1 Detection of Item Degradation Yongwei Yang Abdullah Ferdous Tzu-Yun Chin University of Nebraska-Lincoln In T. L. Hayes (chair), Item degradation: impact, detection, and mitigation, an academic-practitioner collaborative forum conducted at the 22 nd annual conference of the Society of Industrial and Organizational Psychology in New York City, NY, April 2007.

2 Item Degradation  Item’s favorable psychometric characteristics deteriorate over time Psychometric characteristics  Content relevance and representativeness  Technical characteristics (e.g., “difficulty”/“location”, lack of bias)  Utility (e.g., item-criterion relationship) Item Degradation vs. Exposure/Compromise  Item degradation: observed phenomenon  Item exposure/compromise: Items have become known to test takers prior to administration Possible reasons for degradation

3 Detection of Item Degradation Essentially it is about investigating the comparability of item’s psychometric properties over time  “temporal stability of the psychometric characteristics” (Chan, Drasgow, & Sawin, 1999) Can be evaluated under the framework of:  Measurement invariance (MI; Meredith, 1993)  Predictive invariance (PI; Millsap, 1995)

Item Degradation as MI or PI Measurement Invariance (MI) Same relationship across populations between observed indicators and the latent variables Degradation  noninvariance in such relationships over time  Loading, location 4 Predictive Invariance (PI) Same relationship across populations between predictors and criterion Degradation  noninvariance in such relationships over time  Indicator-criterion relationship Let x be observed indicator that measures latent w and predicts y, and v be some population indicator

5 Item Degradation Detection Methods Differential item functioning, item parameter drift Mean & covariance modeling  Assessing invariance in various aspects pertain to measurement or predictive properties Statistical process control Models of change

6 Item Degradation Detection Differential item functioning, item parameter drift Mean & covariance modeling  Assessing invariance in various aspects pertain measurement or predictive properties Statistical process control  Cumulative sum (CUSUM) procedure Models of change

7 CUSUM for Item Degradation Detection Our approach—Conditional CUSUM  Whether item parameters have deviated from target  Make use of observed scores  The importance of controlling for shifts in traits level over time “Conditional”—test takers at different time points were matched based on their total test score Procedures  Initial Item Calibration Compute target item parameter (e.g., difficulty) using the first n job applicants from the operation sample  Define “time group” Every m applicants from the n+1 applicant to the last person under investigation  Define “trait group” (conditioning variable) Divide job applicants into groups of reasonable size based on total test scores  Compute and plot CUSUM statistics for each trait group separately

8 Conditional CUSUM—Calculation Two-sided Standardized CUSUM Initial Status Item VarianceTime Group i Item Variance Time Group i Item MeanTarget Item Mean Reference value (k) and Control limit ( h )

9 Conditional CUSUM—Data Source A web-based personnel selection assessment for selecting managers  103 items measuring job-related non-cognitive attributes  CTT-based test construction and scoring  Fixed-length, linear test  Unproctored Sample:  Job applicants from Oct to Sept  Re-taker excluded  Total N = 7,000

10 Conditional CUSUM—Results Among the 103 items  36 flagged for upward shift in item means for at least one trait group  20 flagged for downward shift in item means for at least one trait group  9 flagged for having both upward and downward shifts for different trait groups  38 not flagged for any trait group A couple examples: it035, it174it035it174 Follow-up analysis:  Were there differences across item types with respect to the likelihood of being flagged by conditional CUSUM?

Conditional CUSUM—Follow-up Multinomial logistic regression  DV: condition CUSUM flag; 3 categories; “Not Flagged” as the reference category  IV: ability (6 levels), item type (3 levels, multiple choice (MC) as the reference group 11 Results  GOF statistic indicates appropriate fit of the main effect model (X 2 =16.83, df=20, p=.664)  The impact of ability levels on the CUSUM flags was not statistically significant (X 2 =13.48, df=10, p=.198)  The impact of item type on the CUSUM flags was statistically significant (X 2 =17.83, df=4, p=.001).  MC items were more likely to be flagged by conditional CUSUM for negative shifts  Forward items were more likely to be flagged by conditional CUSUM for positive shifts

Model of Change Perspective 1:  Understanding patterns of change using examinee characteristics  Do the trajectories of item parameter change vary across different types of examinees? Applicant location, SES, demographics, etc. Perspective 2:  Understanding patterns of change using item characteristics  Do the trajectories of item parameter change vary across different types of items? Item format, complexity, content area, etc. Formulating these questions in a longitudinal analysis framework 12

Perspective 1 Example 13 Using a 2-level longitudinal model to explore:  RQ1: On average, was there a shift in item difficulty?  RQ2: Were there variations in the slope of the shift?  (If Yes to RQ2) RQ3: Could the variations be explained by job applicants characteristics (e.g., trait level, region, etc.)? The model: Analysis with item 174:  RQ1: significant positive slope  RQ2: non-significant variations  RQ3: not pursued Level I: Level II:

Perspective 2 Example 14 Using a 2-level longitudinal model to explore:  RQ1: Across items, on average was there a change in item difficulty over time?  RQ2: Were there variations in the slope of the change across items?  (If Yes to RQ2) RQ3: Could the variations be explained by item characteristics?

Model B: Analysis with this data set:  RQ3: item type did not explain a significant portion of the variations in slopes Perspective 2 Example Model A: Analysis with this data set:  RQ1: average slope across items was not different from zero  RQ2: significant variations in slopes across items 15 Level I Level II

Summary and Discussions Two types of methods that serve different purposes:  Statistical process control (e.g., CUSUM):  Real-time monitoring of degradation  We illustrated conditional CUSUM procedure, but other methods exist (e.g., an IRT- based moving residual approach by Han & Hambleton [2004])  Explicit modeling of patterns of degradation:  Understanding the nature of degradation, exploring potential factors that impact degradation, assisting the development of prevention and mitigation procedures  We illustrated longitudinal modeling methods, but various methods for studying MI/PI may be applied These methods can also be used in monitoring and understanding degradation in other parameters (e.g., item variance, discrimination, response time)  It might be helpful to monitor/model multiple parameters simultaneously to (1) “flag” items more accurately and, (2) understand factors behind degradation 16

Summary and Discussions Understanding temporal stability of measurement properties is essential to:  Valid decisions based on test scores  Valid inferences in substantive research based on assessment outcomes Research on Flynn effect (e.g., Wicherts et al., 2004) Further research is needed, such as  What monitoring approaches would better fit personnel selection assessment programs?  What would lead to or impact degradation?  How would item-level degradation impact test-level decisions and inferences?  Etc. 17

18 Some Useful References MI & PI Concepts  Mellenbergh (1989)  Meredith (1993)  Millsap (1995) Various IPD and Item Exposure Detection Methods  Bock, Muraki, & Pfeiffenberger (1988)  Chan, Drasgow, & Sawin (1999)  DeMars (2004)  Donahue & Isham (1998)  Han & Hambleton (2004)  Kim, Cohen, & Park (1995) CUSUM and Psychometric Applications:  Hawkins & Olwell (1998)  Meijer & van Krimpen-Stoop (2003)  Montgomery (2005)  van Krimpen-Stoop & Meijer (2002)  Veerkamp & Glas (2000)

19 Contacts Yongwei Yang: Abdullah Ferdous: Tzu-Yun Chin: THANK YOU

Item 35 Conditional CUSUM Charts 20 back

Item 174 Conditional CUSUM Charts 21 back