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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 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 > > -------------------------------------------------------------------------- ------ > > > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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