[R] Compositional Data Analysis

[Tim Locke]

Hi All,

I am currently working on a project examining the health effects of physical
activity using a compositional data (CoDa) approach. I am using a
linear regression to measure the effect of physical activity. What I want to
do is predict an outcome, e.g. body mass index, based on the mean physical
activity composition. I then want to alter this composition by reallocating
time from one behavior (such as sedentary) to light intensity physical
activity, and see what effect this has on BMI. I have included the code
below. My problem is that I cannot seem to generate this new composition
correctly.



library(compositions)
attach(Data_Analysis)

#Replace zeros in raw data with 0.00001
bedtimemins[bedtimemins==0] <- 0.00001
sedwakingmins[sedwakingmins==0] <- 0.00001
standingtimemins[standingtimemins==0] <- 0.00001
LIPAmins[LIPAmins==0] <- 0.00001
MVPAmins[MVPAmins==0] <- 0.00001

# make the composition by       binding the components together
comp <- cbind(bedtimemins, sedwakingmins, standingtimemins, LIPAmins,
MVPAmins)
# tell R that comp is a compositional   variable
comp <- acomp(comp)

#Generate variation matrix
PAvar_matrix <- var.acomp(comp)

# make the ilr multiple linear regression model. BMI = body mass index. .
lm <- lm(bmi    ~ ilr(comp) + age)

#determine the mean composition, geometric mean of behaviors which sum to 1
comp.mean <- mean(comp)

# predict BMI for the mean composition from above, keeping age constant at
its mean.
mean.pred       <- predict(lm,  newdata=list(comp=comp.mean, age = mean(age)))

#generate new compostion of PA with 30 minutes of sleep reallocated to 30
mins of LIPA
new.comp        <- acomp(comp.mean +c(-30/1440, 0/1440, 0/1440, 30/1440, 0/1440))

#predict BMI based on new composition
pred    <- predict(lm,  newdata=list(comp=new.comp,     age=mean(age)))

#Estimated difference in BMI for the above reallocation
pred    - mean.pred


When I run the command to generate the new composition, I receive the
message below

new.comp        <- acomp(comp.mean +c(-30/1440, 0/1440, 0/1440, 30/1440, 0/1440))
Warning messages:
1: In acomp(gsi.mul(x, y)) :
  Negative values in composition are used as detection limits
2: In acomp(comp.mean + c(-30/1440, 0/1440, 0/1440, 30/1440, 0/1440)) :
  Negative values in composition are used as detection limits

When I print comp.mean I get a result that seems to make sense:
comp.mean
     bedtimemins    sedwakingmins standingtimemins         LIPAmins       MVPAmins

      0.36410089       0.32460230       0.22278324                0.06948202         0.01903155


I can't say the same for the new composition:
new.comp
     bedtimemins    sedwakingmins standingtimemins         LIPAmins       MVPAmins
       <5.240217              BDL              BDL                             1.000000            BDL

Any help or advice would be greatly appreciated!



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