Introductory Description of IRT
- What is IRT
o Psychologically based theory of mental measurement that specifies information about latent traits and the characteristics of stimuli used to represent them.
o IRT statistics are not non-parametric
- Relation of IRT to CTT
- Cautionary note on studying IRT
o IRT : theory about latencies and the way they can be estimated
IRT and Invariant Measurement for Items and Persons
- Problem of lack of an independent scale in CTT
o Difficulty in comparing "low esteem" in one test vs another test.
o No common zero point
o Converting scores to z scores does not solve problem – then you only have scores expressed in same metric
- Group Dependent Items and Item Dependent Groups
o Left with relative comparisons
o Eg, test on history – what measurement best represents difficulty of test à depends on group who takes test à eg, primary school vs college
o Difficulty value is group dependent
o Reference group
o Measuring examinee ability is item dependent
- IRT as item and person invariant measurement
- Notion of invariant measurement
o Invariance is an estimable concept [GW – not sure I understood or agreed with this section]
Introduction to IRT Models
- Some commonly used IRT Models
- Models are usually identified by number of characteristics they estimate about a test's stimuli
o One – parameter
o Two / more
- Most popular models
o One-parameter
§ Only item difficulty is estimated
o Two parameter
§ Estimates separate difficulty and discrimination parameters for each item
o Three parameter
§ Includes examinee's probability of guessing or pseudochance
Assumptions
- Centrality of assumptions to IRT
- Unidimensionalty of items and tests
o Given test item or exercise is directly targeted at single cognitive process, and in theory it fills that latent space completely
- Local independence
o Examinees response to a given specific measure reflects an independent and autonomous reference to a latent trait in cognition.
o Examinee responds to stimulus of test item or stimulus, also approaches the stimulus without also thinking about other items or exercises.
o Degree of learning as more items are encountered
- Item characteristic curve
o Defined characteristics of test stimuli are reliably estimable functions
- Certainty of response
o Optimal performance
ICC and IRC
- Specifying ICCs generally
- Inflection point
- Scales allow a trace line to describe functional relationship between characteristics of an item and the trait level of examinee
IRT Models
- Likelihood function
o Examinee of particular ability level has certain probability of getting an item correct
o .likelihood function is joint probability of getting several items correct or incorrect
o More on working with the log scale
o The two parameter model
The one-parameter IRT model and Rasch
- The Rasch Model
Other IRT Models
- Nominal and graded response models for polytomous items
- Richly cognitive models
Estimating Item and Ability Parameters
- Iterative estimation procedures
- Developing priors
- Test information function
- Some estimation procedures
Computer Programs Available for parameter estimation
Brief History and major Contributors to IRT
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