# Analytical Model

Read and analyze an article that uses an **analytic model**, and present it to your classmates. Select an article from the list on this page (link). You are also welcome to use an article you find on your own, as long as it meets the criteria for a scientific model.

**Article critiques:** Create a new thread and post a critique of an article. Your critique should be at least 300 words and should address the following questions:

- How would you describe the model? What are the terms in the equation, and what system does the model represent?
- What kind of mathematical structures were used? (Probability? Linear Algebra? Another type?)
- What research question(s) did the authors investigate?
- What did the researchers learn by using this model? What were their results?
- How did the researchers make sure their model is credible? Do you think it is trustworthy enough to investigate their research question(s)?
- Was analytic a good choice for this study, in your opinion?
- Include a link or full citation for your source material.

**Reply posts: **Next, write substantive, thoughtful replies to at least two of your peers' posts. Reply posts should address the following prompts:

- Do you agree with the assessment in the original post? If you do agree, indicate what convinced you. If you don't agree, explain why.
- What other research questions might be addressed by the model?
- What other types of models might address the research aims?
- You may also share any prior knowledge or personal experience you have with the topic to enrich the discussion.
- Reply Post 1:

https://www-sciencedirect-com.proxy.lib.pdx.edu/science/article/pii/S0032063315300696#s0015

Cameron Marical

Week nine discussion

This analytic model used four seismic recording devices placed on the moon in 1969 by the Apollo mission in order to synthesize a model for the seismic effects of the moon in a mathematical equation. The moon affects the tides, and this is the model which mathematically predicts the equation that derives how much. I would list the math if I was anywhere near capable! I find it validated and verified from everything that I researched, however the math for me is a vulnerability so I am unaware of the extent that it is correct, however I assume so with everything else it contains. The model may have been improved by increased technological specs around data, especially when it came to the minute frequencies, however it seemed like a largely complete model to me. Math models are interesting to me.

Reply Post 2:

**How would you describe the model? What are the terms in the equation, and what system does the model represent?**This model is principal-agent based and looks at the process of learning by doing compared to learning by others. They use a social evolutionary learning algorithm (SEL) to represent social learning. They also looked at three different models of learning “reinforcement learning (RL), experience weighted attraction learning (EWA), and individual evolutionary learning (IEL)”.**What kind of mathematical structures were used? (Probability? Linear Algebra? Another type?)**

They used a learning algorithm “A strategy15, mt, belonging to the strategy set, Mt at time t ∈ {1, T0} consists of a share/fee pair, i.e., mt = {st, ft}”. Which was similar to a computable example. They also used a variety of algorithms for each learning model RL, EWA and IEL.

**What research question(s) did the authors investigate?**

Their primary objective is “to investigate whether this learning process leads to knowledge acquisition sufficient for convergence to the theoretically optimal principal-agent contract”.

**What did the researchers learn by using this model? What were their results?**

They realized it was difficult to show learning in a principal-agent model due to “(1) the stochastic environment, (2) the discontinuity in payoffs in a neighborhood of the optimal contract due to the participation constraint and (3) incorrect evaluation of foregone payoffs in the sequential game principal-agent setting”.

**How did the researchers make sure their model is credible? Do you think it is trustworthy enough to investigate their research question(s)?**

They used documentation and research from multiple studies on learning behaviors and it was also peer reviewed. They ran multiple studies per each learning model and chose a one-sided learning framework for trace tractability.

**Was analytic a good choice for this study, in your opinion?**

They realized it was difficult to show learning in a principal-agent model and I agree. Mainly due to the environment. This is something that would be more beneficial with actual human interaction.

**Include a link or full citation for your source material.**

Arifovic, Jasmina, and Alexander Karaivanov. 2010. “Learning by Doing vs. Learning from Others in a Principal-Agent Model.” *Journal of Economic Dynamics and Control* 34 (10): 1967 92. __https://doi.org/10.1016/j.jedc.2010.04.007__.

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