How to create a variable measuring terrorism? I am currently undertaking a project where I will be analyzing the impact that terrorism has on tourism. After doing some research, previous papers have taken to measuring terrorism by simply the number of attacks that take place. I want to take this a step further. I want to create my own variable from four other variables that I have access to. The variables I have access to are, number of people killed, number of attacks, amount of property damage, and attack type(bomb, knife, gun, etc..).
The simplest way to do this would be to assign an arbitrary weight to each of these to create the new variable however that seems to simple. Finding relevant literature has proven unsuccessful thus far. Can someone who encountered a similar situation offer advice or literature on the subject? Thanks.
 A: A common approach to dimensionality reduction is to perform Principal Components Analysis (PCA).
Let's say you have some vector $\mathbf{x}$. Instead of a basis $\mathbf{u}_1 = \begin{bmatrix} 1 \\ 0 \\ 0 \\ \cdots \end{bmatrix}$, $\mathbf{u}_2 = \begin{bmatrix} 0 \\ 1 \\ 0 \\ \cdots \end{bmatrix}$, etc..., the idea is to find a new basis: $\hat{\mathbf{u}}_1, \hat{\mathbf{u}}_2, \ldots$ such that the first dimension captures the most variation, the second dimension captures the second most etc...
For example, I've seen this done with liquidity in finance. People have a sense of what liquidity is, but there's no single measure (or even clean definition). One approach to building a single, rough measure from multiple liquidity measures is to perform PCA and call the first principal component a proxy for liquidity.
How reasonable this approach is depends on what you're trying to do and the specific problem at hand. In some sense, this is related to lossy compression: it can work surprisingly well, but if you try to approximate an image or song with too low a dimension space, what you get may not resemble the original for any practical purpose.
