Model Answer
0 min readIntroduction
Psychometrics, the science of psychological measurement, relies heavily on robust statistical models to ensure the validity and reliability of tests. Classical Test Theory (CTT) has historically been the dominant paradigm, but in recent decades, Item Response Theory (IRT) has emerged as a powerful alternative. CTT focuses on the overall test score, while IRT focuses on the relationship between an individual's latent trait and their performance on each item. This shift represents a move from a test-centric to an item-centric approach, offering more nuanced and informative insights into test-taker abilities. This answer will compare and contrast these two approaches, with a specific focus on evaluating Rasch's model, a prominent example of IRT.
Classical Test Theory (CTT): A Test-Centric Approach
CTT assumes that an observed score on a test is composed of two components: the true score (representing the individual's actual ability) and error. Key parameters in CTT include test reliability (Cronbach's alpha, test-retest reliability) and item difficulty. CTT relies heavily on sample-dependent statistics, meaning that estimates of reliability and item difficulty are specific to the particular sample tested.
Item Response Theory (IRT): An Item-Centric Approach
IRT, in contrast, views test performance as a function of both the individual's latent trait (e.g., intelligence, anxiety) and the characteristics of the test item. IRT models estimate item parameters (difficulty, discrimination, guessing) that are assumed to be sample-independent. This means these parameters are believed to be consistent across different populations. IRT allows for the creation of adaptive tests, where items are selected based on the test-taker's performance, leading to more efficient and precise measurement.
Comparing CTT and IRT
The following table summarizes the key differences between CTT and IRT:
| Feature | Classical Test Theory (CTT) | Item Response Theory (IRT) |
|---|---|---|
| Focus | Test score | Individual item and latent trait |
| Error | Random error affecting the total score | Item-specific error |
| Item Parameters | Item difficulty (sample-dependent) | Item difficulty, discrimination, guessing (sample-independent) |
| Sample Dependence | High | Low |
| Adaptive Testing | Not possible | Possible |
Rasch Model: A Core IRT Model
The Rasch model, developed by Georg Rasch, is a one-parameter IRT model focusing solely on item difficulty. It posits that the probability of a correct response is solely determined by the difference between the test-taker's ability and the item difficulty. A key principle of the Rasch model is "separation," meaning that items should clearly differentiate between individuals with different ability levels. The model produces interval-level measurements, allowing for meaningful comparisons of ability across individuals and items.
Strengths of the Rasch Model
- Simplicity: Its single parameter makes it relatively easy to understand and implement.
- Fundamental Measurement: It aims to provide a true interval scale of measurement, unlike CTT which provides ordinal scales.
- Sample Independence: Item difficulty estimates are less affected by the specific sample tested.
Limitations of the Rasch Model
- Unidimensionality: The Rasch model assumes that the test measures a single underlying trait. Violations of this assumption can lead to inaccurate results.
- Local Independence: Responses to items should be independent of each other, given the test-taker's ability. Item clustering or content overlap can violate this assumption.
- Limited Information: The single-parameter nature of the model provides less information than more complex IRT models (e.g., 2PL, 3PL).
Conclusion
In conclusion, IRT represents a significant advancement over CTT by shifting the focus from the test to the individual item and latent trait. Rasch's model, as a foundational IRT model, offers simplicity and the potential for fundamental measurement, but its limitations regarding unidimensionality and limited information necessitate careful consideration. While more complex IRT models address some of these limitations, the Rasch model remains a valuable tool for test development and analysis, particularly when the assumption of unidimensionality is reasonably met. The choice between CTT and IRT, and among different IRT models, depends on the specific research question and the characteristics of the test being used.
Answer Length
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