hesitate. Actually livestem is a data.frame, each line representing each individual. All dbh.y, dbh.x, spcode and classsizedist are its columns. I have 83 spcodes. classsizedist is the type of size distribution.The same species must have the same type of size distribution. I think that I can use the lmer function in lme4 package to tested whether diameter growth is associated with the size distribution. I don't actually care how diameter growth is related to original diamter, and species identity but taking these variables into account helps reduce the residual sum of square used in the F test for the effect of size distribution on diameter growth. So on the right side of ~, I have three variables: the original diameter, the species, and the size distribution type of the species. There is obvious hierachical structure among these variables,where individuals are nested within species and species are nested within the type of size distribution. What stop me from putting down the results into the manuscript are that I am not quite sure whether the command I use is doing what I want and I cannot interpret the results. I have read some materials and I am confounded by the random effect and the fixed effect. Originally I think random and fixed effect can be set by mysels as I wish. After some reading it seems to me that random effect is something similar to the effect of error but with a different variance and fixed effect is like the mean. The following is the result of gr lmer(log(dbh.y)-log(dbh.x)~scale(log(dbh.x))+(1|spcode/classsizedist),data=livestem)->gr
summary(gr)
Linear mixed model fit by REML
Formula: log(dbh.y) - log(dbh.x) ~ scale(log(dbh.x)) + (1 | spcode/classsizedist)
AIC BIC logLik deviance REMLdev
-29390 -29345 14700 -29419 -29400
Random effects:
Groups Name Variance Std.Dev.
classsizedist:spcode (Intercept) 0.0015012 0.038745
spcode (Intercept) 0.0162077 0.127310
Residual 0.0381650 0.195359
Number of obs: 69669, groups:classsizedist:spcode, 83; spcode, 83
Fixed effects:
Estimate Std. Error t value
(Intercept) 0.123306 0.014759 8.35
scale(log(dbh.x)) -0.084744 0.001102 -76.93
Correlation of Fixed Effects:
(Intr)
scl(lg(d.)) -0.003
pvals.fnc(gr)
$fixed
Estimate MCMCmean HPD95lower HPD95upper pMCMC Pr(>|t|)
(Intercept) 0.1233 0.1234 0.0990 0.1478 0.0001 0
scale(log(dbh.x)) -0.0847 -0.0847 -0.0868 -0.0825 0.0001 0
$random
Groups Name Std.Dev. MCMCmedian MCMCmean HPD95lower
1 classsizedist:spcode (Intercept) 0.0387 0.0448 0.0453 0.0000
2 spcode (Intercept) 0.1273 0.0998 0.0974 0.0633
3 Residual 0.1954 0.1954 0.1954 0.1944
HPD95upper
1 0.0873
2 0.1222
3 0.1964
I think something is wrong with the command because in the output: groups: classsizedist:spcode, 83; spcode, 83
I have 83 species but 2 classsizedist.
I would look forward to your reply.
Thank you very much for your time.
Sincerely,
Bin Yue
--
Bin Yue
Ph.D
College of Life Science,Sun Yat-sen University
Guangdong Province, China
Email:byicymoon at 163.com
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