  The habitats are replicated, sorry for the confusion!

How can I decide if I really need a zero-inflated model or is it just 
expert judgment?
I decided that I need it, because more than 50% of the data are true 
zeros (detectability=100%) and therfore e.g. Martin et al. (2005) or 
Zuur et al., et al. (2009) recommended zero-inflated models.
but:
"In this study it appeared that zero inflated distributions were not 
usually needed, which implies that observations in which a taxon does 
not occur could usually be distinguished from those where the taxon does 
occur (a priori or using environmental variables), i.e. most zeros could 
be attributed to the systematic component of the model, rather than 
taking the more complicated route and incorporating them into the random 
component of the model." (Warton 2005) [p. 288]
--> Does this mean that I do not need a zero inflation model if the 
detectability=100% and therefore "all zeros"="true zeros"?

If I am allowed to use a hurdle model, is something wrong about the 
hurdle-function of the pscl-package?
I think about something like this:
hurdle<- 
hurdle(NumberOfIndividuals~HabitatComplexity+Time+Colour+Treatment+HabitatDensity*Zeit+HabitatDensity*Treatment..., 
dist = "poisson", link = "logit")

Response variables
NumberOfIndividuals: Number of individuals in the habitat

Explanatory variables:
HabitatComplexity: Complexity of the habitat (4 levels) [continuous 
variable]
Colour: Colour of the habitat (4 levels)
Treatment: tap water, tap water + additive 1, tap water + additive 2 (3 
levels)
Time: Resampling every 5 min (5-30 min) (6 levels) [continuous variable]

Citeted literature:

Martin, T.G., Wintle, B.A., Rhodes, J.R., Kuhnert, P.M., Low Choy, S., 
Field, S.A., Tyre, A.J., & Possingham, H.P. (2005) Zero tolerance 
ecology: improving ecological inference by modelling the source of zero 
observations. /Ecology Letters/, 8, 1235-1246

Warton, D. I. 2005. Many zeros do not mean zero inﬂation: comparing the 
goodness-of-ﬁt of parametric models to multivariate abundance data. 
Environmetrics 16:275-289. doi: 10.1002/env.702 
<http://dx.doi.org/10.1002/env.702>

A.F. Zuur et al.(2009). Mixed effects models and extensions in ecology 
with R. Chapter 11 Zero-Truncated and Zero-Inflated Models for Count Data.

Am 31/08/2010 11:21, schrieb Ben Bolker:
>    A few comments:
>
>    are the habitats replicated? If not, you have a fairly serious
> experimental design problem -- you can't statistically distinguish
> between the measured covariates and other, unmeasured/unintentional
> differences among the habitats ...
>
>    * are you willing to treat complexity as a continuous variable, or do
> you not want to assume that the 'distance' between neighboring
> values of complexity is the same (an ordinal variable)?
>
>   * for colour and water, you should probably simply leave these as
> single categorical variables and let R sort out the construction of
> dummy variables for you.
>
>   * you should think about whether you want to look for regular/monotonic
> trends with time (i.e. code time as a continuous
> variable) or allow for any possible temporal variable (code time a
> fixed, or possibly random-effect, categorical variable)
>    if habitats are indeed replicated you probably want something like
>
> MCMCglmm(fixed=number_in_habitat~complexity+colour+water+time,random=~habitat,
>     family=zipoisson,data=...)
>
>    you have a few options for the family depending on how you want to
> treat the zeros (hurdle vs. zero-inflated)
>
>    are you sure the data are zero-inflated  (Warton, D. I. 2005. Many
> zeros do not mean zero inﬂation: comparing the goodness-of-ﬁt of
> parametric models to multivariate abundance data. Environmetrics
> 16:275-289. doi: 10.1002/env.702<http://dx.doi.org/10.1002/env.702>.  ) ?
>
>
>
> Renke Lühken wrote:
>>   Hi all,
>> I want to analyse an experiment at which insects were allowed to
>> choose between four habitats with different characteristics (see
>> below). Number of individuals per habitat were resampled six times
>> (every 5 min). I want to know which variables and which interactions
>> of the variables have an influence on the number of individuals in the
>> habitats.
>>
>> Problem: The response variable shows a zero inflation (>50% of the
>> data) by true zeros (100% detectability).
>>
>> Question: Can I use a hurdle model (ZAP) for that or do you recommend
>> another method for the data analysis?
>>
>> Thanks in advance,
>> Renke Lühken
>>
>>
>> Response variables
>> Number of individuals in the habitat
>>
>> Explanatory variables:
>> Complexity of the habitat (4 levels)
>> Habitat has the Colour 1 (yes/no)
>> Habitat has the Colour 2 (yes/no)
>> Habitat has the Colour 3 (yes/no)
>> Habitat has the Colour 4 (yes/no)
>> Water additive 1 (yes/no)
>> Water additive 2 (yes/no)
>> Time (6 levels: 5-30 min [resampling every 5 min])
>>
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>


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