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 It’s about linear algebra—matrices in particular—so it won’t exactly go out of date, and he’s looking forward to seeing the comments.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…

The 2011 Stata Conference will be held on July 14 and 15 at the University of Chicago’s Gleacher Center. I’ve enjoyed meeting many enthusiastic Stata users at previous Stata Conferences, and I’m looking forward to seeing both familiar and new faces this year in Chicago.

The organizing committee recently posted a call for presentations on Statalist. That posting is included below. Read more…

Excuse me, but I’m going to toot Stata’s horn.

I got an email from Nicholas Cox (an Editor of the Stata Journal) yesterday. He said he was writing something for the Stata Journal and wanted the details on how we calculated a^b. He was focusing on examples such as (-8)^(1/3), where Stata produces a missing value rather than -2, and he wanted to know if our calculation of that was exp((1/3)*ln(-8)). He didn’t say where he was going, but I answered his question.

I have rather a lot to say about this.

Nick’s supposition was correct, in this particular case, and for most values of a and b, Stata calculates a^b as exp(b*ln(a)). In the case of a=-8 and b=1/3, ln(-8)==., and thus (-8)^(1/3)==.. Read more…

Most software stores dates and times numerically, as durations from some sentinel date, but they differ on the sentinel date and on the units in which the duration is stored. Stata stores dates as the number of days since 01jan1960, and datetimes as the number of milliseconds since 01jan1960 00:00:00.000. January 3, 2011 is stored as 18,630, and 2pm on January 3 is stored as 1,609,682,400,000. Other packages use different choices for bases and units.

It sometimes happens that you need to process in Stata data imported from other software and end up with a numerical variable recording a date or datetime in the other software’s encoding. It is usually possible to adjust the numeric date or datetime values to the sentinel date and units that Stata uses. Below are conversion rules for SAS, SPSS, R, Excel, and Open Office. Read more…