Re: [R] glmer with non integer weights

2010-04-23 Thread Kay Cichini

hello,

krebs (1995) states MH as prob., but yes it's rather a ratio of probs.
at each site i had 4 blocks with 2 treatments (treat vs. control) - after
treating i looked for similarity between each of those pairs. 

it is of interest if changes in similarity due to treatment differ between
stages.

hope this clarifies the thing a bit.

greetings,
kay
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Re: [R] glmer with non integer weights

2010-04-22 Thread Emmanuel Charpentier
Sorry for this late answer (I've had a seriously nonmaskable interrupt).

Since I have technical questions not related to R, I take the liberty to
follow this up by e-mail.

I might post a followup summary if  another R problem arises...

Emmanuel Charpentier

Le lundi 19 avril 2010 à 23:40 -0800, Kay Cichini a écrit :
 hello,
 
 it's the Morisita Horn Index, which is an ecological index for similarity
 between two multivariate objects (vegetation samples with species and its
 abundance) where a value of one indicates completely same relative
 importance of species in both samples and 0 denotes total absence of any
 same species.
 
 it can be expressed as a probability:
 
 (prob. that an individual drawn from sample j 
 and one from sample k belong to the same species)
 -   = MH-INdex
 (prob. that two ind. drawn from either sample will 
 belong to same species)

[ Technical rambling ]

Hmmm ... that's the *ratio* of two probabilities, not a probability.
According to http://www.tnstate.edu/ganter/B412%20Ch%201516%
20CommMetric.html, that I found in the first page of answers to a simple
google query, in can also be thought of the ratio of two distances
between sites : (maximal distnce - actual distance) / maximal distance
(with a massive (over-?) simplification). There is no reason to think a
priori that the logit transformation (or the asin(sqrt()) transformation
has better properties for this index than any other mapping from [0 1]
to R.

(BTW, a better mapping might be from [0 1] to [0 Inf] or conversely, but
negative distances have no (obvious) meaning. Here asin(sqrt()) might
make more sense that qlogis().)

[ End of technical rambling ]

But I have trouble understanding how a similarity or distance index
can characterize *one* site... Your data clearly associate a MH.Index to
each site : what distance or similarity do you measure at this site ?

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Re: [R] glmer with non integer weights

2010-04-20 Thread Kay Cichini

hello,

it's the Morisita Horn Index, which is an ecological index for similarity
between two multivariate objects (vegetation samples with species and its
abundance) where a value of one indicates completely same relative
importance of species in both samples and 0 denotes total absence of any
same species.

it can be expressed as a probability:

(prob. that an individual drawn from sample j 
and one from sample k belong to the same species)
-   = MH-INdex
(prob. that two ind. drawn from either sample will 
belong to same species)

it is also covered in
library(vegan);?vegdist
here it is its complement: 1-MH, which then is a dissimilarity measure

best regards,
kay

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Re: [R] glmer with non integer weights

2010-04-19 Thread Kay Cichini

hi emmanuel,

thanks a lot for your extensive answer.
do you think using the asin(sqrt()) transf. can be justified for publishing
prurpose or do i have to expect criticism.

naivly i excluded that possibility, because of violated anova-assumptions,
but if i did get you right the finite range rather posses a problem here.

why is it in this special case an advantage? 

greetings,
kay

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Re: [R] glmer with non integer weights

2010-04-19 Thread Emmanuel Charpentier
Le lundi 19 avril 2010 à 03:00 -0800, Kay Cichini a écrit : 
 hi emmanuel,
 
 thanks a lot for your extensive answer.
 do you think using the asin(sqrt()) transf. can be justified for publishing
 prurpose or do i have to expect criticism.

Hmmm ... depends of your reviewers. But if an half-asleep dental surgeon
caught that after an insomnia, you might expect that a fully caffeinated
reviewer will. Add Murphy's law to the mix and ... boom !

 naivly i excluded that possibility, because of violated anova-assumptions,
 but if i did get you right the finite range rather posses a problem here.

No. your problem is that you model a probability as a smooth (linear)
finite function of finite variables. Under those assumptions, you can't
get a *certitude* (probability 0 or 1). Your model is *intrinsically*
inconsistent with your data.

In other word, I'm unable to believe both your model (linear
whathyoumaycallit regression) and your data (wich include certainties)
*simultaneously*.

