Question

Suppose you have a dataset with a variable, Y_i, which represents the number of years which a student spent in primary and secondary school. You decide to model this variable using a distribution, with parameters β=(μ,σ) where μ is the mean of Y_i and σ is the standard deviation. In other words, your model assumes that: P(Y_i=y)=f(y∣β)=f(y∣μ,σ) Where f is a PDF. Which of the following would be an important drawback of this model? This means a drawback which is both a serious limitation of the model and which cannot be handled easily by a researcher using this data. A. The model is primarily structural in nature, which means it will require a lot of data about Y_i to evaluate accurately.

Answer 1

The primary drawback of the model you've described is not related to its structural nature but rather to its assumption about the distribution of the data. The assumption that the variable Y_i follows a specific distribution (e.g., normal distribution) with fixed parameters μ and σ can be a serious limitation for modeling real-world data for several reasons:

B. The model assumes a specific distribution form (e.g., normal distribution) for Y_i, which may not accurately capture the true underlying distribution of the data. In many cases, real-world data may not follow a simple parametric distribution, and forcing it into such a distribution can lead to model inaccuracies.

This limitation is significant because if the data does not conform to the assumed distribution, it can result in biased parameter estimates and poor model performance. Researchers may need to consider more flexible distributional assumptions or non-parametric methods to model the data accurately.

Additionally, even if the distributional assumption is reasonable, estimating the parameters μ and σ accurately from limited data can be challenging. The model's performance heavily depends on having a sufficient amount of data to estimate these parameters reliably.

So, option B is an important drawback of the model because it highlights the potential limitations of assuming a specific distribution for the data, which may not reflect the true data-generating process accurately.

Explanation: