Why is maximum likelihood estimation the main way to calculate parameters for the IRT (Item Response Theory)?

Maximum Likelihood Estimation (MLE) is the main method for estimating parameters in Item Response Theory (IRT) for several compelling reasons:

1. Statistical Justification: MLE is a statistically rigorous method that provides parameter estimates that are consistent, asymptotically efficient, and asymptotically normally distributed when sample sizes are sufficiently large. This makes it a robust and reliable approach for estimating IRT model parameters.

2. Model Flexibility: IRT encompasses various models, such as the Rasch model, two-parameter logistic model (2PL), and three-parameter logistic model (3PL), each with different assumptions about the relationships between item responses and latent traits. MLE can be applied to estimate parameters for all these models, making it versatile and adaptable to different test situations.

3. Likelihood Function: IRT models are based on the concept of a likelihood function, which represents the probability of observing a particular response pattern given the model parameters and latent traits. MLE aims to maximize this likelihood function, which essentially means finding parameter values that make the observed data most probable under the model. This aligns well with the core principles of IRT.

4. Handling Missing Data: MLE can handle missing data effectively. In practice, not all examinees may respond to all items, and MLE can still provide parameter estimates even when data are missing, as long as the missing data mechanism is ignorable (i.e., missingness does not depend on the unobserved trait).

5. Asymptotic Properties: MLE estimates are asymptotically unbiased, which means that as the sample size increases, the parameter estimates converge to the true population values. This is particularly advantageous when dealing with large-scale testing situations.

6. Comparison and Model Fit: MLE allows for meaningful comparisons of item difficulty and discrimination parameters across different items. It also enables assessing model fit to the data, which is crucial for evaluating the appropriateness of the chosen IRT model.

7. Software Availability: There are various software packages available for IRT analysis that implement MLE estimation methods, making it accessible to researchers and practitioners.

Despite its advantages, it’s essential to note that MLE has certain assumptions, such as unidimensionality and local independence, that should be carefully considered when applying IRT models. Researchers should also be mindful of the potential for model misspecification and the need for appropriate model selection and assessment techniques. Nonetheless, MLE remains a widely used and robust method for estimating parameters in Item Response Theory.