I'd reconsider your 0 or 1, as meaning *censored* quantities (i. e. no
farther than some epsilon from 0 or 1), with *hard* data (i. e. not a
cooked-up estimate such as the ones i used) to estimate epsilon. There
are *lots* of ways to fit models with censored dependent variables.

 why is it in this special case an advantage? 

It's bloody hell *not* a specific advantage : if you want to fit a
linear model to a a probability, you *need* some function mapping R to
the open ]0 1[ (i. e. all reals strictly superior to 0 and strictly
inferior to 1 ; I thing that's denoted (0 1) in English/American usage).
Asin(sqrt()) does that.

However, (asin(sqrt()))^-1 has a big problem (mapping back [0 1] i. e.
*including* 0 and 1, *not* (0 1), to R) which *hides* the (IMHO bigger)
problem of the inadequacy of your model to your data ! In other words,
it lets you shoot yourself in the foot after a nice sciatic nerve
articaïne block making the operation painless (but still harmful). On
the other hand, logit (or, as pointed by Martin Maechler, qlogis), is
kind enough to choke on this (i. e. returning back Inf values, which
will make the regression program choke).

So please quench my thirst : what exactly is MH.Index supposed to be ?
How is it measured, estimated, guessed or divined ?

HTH,

Emmanuel Charpentier

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Re: [R] glmer with non integer weights

2010-04-18 Thread Emmanuel Charpentier
Le vendredi 16 avril 2010 à 00:15 -0800, Kay Cichini a écrit :
 thanks thierry,
 
 i considered this transformations already, but variance is not stabilized
 and/or normality is neither achieved.
 i guess i'll have to look out for non-parametrics?

Or (maybe) a model based on a non-Gaussian likelihood ? A beta
distribution comes to mind, either fitted by maximum likelihood or (if
relevant prior information is available) in a Bayesian framework ?

But beware : you have a not-so-small problem ...

Your data have zeroes and ones, which, if you have no information on a
sample size, are sharp zeroes and ones, and there therefore
theoretically bound to infinite linear predictors (in plain English :
bloody unlikely). These values make a fixed effect analysis
impossible : these points at infinite will make regression essentially
impossible. Consider :

 logit-function(x)log(x/(1-x))
 ilogit-function(x)1/(1+exp(-x))
 ilogit(coef(lm(logit(MH.Index)~0+stage,data=similarity)))
Erreur dans lm.fit(x, y, offset = offset, singular.ok =
singular.ok, ...) : 
  NA/NaN/Inf dans un appel à une fonction externe (argument 4)

You need to have some information on the precision of your zeroes and
ones nd use it to get some possible values of MH.Index

One might be tempted to unround them by a small amount (representing a
reasonable guess on your precision :
 epsilon=0.01
 ilogit(coef(lm(logit(MH.Index)~0
+stage,data=within(similarity,{MH.Index-pmax(epsilon,pmin(1-epsilon,MH.Index))}
   stageAstageBstageCstageD 
0.6490997 0.2914323 0.5087639 0.5721789 

BUT :

 epsilon=0.01
 ilogit(coef(lm(logit(MH.Index)~0
+stage,data=within(similarity,{MH.Index-pmax(epsilon,pmin(1-epsilon,MH.Index))}
   stageAstageBstageCstageD 
0.6588222 0.1020177 0.5087639 0.5721789 

The estimation for stageB depends critically of the unrounding amount
chosen.

I tried a small fixed effect logit model in JAGS : it won't initialize
with the original data (O and 1 are effectively impossible with possible
values of the beta coefficients), and seems to exhibit, the same kind of
sensitivity to unrounding amount that the linear model :

