Posted on 1 Comment on Don’t use correlation to track prediction performance

Don’t use correlation to track prediction performance

Using correlation to track model performance is “a mistake that nobody would ever make” combined with a vague “what would be wrong if I did do that” feeling. I hope after reading this feel a least a small urge to double check your work and presentations to make sure you have not reported correlation where R-squared, likelihood or root mean square error (RMSE) would have been more appropriate.

It is tempting (but wrong) to use correlation to track the performance of model predictions. The temptation arises because we often (correctly) use correlation to evaluate possible model inputs. And the correlation function is often a convenient built-in function. Continue reading Don’t use correlation to track prediction performance

Posted on 3 Comments on Revisiting Cleveland’s The Elements of Graphing Data in ggplot2

Revisiting Cleveland’s The Elements of Graphing Data in ggplot2

I was flipping through my copy of William Cleveland’s The Elements of Graphing Data the other day; it’s a book worth revisiting. I’ve always liked Cleveland’s approach to visualization as statistical analysis. His quest to ground visualization principles in the context of human visual cognition (he called it “graphical perception”) generated useful advice for designing effective graphics .

I confess I don’t always follow his advice. Sometimes it’s because I don’t agree with him, but also it’s because I use ggplot for visualization, and I’m lazy. I like ggplot because it excels at layering multiple graphics into a single plot and because it looks good; but deviating from the default presentation is often a bit of work. How much am I losing out on by this? I decided to do the work and find out.

Details of specific plots aside, the key points of Cleveland’s philosophy are:

• A graphic should display as much information as it can, with the lowest possible cognitive strain to the viewer.
• Visualization is an iterative process. Graph the data, learn what you can, and then regraph the data to answer the questions that arise from your previous graphic.

Of course, when you are your own viewer, part of the cognitive strain in visualization comes from difficulty generating the desired graphic. So we’ll start by making the easiest possible ggplot graph, and working our way from there — Cleveland style.

Posted on Categories Opinion, Statistics, Tutorials2 Comments on More on ROC/AUC

More on ROC/AUC

A bit more on the ROC/AUC

The issue

The receiver operating characteristic curve (or ROC) is one of the standard methods to evaluate a scoring system. Nina Zumel has described its application, but I would like to call out some additional details. In my opinion while the ROC is a useful tool, the “area under the curve” (AUC) summary often read off it is not as intuitive and interpretable as one would hope or some writers assert.

Posted on 3 Comments on Error Handling in R

Error Handling in R

It’s often the case that I want to write an R script that loops over multiple datasets, or different subsets of a large dataset, running the same procedure over them: generating plots, or fitting a model, perhaps. I set the script running and turn to another task, only to come back later and find the loop has crashed partway through, on an unanticipated error. Here’s a toy example:

``` > inputs = list(1, 2, 4, -5, 'oops', 0, 10) > for(input in inputs) { + print(paste("log of", input, "=", log(input))) + }  "log of 1 = 0"  "log of 2 = 0.693147180559945"  "log of 4 = 1.38629436111989"  "log of -5 = NaN" Error in log(input) : Non-numeric argument to mathematical function In addition: Warning message: In log(input) : NaNs produced ```

The loop handled the negative arguments more or less gracefully (depending on how you feel about NaN), but crashed on the non-numeric argument, and didn’t finish the list of inputs.

How are we going to handle this?

Posted on Categories Expository Writing, Mathematics, Tutorials

Rudie can’t fail (if majorized)

We have been writing for a while about the convergence of Newton steps applied to a logistic regression (See: What does a generalized linear model do?, How robust is logistic regression? and Newton-Raphson can compute an average). This is all based on our principle of working examples for understanding. This eventually progressed to some writing on the nature of problem solving (a nice complement to our earlier writing on calculation). In the course of research we were directed to a very powerful technique called the MM algorithm (see: “The MM Algorithm” Kenneth Lang, 2007; “A Tutorial on MM Algorithms”, David R. Hunter, Kenneth Lange, Amer. Statistician 58:30–37, 2004; and “Monotonicity of Quadratic-Approximation Algorithms”, Dankmar Bohning, Bruce G. Lindsay, Ann. Inst. Statist. Math, Vol. 40, No. 4, pp 641-664, 1988). The MM algorithm introduces an essential idea: majorized functions (not to be confused with the majorized order on R^d). Majorization it is an interesting way to modify Newton methods to be reliable contractions (and therefore converge in a manner similar to EM algorithms).

Here we will work an example of the MM method. We will not work it in its most general form, but in a form that quickly reveals much of the beauty of the method. We also introduce a “collared Newton step” which guarantees convergence without resorting to line-search (essentially resolving the issues in solving a logistic regression by Newton style methods). Continue reading Rudie can’t fail (if majorized)

Posted on 4 Comments on Level fit summaries can be tricky in R

Level fit summaries can be tricky in R

Model level fit summaries can be tricky in R. A quick read of model fit summary data for factor levels can be misleading. We describe the issue and demonstrate techniques for dealing with them. Continue reading Level fit summaries can be tricky in R

Posted on 6 Comments on How robust is logistic regression?

How robust is logistic regression?

Logistic Regression is a popular and effective technique for modeling categorical outcomes as a function of both continuous and categorical variables. The question is: how robust is it? Or: how robust are the common implementations? (note: we are using robust in a more standard English sense of performs well for all inputs, not in the technical statistical sense of immune to deviations from assumptions or outliers.)

Even a detailed reference such as “Categorical Data Analysis” (Alan Agresti, Wiley, 1990) leaves off with an empirical observation: “the convergence … for the Newton-Raphson method is usually fast” (chapter 4, section 4.7.3, page 117). This is a book that if there is a known proof that the estimation step is a contraction (one very strong guarantee of convergence) you would expect to see the proof reproduced. I always suspected there was some kind of Brouwer fixed-point theorem based folk-theorem proving absolute convergence of the Newton-Raphson method in for the special case of logistic regression. This can not be the case as the Newton-Raphson method can diverge even on trivial full-rank well-posed logistic regression problems. Continue reading How robust is logistic regression?

Posted on 1 Comment on What does a generalized linear model do?

What does a generalized linear model do?

What does a generalized linear model do? R supplies a modeling function called `glm()` that fits generalized linear models (abbreviated as GLMs). A natural question is what does it do and what problem is it solving for you? We work some examples and place generalized linear models in context with other techniques. Continue reading What does a generalized linear model do?

Posted on 5 Comments on Minimal Version Control Lesson: Use It

Minimal Version Control Lesson: Use It

There is no excuse for a digital creative person to not use some sort of version control or source control. In the past disk space was too dear, version control systems were too expensive and software was not powerful enough; this is no longer the case. Unless your work is worthless both back it up and version control it. We will demonstrate a minimal set of version control commands that will one day save your bacon. Continue reading Minimal Version Control Lesson: Use It