# [R-sig-ME] Interpreting Growth curves

David Duffy davidD at qimr.edu.au
Fri Mar 18 07:54:30 CET 2011

```On Thu, 17 Mar 2011, Dieter Menne wrote:

> I have growth curves of new bone material under 3 treatments a, b, c. By
> definition, at t=0 we have no new bone, so fitting a linear slope without
> intercept is a reasonable model. For each animal, data are available only at
> one point in time, but several samples are taken at each location with large
> variation.

Well, I am not a particular expert in this area, but it seems to me that
the growth curve part of things is a distraction, since you don't have
usually have useful repeat measures *within* animals.  So, the major
interest is in maximal bone growth response.  Since both the means and
variances of bone measurements for B are so much larger than A and C, a
variance stabilizing transform of bone is one approach, and may well
capture measurement error.  I looked at

plot(bone ~ as.integer(animal), data=gp, col=as.integer(treat),
pch=16+as.integer(time >= 8), axes=F, xlab="Animal", ylab="Bone")
axis(1, at=1:length(unique(gp\$animal)), labels=levels(gp\$animal))
axis(2)

Is a sqrt measurement error mechanism plausible?

Just 2c, David Duffy.

PS or ???
> anova(s1,s2,s3)
Data: gp
Models:
s1: bone ~ -1 + treat:time + (1 | dummy)
s2: bone ~ -1 + treat:time + (1 | dummy) + (1 | animal)
s3: bone ~ -1 + treat:time + (1 | dummy) + (treat | animal)

Df     AIC    BIC  logLik   Chisq Chi Df Pr(>Chisq)
s1  5 1149.76 1165.9 -569.88
s2  6 1006.50 1025.8 -497.25 145.256      1  < 2.2e-16 ***
s3 11  991.29 1026.7 -484.65  25.211      5  0.0001268 ***

PPS I can't remember if glmer with gaussian(link="sqrt") works, but it
does require starting values.

--
| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v

```

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