LogitModFix-local({
  Modele-function(){
for(k in 1:nobs) {
  ## logit(MH.Index[k])-lpi.i[k]
  lpi.i[k]~dnorm(lpi[stage[k]], tau.lpi[stage[k]])
}
for(i in 1:nstage) {
  lpi[i]~dnorm(0,1.0E-6)
  tau.lpi[i]-pow(sigma.lpi[i],-2)
  sigma.lpi[i]~dunif(0,100)
  pi[i]-ilogit(lpi[i])
}
  }
  Data-function() {
for (i in 1:nobs) {
  lpi.i[i]-logit(MH.Index[i])
}
  }
  tmpf-tempfile()
  ## write.model has been shoplifted from R2WinBUGS and adapted to JAGS
  ## by allowing a data argument for transformations
  write.model(Modele,tmpf, data=Data)
  epsilon-0.1
  Modele.jags-jags.model(tmpf,
  data=with(similarity,

list(MH.Index=pmax(epsilon,pmin(1-epsilon,MH.Index)),
 ## MH.Index=MH.Index,
 stage=stage,
 nobs=nrow(similarity),
 nstage=nlevels(stage))),
  n.chains=3)
  unlink(tmpf)
  Modele.coda-coda.samples(Modele.jags,
variable.names=c(deviance, pi,
sigma.lpi),
n.iter=1000)
  list(Modele.jags, Modele.coda)
})

## Convergence (not shown) is quite acceptable

 summary(LogitModFix[[2]])

Iterations = 1001:2000
Thinning interval = 1 
Number of chains = 3 
Sample size per chain = 1000 

1. Empirical mean and standard deviation for each variable,
   plus standard error of the mean:

 Mean  SD  Naive SE Time-series SE
deviance 660.5656 4.71697 0.0861196  0.1672079
pi[1]  0.6304 0.21666 0.0039557  0.0040347
pi[2]  0.1506 0.08036 0.0014671  0.0014460
pi[3]  0.5082 0.03956 0.0007222  0.0006777
pi[4]  0.5696 0.07473 0.0013644  0.0012952
sigma.lpi[1]   6.9409 0.86442 0.0157821  0.0287626
sigma.lpi[2]   4.2775 0.49281 0.0089974  0.0132247
sigma.lpi[3]   1.0875 0.11506 0.0021006  0.0026048
sigma.lpi[4]   0.8801 0.29371 0.0053623  0.0118630

2. Quantiles for each variable:

 2.5%   25%  50%  75%97.5%
deviance 654.0216 657.13069 659.6788 662.9535 672.2101
pi[1]  0.1695   0.47600   0.6681   0.8107   0.9485
pi[2]  0.0413   0.09206   0.1345   0.1914   0.3564
pi[3]  0.4320   0.48079   0.5078   0.5366   0.5851
pi[4]  0.4154   0.52518   0.5722   0.6168   0.7135
sigma.lpi[1]   5.5553   6.33366   6.8287   7.4412   8.8207
sigma.lpi[2]   3.5082   3.93440   4.2274   4.5598   5.3497
sigma.lpi[3]   0.8833   1.00397   1.0805   1.1565   1.3412
sigma.lpi[4]   0.5304   0.67740   0.8189   1.0067   1.5987

The same model re-fitted with epsilon=0.01 gives :

 summary(LogitModFix[[2]])

Iterations = 1001:2000
Thinning interval = 1 
Number of chains = 3 
Sample size per chain = 1000 

1. Empirical mean and 

Re: [R] glmer with non integer weights

2010-04-18 Thread Emmanuel Charpentier
Addendum to my previous answer :

In that special case, the limited range of the asin(sqrt())
transformation, which is a shortcoming, turns out to be useful. The
fixed-effect doefficients seem semi-reasonable (except for stageB) :

 (sin(coef(lm(asin(sqrt(MH.Index))~0+stage, data=similarity^2
   stageAstageBstageCstageD 
0.6164870 0.3389430 0.5083574 0.5672021 

The random effects being nested in the fixed efect, one can't afford to
be lazy in the parametrization of the corresponding random effect :

 summary(lmer(asin(sqrt(MH.Index))~stage+(stage|site),
data=similarity))
Linear mixed model fit by REML 
Formula: asin(sqrt(MH.Index)) ~ stage + (stage | site) 
   Data: similarity 
   AIC BIC logLik deviance REMLdev
 155.3 199 -62.65111.8   125.3
Random effects:
 Groups   NameVariance Std.Dev. Corr 
 site (Intercept) 0.043579 0.20876   
  stageB  0.033423 0.18282  -0.999   
  stageC  0.043580 0.20876  -1.000  0.999
  stageD  0.043575 0.20875  -1.000  0.999  1.000 
 Residual 0.128403 0.35833   
Number of obs: 136, groups: site, 39

