Dear colleagues!
As a postdoctoral fellow I’m learning IRT and would like to use gllamm, since I am familiar with STATA.
I searched the literature and the web, but I am still confused and would appreciate your help in clarifying the following:
1) Is the code bellow the right specification of 2-parameter-logistic model in gllamm?
2) And is the reparametrisation from ‘factor analysis’ into item difficulty and discrimination (according to classical IRT) correctly specified in ‘nlcom’ command?
Thank you in advance,
Mirjana
***The model of my interest has 4 items with responses stacked in variable y:
**variables in long dataset: y==response; d1-d4==indicators of y; psunew==cluster id (product term of strata&cluster → two levels of clustering in sampling design (levels3 and 2, individuals are level1), pwt1=probability weight at individual level,
**items to be discriminated
eq discrima: d1-d4
**variance of latent variable fixed to 1
constraint def 1 [id1_1]d1=1
*2PL IRT for criteria
gllamm y d1-d4, nocons link(logit) fam(bin) i(id) pweight( pwt) w(wt) eqs(discrima) cluster( psunew) constr(1) frload(1) adapt dot allc
matrix list e(b)
e(b)[1,9]
y: y: y: y: id1_1l: id1_1l: id1_1l:
d1 d2 d3 d4 d1 d2 d3
y1 -.95823763 -.23533402 -1.8652342 -2.4782268 1.1974265 .25759158 .13494323
id1_1l: id1_1:
d4 d1
y1 2.7355371 1
***Difficulty: b=thau/a=-beta/loading
**dificulty of 1st criterion
. nlcom difabcr1: -[y]d1/[id1_1l]d1
difabcr1: -[y]d1/[id1_1l]d1
------------------------------------------------------------------------------
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
difabcr1 | .8002475 .1529222 5.23 0.000 .5005256 1.099969
------------------------------------------------------------------------------
***!!!Discrimination: a=loading/sqrt(1-loading^2)
** discrimination of 1st criterion
. nlcom disabcr1: [id1_1l]d1/sqrt(1-[id1_1l]d1^2)
disabcr1: [id1_1l]d1/sqrt(1-[id1_1l]d1^2)
------------------------------------------------------------------------------
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
disabcr1 | .7675448 .0701129 10.95 0.000 .630126 .9049636
------------------------------------------------------------------------------
***************************************
Mirjana Radovanovic, M.D., M.Sc.
Postdoctoral Fellow
Michigan State University
College of Human Medicine
Department of Epidemiology
B601 West Fee Hall
East Lansing, MI 48824
Tel. 517-353-8623
Fax: 517-432-1130
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