Ron D. Hays, PhD

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Item Response Theory and Other Psychometric Issues



Hays, Ron D.  Spritzer, Karen L. (September 18, 2017 - updated).  Estimating theta using existing item parameters with flexMIRT® software.


Estimating reliability from CAT



(promisgph.pdf results)

Item Response Theory: What It Is and How You Can Use the IRT Procedure to Apply It - Xinming An and Yiu-Fai Yung, SAS Institute, Paper SAS364-2014

Hochberg, Y.  (1988).  A sharper Bonferroni procedure for multiple tests of significance.  Biometrika, 75, 800-802.
Background on computations: hochberg.doc

SAS code to compute hochberg adjustment:
example 1:, hochberg.lst
example 2:, hochberg.lst

STATA has a module that can implement hochberg adjustment (install multproc):
example 1: hochberg.log
example 2: hochberg2.log

Cohen's rule of thumb for correlations that correspond to effect size rules of 0.20 SD, 0.50 SD and 0.80 SD are as follows:

0.100 is small correlation
0.243 is medium correlation
0.371 is large correlation
Note, however, that r's of 0.10, 0.30 and 0.50 are often cited as small, medium and large, respectively.

Effect size calculators:

More about effect sizes:


Linear transformation of item parameters (using, e.g., Stocking-Lord transformation constants):

Transformed slope = Slope/Slope transformation constant

Transformed thresholds are: (Threshold * Slope transformation constant) + Intercept


Information      Reliability   SE
    10           0.90        0.32
    6.7          0.85        0.39
    5            0.80        0.45

Note: SE = standard error. Calculations are for z-scores metric and ML estimation.


Information = 1/(1-reliability) = 1/SE**2

Reliability = (INF-1)/INF = 1 - SE**2

SE = 1/SQRT(INF) = SQRT(1-Reliability)

Reeve et al. (2007) in Medical Care provided the following guidelines for good fit to
a one-factor model (for evaluation of unidimensionality assumption):

RMSEA < 0.06
SRMR < 0.08
Average absolute residual correlation < 0.10

Summary of steps to produce raw score conversion to theta estimates for PROMIS global mental health items   (6/22/2009)

Karen Spritzer with assistance from Ron D. Hays
Summary of steps to produce raw score conversion to theta estimates for PROMIS global physical health items (6/19/2009)
Karen Spritzer with assistance from Ron D. Hays
The authors are eternally grateful to Seung Choi for his expertise and guidance.

PPV = (sensitivity)(prevalence)/(sensitivity)(prevalence)+(1-specificity)(1-prevalence))
PPV=postive predictive value

NPV=negative predictive value

Rasch Model infit and outfit mean square statistics (4/6/2009)
The infit statistic provides information about responses within a patient’s ability level.  The outfit statistic assesses items that are far beyond a person’s ability level. Poor item fit has been defined as infit or outfit < 0.6 or > 1.4