* Example with simulated NAEP data.

cap program drop openirt

clear

set mem 50m

* Estimate both item parameters and ability

openirt, id(id) item_prefix(item) save_item_parameters("items.dta") save_trait_parameters("traits.dta")

* Merge in ability estimates

merge id using traits, sort

v 1.0

d openirt. Bayesian and Maximum Likelihood Estimation of Item Response Theory (IRT) models.

d

d OpenIRT estimates 2PL and 3PL Item Response Theory (IRT) models for dichotomous data.

d It includes Bayesian MCMC estimation of item parameters and abilities, and maximum

d and responses to be missing.  For instance, fixed anchor items can be used to place

d children and items on a known scale; missing responses can be used to link multiple

d overlapping test forms; and known abilities can be used to calibrate new items 

f openirt.ado

f openirt.sthlp

{synopthdr}

{synoptline}

{syntab:Required options}

{synopt :{opt save_item_parameters("filename")}}filename to save item parameter estimates{p_end}

{synopt :{opt save_trait_parameters("filename")}}filename to save trait/ability parameter estimates{p_end}

{opt theta(varname)} specifies variable name holding fixed trait or ability parameters.  Any missing entries will be treated as free parameters.

{phang}

{dlgtab:MCMC Options}

{opt samplesize(2000)} specifies the number of post burn in MCMC iterations (default = 2000). Plausible values are drawn at evenly spaced intervals from this sample, and EAP estimates are based on the mean of the entire sample. Larger sample sizes will reduce the monte carlo standard error.  In most applications the standard error of measurement dominates the monte carlo standard error after several thousand iterations.

{phang}

{title:Discussion}

{pstd}OpenIRT estimates 2PL and 3PL Item Response Theory (IRT) models for dichotomous (correct / incorrect) data using both Bayesian and Maximum Likelihood methods.{p_end}

{pstd}Unlike some other IRT software, OpenIRT includes both Bayesian MCMC and Maximum Likelihood estimates.  The software estimates expected posterior (EAP), plausible value (PV), and maximum likelihood (MLE) estimates of the underlying latent trait -- often called theta or ability.{p_end}

{pstd}Plausible values, or multiple imputations, are draws from the posterior of each respondent's ability parameter.  While potentially poor measures of each respondent's ability, plausible values allow accurate estimation of distributional quantities, such as the upper and lower quartiles, or fraction of students passing a particular threshold.  If the number of items is small, EAP and MLE estimates will generally yield very poor estimates of such quantities, with EAP understanding the standard deviation and MLE estimates overestimating the standard deviation.  See Das and Zajonc (2009) and Mislevy et al (1992).{p_end}

{title:Examples:  Scoring single form.}

{phang2}{cmd:. sysuse naep_children, clear}{p_end}

{title:Examples:  Scoring multiple overlapping forms.}

{phang2}{cmd:. recode item3 item4 (0/1 = .) if _n > 250}{p_end}

{phang}Score overlapping exams:{p_end}

{phang}Create 10 fixed items:{p_end}

{phang2}{cmd:. sysuse naep_items, clear}{p_end}

{phang}Score exam using mixed fixed and free items:{p_end}

{phang2}{cmd:. sysuse naep_children, clear}{p_end}

{title:References}

{pstd}Tristan Zajonc{p_end}

{pstd}John F. Kennedy School of Government{p_end}

{pstd}Harvard University, Cambridge, MA 02138.{p_end}