University:
California State University, Northridge
Course:
PSY 427 | Introduction to Psychological Testing
Academic year:

2024
Views:

52

Pages:

20
Author:

Nadia Crane

IRT – Item Information Function  Item Information Function (IIF) – Item reliability is replaced by item information in IRT.  Each IRF can be transformed into an item information function (IIF); the precision an item provides at all levels of the latent trait.  The information is an index representing the item’s ability to differentiate among individuals. IRT – Item Information Function  The standard error of measurement (which is the variance of the latent trait level) is the reciprocal of information, and thus, more information means less error.  Measurement error is expressed on the same metric as the latent trait level, so it can be used to build confidence intervals. IRT – Item Information Function  Difficulty parameter - the location of the highest information point  Discrimination - height of the information.  Large discriminations - tall and narrow IIFs; high precision/narrow range  Low discrimination - short and wide IIFs; low precision/broad range. 1 0.9 0.8 Probability 0.7 0.6 0.5 0.4 0.3 0.2 2plm 3plm 4plm 0.1 0 -3 -2 -1 0 Trait Level 1 2 3 1 2plm 3plm 4plm 0.9 0.8 Information 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -3 -2 -1 0 Trait Level 1 2 3 IRT – Test Information Function  Test Information Function (TIF) – The IIFs are also additive so that we can judge the test as a whole and see at which part of the trait range it is working the best. 1.4 1.2 Information 1 0.8 0.6 0.4 0.2 0 -3 -2 -1 0 Trait Level 1 2 3 2.4 30 25 Information 1.2 15 10 5 0 0 -3 -2 -1 0 Latent Trait 1 2 3 Standard Error 20 Item Response Theory Example The same 24 items from the MMPI-2 that assess Social Discomfort  Dichotomous Items; 1 represents an endorsement of the item in the direction of discomfort  Assess a 2pl IRT model of the data to look at the difficulty, discrimination and information for each item  IRT - Invariance  Invariance - IRT model parameters have an invariance property  Examinee trait level estimates do not depend on which items are administered, and in turn, item parameters do not depend on a particular sample of examinees (within a linear transformation).  Invariance allows researchers to: 1) efficiently “link” different scales that measure the same construct, 2) compare examinees even if they responded to different items, and 3) implement computerized adaptive testing. IRT - Assumptions  Monotonicity - logistic IRT models assume a monotonically increasing functions (as trait level increases, so does the probability of endorsing an item).  If this is violated, then it makes no sense to apply logistic models to characterize item response data. IRT - Assumptions  Unidimensionality – In the IRT models described above, individual differences are characterized by a single parameter, theta.  Multidimensional IRT models exist but are not as commonly applied  Commonly applied IRT models assume that a single common factor (i.e., the latent trait) accounts for the item covariance.  Often assessed using specialized Factor Analytic models for dichotomous items IRT - Assumptions  Local independence - The Local independence (LI) assumption requires that item responses are uncorrelated after controlling for the latent trait.  When LI is violated, this is called local dependence (LD).  LI and unidimensionality are related  Highly univocal scales can still have violations of local independence (e.g. item content, etc.). IRT - Assumptions  Local dependence: distorts item parameter estimates (i.e., can cause item slopes to be larger than they should be), 2. causes scales to look more precise than they really are, and 3. when LD exists, a large correlation between two or more items can essentially define or dominate the latent trait, thus causing the scale to lack construct validity. 1. IRT - Assumptions  Once LD is identified, the next step is to address it:  Form testlets (Wainer & Kiely, 1987) by combining locally dependent items  Delete one or more of the LD items from the scale so local independence is achieved. IRT - Assumptions  Qualitatively homogeneous population - IRT models assume that the same IRF applies to all members of the population  Differential item functioning (DIF) is a violation of this and means that there is a violation of the invariance property  DIF occurs when an item has a different IRF for two or more groups; therefore examinees that are equal on the latent trait have different probabilities (expected scores) of endorsing the item.  No single IRF can be applied to the population