Fixed effects:
Estimate Std. Error t value
(Intercept)  0.930360.08431  11.035
stageB  -0.308790.10079  -3.064
stageC  -0.136600.09981  -1.369
stageD  -0.077550.14620  -0.530

Correlation of Fixed Effects:
   (Intr) stageB stageC
stageB -0.836  
stageC -0.845  0.707   
stageD -0.577  0.482  0.487
 v-fixef(lmer(asin(sqrt(MH.Index))~stage+(stage|site),
data=similarity))
 v[2:4]-v[1]+v[2:4]
 names(v)[1]-stageA
 (sin(v))^2
   stageAstageBstageCstageD 
0.6429384 0.3390903 0.5083574 0.5672021 

But again, we're exploiting a shortcoming of the asin(sqrt())
transformation.

HTH,

Emmanuel Charpentier

Le vendredi 16 avril 2010 à 00:15 -0800, Kay Cichini a écrit :
 thanks thierry,
 
 i considered this transformations already, but variance is not stabilized
 and/or normality is neither achieved.
 i guess i'll have to look out for non-parametrics?
 
 best regards,
 kay

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Re: [R] glmer with non integer weights

2010-04-16 Thread Kay Cichini

thanks thierry,

i considered this transformations already, but variance is not stabilized
and/or normality is neither achieved.
i guess i'll have to look out for non-parametrics?

best regards,
kay
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Re: [R] glmer with non integer weights

2010-04-16 Thread Kay Cichini

thank you thomas for the helpful hint!

yours,
kay
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Re: [R] glmer with non integer weights

2010-04-13 Thread ONKELINX, Thierry
Dear Kay,

There is a R list about mixed models. Which is a better place for your
questions.

The (quasi)binomial family is used with binary data or a ratio that
originates from binary data. In case of a ratio you need to provide the
number of trials through the weights argument.

Further I would suggest to drop stage from either the random effects or
the fixed effects. You are trying to estimate the same effect twice in a
model.

HTH,

Thierry



ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek
team Biometrie  Kwaliteitszorg
Gaverstraat 4
9500 Geraardsbergen
Belgium

Research Institute for Nature and Forest
team Biometrics  Quality Assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium

tel. + 32 54/436 185
thierry.onkel...@inbo.be
www.inbo.be

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to
say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of
data.
~ John Tukey
  

 -Oorspronkelijk bericht-
 Van: r-help-boun...@r-project.org 
 [mailto:r-help-boun...@r-project.org] Namens Kay Cichini
 Verzonden: maandag 12 april 2010 16:12
 Aan: r-help@r-project.org
 Onderwerp: [R] glmer with non integer weights
 
 
 hello,
 
 i'd appreciate help with my glmer.
 i have a dependent which is an index (MH.index) ranging from 
 0-1. this index can also be considered as a propability. as i 
 have a fixed factor (stage) and a nested random factor (site) 
 i tried to model with glmer. i read that it's possible to use 
 a quasibinomial distribution, for this kind of data, which i 
 than actually did - but firstly 
 
 (1) i'm not quite sure if that's appropiate for my data, secondly
 (2) i wondered if the model can be correct when variance of 
 then main and nested factor are zero.
 (3) also i could not yield p-values for that model.
 
 here's data, call and output:
 
 ##
 #call:
 ##
 
 glmer(MH~stage+(1|stage/site),family=quasibinomial)
 
 ##
 #output:
 ##
 #Generalized linear mixed model fit by the Laplace approximation
 #Formula: MH ~ stage + (1 | stage/site) 
 #  AIC   BIC logLik deviance
 # 66.03 86.47 -26.0152.03
 #Random effects:
 # Groups NameVariance Std.Dev.
 # site:stage (Intercept) 0.00 0.000   
 # stage  (Intercept) 0.00 0.000   
 # Residual   0.076175 0.276   
 # Number of obs: 137, groups: site:stage, 39; stage, 4
 
 #Fixed effects:
 #Estimate Std. Error t value
 #(Intercept)  0.392050.09009   4.352
 #stageB  -0.872140.12498  -6.978
 #stageC  -0.361530.12202  -2.963
 #stageD  -0.098840.19811  -0.499
 
