zero-truncated mixed effects logistic regression?

The problem I have is similar to the capture-recapture approach for
estimating abundance. In my case the captured animals are design flaws of
software.

A given number of testers independently tries to find these flaws, which
makes it a binomial problem. However, flaws that were never discovered
during the study are not known to the experimenter.

Furthermore this is a crossed mixed-effects 
situation as
discovery trials are repeated over testers and flaws.

(1)    Does effectiveness of testers increases with years of experience?
(2)    Are certain classes of flaws easier to find than others?

A general finding of previous research is that testers as well as flaws are
heterogeneous. Some flaws are less visible than others and testers differ in
overall effectiveness. Hence, random effects are needed to account for
overdispersion, right?

I may be corrected, but I think your setup is "actually" a Rasch type 
model with each flaw being an item.  Some flaws are just too difficult to 
see, ie the item is "too hard".  I presume, given your research questions, 
you are not actually interested in estimating the number of undetected 
flaws from each class, so a missing data type setup is not really needed.

http://www.jstatsoft.org/v20/a02/paper

is one paper from our esteemed leader ;)

| 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

The problem I have is similar to the capture-recapture approach for
estimating abundance. In my case the captured animals are design flaws
of software.

A given number of testers independently tries to find these flaws,
which makes it a binomial problem. However, flaws that were never
discovered during the study are not known to the experimenter.

I may be corrected, but I think your setup is "actually" a Rasch type

model

with each flaw being an item.  Some flaws are just too difficult to see,

ie the

item is "too hard".  I presume, given your research questions, you are not
actually interested in estimating the number of undetected flaws from each
class, so a missing data type setup is not really needed.

http://www.jstatsoft.org/v20/a02/paper

is one paper from our esteemed leader ;)

In one of my works on that topic I, indeed, viewed this as a Rasch type
model. And I well remember how excited I got when reading above paper,
because that would allow me to deal with predictors in a straight forward
way.

However, the number of undetected flaws is crucial by itself as it means to
go on testing. Capture-recapture models are a good way to estimate these,
but they don't allow for predictors. So, if I run a crossed mixed effects
logistic regression on my data, I have missing values.

So, while the above paper merges IRT models with (crossed) mixed effects
models (and that's great!), I would need sth. that merges the latter with
C-R models. C-R models do deal with sort of random effects: the
heterogeneous capturability of animals (denoted "h") and variability in
trials ("t"). So called Mht models could thus be viewed as crossed random
effects models, but: C-R models (afaik) don't deal with predictors and
mixed-effects models require at least missing-at-random, which is not the
case.

Any ideas?

CU, Martin

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