We extend a recent didactic by Magis, Raîche, and Béland on the use of the lz and lz* person-fit statistics. We discuss a number of possibly confusing details and show that it is important to first investigate item response theory model fit before assessing person fit. Furthermore, it is argued that appropriate distributions are only a first step for practical use of person-fit statistics.
ChenW. H.ThissenD. (1997). Local dependence indexes for item pairs: Using item response theory. Journal of Educational and Behavioral Statistics, 22, 265–289.
3.
ConradK. J.BezruczkoN.ChanY.-F.RileyB.DiamondGDennisM. L. (2010). Screening for atypical suicide risk with person fit statistics among people presenting to alcohol and other drug treatment. Drug and Alcohol Dependence, 106, 92–100.
4.
DrasgowF.LevineM. V.WilliamsE. A. (1985). Appropriateness measurement with polychotomous item response models and standardized indices. British Journal of Mathematical and Statistical Psychology, 38, 67–86.
5.
EmbretsonS. E.ReiseS. P. (2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum.
6.
FerrandoP. J. (2011). Assessing inconsistent responding in E and N measures: An application of person-fit analysis in personality. Personality and Individual Differences, 52, 718–722.
7.
KlauerK. C. (1995). The assessment of person fit. In FischerG. H.MolenaarI. W. (Eds.), Rasch models: Foundations, recent developments, and applications (pp. 97–110). New York, NY: Springer Verlag.
8.
LuteijnF.van DijkH.BareldsD.P.H. (2005). NPV-J: Junior Nederlandse Persoonlijkheidsvragenlijst. Herziene handleiding 2005[NPV-J: Dutch Personality Questionnaire–Junior: Professional manual (revised)]. Amsterdam, The Netherlands: Harcourt Assessments.
9.
MagisD.RaîcheG.BélandS. (2012). A didactic presentation of Snijders’s l(z)* index of person fit with emphasis on response model selection and ability estimation. Journal of Educational and Behavioral Statistics, 37, 57–81.
10.
MeijerR. R.EgberinkI. J. L.EmonsW. H. M.SijtsmaK. (2008). Detection and validation of unscalable item score patterns using item response theory: An illustration with Harter’s self-perception profile for children. Journal of Personality Assessment, 90, 227–238.
11.
MeijerR. R.MolenaarI. W.SijtsmaK. (1994). Influence of test and person characteristics on nonparametric appropriateness measurement. Applied Psychological Measurement, 18, 111–120.
12.
MeijerR. R.SijtsmaK. (2001). Methodology review: Evaluating person fit. Applied Psychological Measurement, 25, 107–135.
13.
MolenaarI. W.HoijtinkH. (1990). The many null distributions of person fit indexes. Psychometrika, 55, 75–106.
14.
OrlandoM.ThissenD. (2003). Further investigation of the performance of S-X2: An item fit index for use with dichotomous item response theory models. Applied Psychological Measurement, 27, 289–298.
15.
SnijdersT. A. B. (2001). Asymptotic null distribution of person-fit statistics with estimated person parameter. Psychometrika, 66, 331–334.
16.
TendeiroJ. N.MeijerR. R. (2012a). A CUSUM to detect person misfit: A discussion and some alternatives for existing procedures. Applied Psychological Measurement, 36, 420–442.
17.
TendeiroJ. N.MeijerR. R. (2012b). The probability of exceedance as a nonparametric person-fit statistic for tests of moderate length. Manuscript submitted for publication.
18.
TukeyJ. W. (1977). Exploratory data analysis. Reading, MA: Addison-Wesley.
19.
van Krimpen-StoopE. M. L. A.MeijerR. R. (1999). The null distribution of a person-fit statistic in fixed- and computerized adaptive testing. Applied Psychological Measurement, 23, 327–345.
20.
WeekersA. M.MeijerR. R. (2008). Scaling response processes on personality items using unfolding and dominance models: An illustration with a Dutch dominance and unfolding personality inventory. European Journal of Psychological Assessment, 24, 65–77.
