When most people first think about software designed to run on multiple cores such as Stata/MP, they think to themselves, two cores, twice as fast; four cores, four times as fast. They appreciate that reality will somehow intrude so that two cores won’t really be twice as fast as one, but they imagine the intrusion is something like friction and nothing that an intelligently placed drop of oil can’t improve.

In fact, something inherent intrudes. In any process to accomplish something—even physical processes—some parts may be able to to be performed in parallel, but there are invariably parts that just have to be performed one after the other. Anyone who cooks knows that you sometimes add some ingredients, cook a bit, and then add others, and cook some more. So it is, too, with calculating x_t = f(x_t-1) for t=1 to 100 and t₀=1. Depending on the form of f(), sometimes there’s no alternative to calculating x₁ = f(x₀), then calculating x₂ = f(x₁), and so on. Read more…

Jim Hufford, Esq. had his first Stata lesson: “This is going to be awesome when I understand what all those little letters and things mean.”

Along those lines—awesome—Jim may want to see these nice Stata scatterplots from the “wannabe economists of the Graduate Institute of International and Development Studies in Geneva” at Rigotnomics.

If you want to graph data onto maps using Stata—and see another awesome graph—see Mitch Abdon’s “Fun with maps in Stata” over at the Stata Daily.

And if you’re interested in geocoding to obtain latitudes and longitudes from human-readable addresses or locations, see Adam Ozimek’s “Computers are taking our jobs: Stata nerds only edition” over at Modeled Behavior and see the related Stata Journal article “Stata utilities for geocoding and generating travel time and travel distance information” by Adam Ozimek and Daniel Miles.

See this video, by Vi Hart:

This link was passed on to me by my friend Marcello. I’ve been bold enough to make up words such as eigenaxis and eigenpoint, but it takes real courage to suggest redefining π, even when you’re right!

After seeing the video, you can go here and here to learn more about what is being proposed.

Don’t click on comments until you’ve seen the video. Ms. Hart does a better job presenting the proposal than any of us can.

Last time, I showed you a way to graph and to think about matrices. This time, I want to apply the technique to eigenvalues and eigenvectors. The point is to give you a picture that will guide your intuition, just as it was previously.

Before I go on, several people asked after reading part 1 for the code I used to generate the graphs. Here it is, both for part 1 and part 2: matrixcode.zip. Read more…

To get to them, just click on the title of the post and scroll to the bottom of the page. To begin, we are allowing guest comments, so you do not even have to register, although registration is easy.

I want to show you a way of picturing and thinking about matrices. The topic for today is the square matrix, which we will call A. I’m going to show you a way of graphing square matrices, although we will have to limit ourselves to the 2 x 2 case. That will be, as they say, without loss of generality. The technique I’m about to show you could be used with 3 x 3 matrices if you had a better 3-dimensional monitor, and as will be revealed, it could be used on 3 x 2 and 2 x 3 matrices, too. If you had more imagination, we could use the technique on 4 x 4, 5 x 5, and even higher-dimensional matrices. Read more…

Our target date for tuning on comments is Wednesday of next week. Don’t hold us to it, but we’re optimistic on meeting our deadline.

In the meantime, Bill Gould is so excited he’s put on hold his latest blog entry. It’s about linear algebra—matrices in particular—so it won’t exactly go out of date, and he’s looking forward to seeing the comments. Bill’s very proud of what he’s written, so be gentle. We’ll put up his posting right after comments are enabled.

From time to time, we get a question from a user puzzled about getting a positive log likelihood for a certain estimation. We get so used to seeing negative log-likelihood values all the time that we may wonder what caused them to be positive.

First, let me point out that there is nothing wrong with a positive log likelihood.

The likelihood is the product of the density evaluated at the observations. Usually, the density takes values that are smaller than one, so its logarithm will be negative. However, this is not true for every distribution. Read more…

In my previous posting last week, I explained how computers store binary floating-point numbers, how Stata’s %21x display format displays with fidelity those binary floating-point numbers, how %21x can help you uncover bugs, and how %21x can help you understand behaviors that are not bugs even though they are surpising to us base-10 thinkers. The point is, it is sometimes useful to think in binary, and with %21x, thinking in binary is not difficult.

This week, I want to discuss double versus float precision. Read more…

%21x is a Stata display format, just as are %f, %g, %9.2f, %td, and so on. You could put %21x on any variable in your dataset, but that is not its purpose. Rather, %21x is for use with Stata’s display command for those wanting to better understand the accuracy of the calculations they make. We use %21x frequently in developing Stata. Read more…