Thanks very much to Joseph Coveney for the original response below. My
question relates to a dataset from an experimental protocol completed by 66
subjects
<http://www.brown.edu/Administration/Emergency_Medicine/thresh.dta>. It is
assumed that all subjects have the ability to detect an added resistance to
breathing, but that each has a different threshold. We first measure each
subjects intrinsic resistance and present added resistances which are a
percentage of intrinsic. An added resistance to breathing (per_intr) is
presented which is approximately 0, 20, 40, 60, 80, 100, 120, 140, 160, 180
and 200 percent of intrinsic resistance. In random order, non-zero stimuli
are presented three times and the zero level is presented six times for a
total of 36 trials per subject.
My goal is to estimate a threshold (and its variance) for each subject.
My first thought was to run 66 separate logistic regression models (as
below) and calculate a threshold as the resistance at which the predicted
probability of detection was 50% ( - (b_cons)/b_per_intr). One problem is
that some subjects appear to have a very well defined threshold and the
logit models fails when response is "completely determined".
****
use http://www.brown.edu/Administration/Emergency_Medicine/thresh.dta
statsby "logit response per_intr" _b, by(idnum)
generate threshold = -b_cons/b_per_intr
list
****
I had trouble running the unconditional fixed-effects probit model
suggested. I'd appreciate any guidance on how to run this model as well as
in how to use -gllamm- / - gllapred- to estimate the corresponding
random-effects estimator of each subject's threshold.
Thanks! --Dale
----- Original Message -----
From: "Joseph Coveney" <[email protected]>
To: "Statalist" <[email protected]>
Sent: Saturday, September 20, 2003 12:40 AM
Subject: Re: st: Clustered dataset question
> Dale Steele posted:
>
> --------------------------------------------------------------------------
-----
>
> I have a dataset containing information on 66 different subjects. Each
> subject is presented with a series of 36 stimuli (including zero
> magnitude) in random order. Their response to each stimulus is coded as
> 0 - not detected, 1-detected. Each subject is presumed to have a
> "threshold" magnitude at which the stimulus can be detected. My goal is
> to estimate that threshold (and its variance) for each subject.
>
> I have been thinking of the threshold as the predicted stimulus magnitude
> for which the probability of detection is 50%. My naive initial approach
> was to run 66 separate logistic regression models. Is there a better
> way? Thanks!
>
> --------------------------------------------------------------------------
------
>
> I believe that there is a body of psychometrics literature dealing with
this
> kind of problem. -findit- or google for item response theory (IRT) or
Rasch
> model might provide an entrypoint.
>
> Of interest is the FAQ written by Jeroen Weesie on Stata Corp's website,
> www.stata.com/support/faqs/stat/rasch.html . Quoting from that, "Another
> purpose of a Rasch analysis is to estimate the subject parameter eta. In
the
> fixed-effects approach, the etas are commonly estimated by maximum
likelihood
> conditional on the CLM theta-estimates. For the random-effects case, the
etas
> are commonly estimated by posterior means." CML (conditional maximum
> likelihood), here, is referring to -xtlogit , fe-. I believe
that -gllamm- / -
> gllapred- will provide the corresponding random-effects estimator of each
> subject's threshold.
>
> There is also a body of literature in psychophysics dealing with assessing
> stimulus-detection thresholds; Stata's commands that allow estimating
receiver
> operating characteristic (ROC) functions might also be of interest.
>
> The impetus to perform individual logistic regressions for each subject is
in
> the same spirit that was expressed in Stata Corp's admonishment against
> unconditional fixed-effects ordered probit a couple of weeks ago on the
list.
> They recommended avoiding unconditional fixed-effects nonlinear regression
> unless you feel comfortable with estimating each panel separately.
>
> At the risk of getting trounced on the list twice in as many weeks for the
> same thing, I'll mention unconditional fixed-effects probit as an
alternative
> in Dale's case. In general, unconditional maximum likelihood estimators
for
> fixed-effects nonlinear (and linear) models cannot provide consistent
> estimators for the subject-specific intercept terms, so these coefficients
> (and, in nonlinear models, other parameter estimates as well) will have at
> least some bias. For this reason, fixed-effects logit, probit, ordered
> regression models and so on are avoided, in general. But for some
practical
> applications, the situation is not always so dismal as the received wisdom
> would lead us to believe--Prof. William Greene's website at New York
> University's Stern School is an excellent source of information on this
topic.
> As an illustration, I've provided a quick-and-dirty Monte Carlo simulation
of a
> probit-parameterized model of Dale's situation, with 70% intraclass
correlation
> for the threshold latent variable. If I've got things correctly specified
(a
> big if), then the bias in individual-subject estimates of threshold is in
the
> neighborhood of 5% with an unconditional fixed-effects probit model. If
this
> magnitude of bias is acceptible in practice for Dale's purposes, then
> unconditional nonlinear regression represents a viable alternative with
this
> sample size.
>
> In addition, there are approaches to ameliorate such bias, such as the
> jackknife (Hahn and Whitney, 2003), which in my simulations with
fixed-effects
> ordered probit works quite well when panel depths are at least five or
eight,
> even using Professor Greene's challenging specification for the
fixed-effects
> ordered probit model in his numerical study (Greene, 2002). Note that
these
> simulations take a long time when the sample size is in the
hundreds--there is
> a method for improving efficiency in fixed-effects nonlinear regressions
with
> dummy variables for individual subjects that is described in documents on
> Professor Greene's website, but I cannot find where Stata has implemented
it.
>
> Greene, William (2002 February), The behavior of the fixed effects
estimator in
> nonlinear models. Unpublished; available on his website,
> www.stern.nyu.edu/~wgreene, as document EC-02-05Greene.pdf.
>
> Hahn, Jinyong, and Newey, Whitney (2003 July), Jackknife and analytical
bias
> reduction for nonlinear panel models. Available at
> http://econ-www.mit.edu/faculty/?prof_id=wnewey&type=paper.
>
> Joseph Coveney
>
> --------------------------------------------------------------------------
------
>
> program define simsteele, rclass
> version 8.1
> drop _all
> set obs 66
> generate byte subject = _n
> generate float subject_threshold = invnorm(uniform())
> forvalues stimulus = 1/36 {
> generate float subject_stimulus_threshold`stimulus' = ///
> 0.7 * subject_threshold + sqrt(1 - 0.7^2) * invnorm(uniform())
> generate byte detected`stimulus' = ///
> subject_stimulus_threshold`stimulus' > invnorm(`stimulus' / 37)
> }
> keep subject subject_threshold detected*
> reshape long detected, i(subject) j(stimulus)
> xi: probit detected i.stimulus i.subject
> predict float linear_predictor, xb
> by subject: egen float threshold_hat = mean(linear_predictor)
> regress threshold_hat subject_threshold if _Istimulus_2
> return scalar slope = _b[subject_threshold]
> return scalar intercept = _b[_cons]
> end
> *
> clear
> set more off
> set seed 20030920
> simulate "simsteele" slope = r(slope) intercept = r(intercept), ///
> reps(400)
> summarize slope intercept, detail
> exit
>
> --------------------------------------------------------------------------
------
>
>
>
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