 #Correlation of Fixed Effects:
 #   (Intr) stageB stageC
 #stageB -0.721  
 #stageC -0.738  0.532   
 #stageD -0.455  0.328  0.336
 ##
 #my data:
 ##
 similarity-data.frame(list(structure(list(stage = 
 structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 
 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 
 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 
 4L, 4L, 4L, 4L), .Label = c(A, B, C, D), class = 
 factor), site = structure(c(1L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 
 3L, 3L, 4L, 4L, 4L, 4L, 5L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 8L, 
 8L, 8L, 8L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 11L, 11L, 
 12L, 12L, 12L, 13L, 13L, 13L, 14L, 14L, 14L, 14L, 15L, 15L, 
 15L, 15L, 16L, 16L, 16L, 17L, 17L, 17L, 17L, 18L, 18L, 19L, 
 19L, 19L, 19L, 20L, 20L, 20L, 20L, 21L, 21L, 21L, 21L, 22L, 
 22L, 22L, 22L, 23L, 23L, 23L, 24L, 24L, 24L, 24L, 25L, 25L, 
 25L, 25L, 26L, 26L, 26L, 26L, 27L, 27L, 27L, 27L, 28L, 28L, 
 28L, 28L, 29L, 29L, 29L, 30L, 30L, 30L, 30L, 31L, 31L, 32L, 
 32L, 32L, 32L, 33L, 33L, 33L, 33L, 34L, 34L, 34L, 34L, 35L, 
 35L, 35L, 35L, 36L, 36L, 36L, 36L, 37L, 37L, 38L, 38L, 38L, 
 38L, 39L, 39L, 39L ), .Label = c(A11, A12, A14, A15, 
 A16, A17, A18, A19, A20, A5, A7, A8, B1, 
 B12, B13, B14, B15, B17, B18, B2, B4, B7, 
 B8, B9, C1, C10, C11, C15, C17, C18, C19, 
 C2, C20, C3, C4, C6, D1, D4, D7), class = 
 factor), 

Re: [R] glmer with non integer weights

2010-04-13 Thread Kay Cichini

thanks thierry,

my problem is that the index is a propability which is not derived from
incidents per nr. of observations, thus i don't have those numbers but only
the plain index, which i want to test.

greatings,
kay
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Re: [R] glmer with non integer weights

2010-04-13 Thread ONKELINX, Thierry
So your respons variable behaves like a continuous variable except that
is range is limited to the 0-1 interval. In such a case I would
transform the respons variable (e.g. logit, sqrt(arcsin())) and use a
gaussian model.

HTH,

Thierry



ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek
team Biometrie  Kwaliteitszorg
Gaverstraat 4
9500 Geraardsbergen
Belgium

Research Institute for Nature and Forest
team Biometrics  Quality Assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium

tel. + 32 54/436 185
thierry.onkel...@inbo.be
www.inbo.be

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to
say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of
data.
~ John Tukey
  

 -Oorspronkelijk bericht-
 Van: r-help-boun...@r-project.org 
 [mailto:r-help-boun...@r-project.org] Namens Kay Cichini
 Verzonden: dinsdag 13 april 2010 13:37
 Aan: r-help@r-project.org
 Onderwerp: Re: [R] glmer with non integer weights
 
 
 thanks thierry,
 
 my problem is that the index is a propability which is not 
 derived from incidents per nr. of observations, thus i don't 
 have those numbers but only the plain index, which i want to test.
 
 greatings,
 kay
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Re: [R] glmer with non integer weights

2010-04-13 Thread Thomas Lumley

On Tue, 13 Apr 2010, ONKELINX, Thierry wrote:


So your respons variable behaves like a continuous variable except that
is range is limited to the 0-1 interval. In such a case I would
transform the respons variable (e.g. logit, sqrt(arcsin())) and use a
gaussian model.


A logit-Normal has variance roughly mu^2(1-mu)^2 and a quasibinomial logistic 
uses mu(1-mu),  with the parameters having the same interpretations. The 
question of which variance function best approximates the data should really be 
an empirical one, not an a prioiri one.  There is an example of exactly this in 
the quasilikelihood chapter in McCullagh and Nelder, where the observations are 
the proportion of damage on a set of leaves.

  -thomas

Thomas Lumley   Assoc. Professor, Biostatistics
tlum...@u.washington.eduUniversity of Washington, Seattle

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