## Very Brief Update

This week I didn’t get any work done on my paper. This coming week I will finish my paper, and turn it in on Friday.

## Presenting

This week I finished my beamer presentation and presented my capstone. I received what seemed like very few questions.

In the coming week I’ll put some more work into my paper. It’s almost done, but has a couple more things that should be added to it.

## Not Much to Report

This past week has been full of midterms. Hence, little progress has been made on my capstone. I did, however, receive some helpful comments on my rough draft from Prof. Edgar.

This next week I want to do what I had hoped to do this week. I want to fully outline my presentation, and edit my paper. Maybe if I’m lucky I’ll even start working on my beamer file.

## Finished Rough Draft

This past week I finished my rough draft and turned it in. It took a long time because the sources I used were inconsistent with each other. I had to interpret things from each book in terms of the other books in order to make it all work well together.

In the coming week, I hope to start outlining my presentation and start editing my paper. Prof. Munson will also be going over the math in my paper to make sure it’s right.

## Capstone Outline

This week I outlined my paper in LaTeX (Burns Capstone Outline). I also began searching for a good proof regarding panel data to include in my paper. What I’ve found so far are rather lengthy and technical papers with titles that sound appealing for my purposes.

Next week I plan on reading through some of the materials I have gathered. This will be a continuation of searching for a good proof, as well as gathering information to include in my paper. I may also begin filling in my outline, if time allows.

## Outlining Capstone

This week I spent about five minutes writing a very broad outline of my paper. I then went to Prof. Munson’s office to go over it with her. She said it looked good.

What I need to do next is type my outline in LaTeX and start filling it in with detailed information. Also, I was told that a proof exists that would be great to include in my paper. Thus, I will also spend some time searching for that proof.

## Capstone Update 2

Last weekend I participated in the Mathematical Competition in Modeling (MCM). This event took place over a 96-hour period starting on Thursday night at 5 Pm and ending Monday night at 5 PM. Having dedicated my entire weekend (and then some) to this endeavor, I was thus forced to spend the rest of the week playing catch up on my homework. Consequently, very little progress was made on my capstone project.

Over the next week I hope to finish constructing the basic forms of the panel data model at their simplest levels. I then will type them using LaTeX so they are easier to read and understand.

## Fixed Effects

In one of my earlier posts, I discussed panel data modeling and my intentions to use it as my capstone. A panel data model is rather general, however, and thus I want to consider specific variations of it. The first variation that I have decided to take a closer look at is the fixed effects model.

The fixed effects model operates under the assumption that unobserved variables are correlated with variables included in the regression. Consequently, studies conducted using this model can only be used to describe the effects of the included independent variables on the dependent variable, and thus cannot extend their results to explain the effects of other variables on the dependent variable.

Recall the general form of a panel data model: $y_{it} = \alpha_i + \beta'x_{it} + \epsilon_{it}$. The fixed effects model assumes that the individual effects coefficients ($\alpha_i$) vary across each cross-sectional unit, while the $\beta'$ coefficient is held constant.  As a result of the variability in the individual effects coefficients, it becomes necessary to use dummy variables representing each cross-sectional unit in order to properly estimate the regression. The resulting equation is $y_{it} = D \alpha_i + \beta'x_{it} + \epsilon_{it}$ where $D$ is the set of dummy variables.

## Searching for Capstone

As everyone (in MATH 499A) knows, last week we were instructed on how to search for articles relating to math, and eventually our specific capstone topic. While helpful, my time in the library proved to be more frustrating than fruitful. That, however, was mostly my fault. Let me try to explain.

I am also an Economics major. The ECON department has a 4-credit Capstone course that takes place in one semester. This makes for a bit of an accelerated pace relative to the MATH Capstone. Therefore, I have already chosen a topic, which is: Efficacy of the influenza vaccination against flu-related death in adults in the United States using time-series data. For the purpose of the MATH Capstone, with guidance from Prof. Munson and the use of some (hopefully advanced) statistics, I will try to determine how effective the flu vaccine is against flu-related death. Already knowing my topic is what caused my frustration in the library.

While in the library, my search terms were far too specific. Already having my topic narrowed down has made searching for articles difficult. While there are copious articles out there similar to what I am trying to do, there is nothing exactly like what I want to do (I suppose this is good, in a way, because it means my work will be somewhat original). Given the specificity of my topic, I had to learn to broaden my search horizons. For instance, instead of searching specifically for the effectiveness of the influenza vaccination, I simply searched for vaccination. From there I added a search term, like efficacy or effectiveness. In doing such, I have been able to find numerous articles that I am interested in. One, for example, is titled Estimation of Vaccine Efficacy and the Vaccination Threshold. This article discusses the how to measure vaccine efficacy, and points out that the number of people who would have to be vaccinated to avoid an epidemic varies with vaccine efficacy and virus reproduction.

Unfortunately, many of the articles I have found, PLU does not have direct access to. Thank goodness for Interlibrary Loan.