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Re: st: Clustered dataset question - Estimating Individual threshold

From   "Dale Steele" <[email protected]>
To   <[email protected]>
Subject   Re: st: Clustered dataset question - Estimating Individual threshold
Date   Mon, 13 Oct 2003 12:57:19 -0400

Thanks very much to Joseph Coveney for the original response below.  My
question relates to a dataset from an experimental protocol completed by 66
<>.  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".
statsby "logit response per_intr" _b, by(idnum)
generate threshold = -b_cons/b_per_intr
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
> kind of problem.  -findit- or google for item response theory (IRT) or
> model might provide an entrypoint.
> Of interest is the FAQ written by Jeroen Weesie on Stata Corp's website,
> .  Quoting from that, "Another
> purpose of a Rasch analysis is to estimate the subject parameter eta. In
> fixed-effects approach, the etas are commonly estimated by maximum
> conditional on the CLM theta-estimates. For the random-effects case, the
> 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
> operating characteristic (ROC) functions might also be of interest.
> The impetus to perform individual logistic regressions for each subject is
> the same spirit that was expressed in Stata Corp's admonishment against
> unconditional fixed-effects ordered probit a couple of weeks ago on the
> 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
> in Dale's case.  In general, unconditional maximum likelihood estimators
> 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
> 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
> 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
> for the threshold latent variable.  If I've got things correctly specified
> big if), then the bias in individual-subject estimates of threshold is in
> neighborhood of 5% with an unconditional fixed-effects probit model.  If
> magnitude of bias is acceptible in practice for Dale's purposes, then
> unconditional nonlinear regression represents a viable alternative with
> sample size.
> In addition, there are approaches to ameliorate such bias, such as the
> jackknife (Hahn and Whitney, 2003), which in my simulations with
> ordered probit works quite well when panel depths are at least five or
> even using Professor Greene's challenging specification for the
> ordered probit model in his numerical study (Greene, 2002).  Note that
> 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
> dummy variables for individual subjects that is described in documents on
> Professor Greene's website, but I cannot find where Stata has implemented
> Greene, William (2002 February), The behavior of the fixed effects
estimator in
> nonlinear models. Unpublished; available on his website,
>, as document EC-02-05Greene.pdf.
> Hahn, Jinyong, and Newey, Whitney (2003 July), Jackknife and analytical
> reduction for nonlinear panel models.  Available at
> 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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