An important application of nonlinear optimization is finding parameters of a model that fit data. For some models, the parameters are constrained by the data. A canonical example is the maximum likelihood estimation of a so-called "threshold parameter" for the three-parameter lognormal distribution. For this distribution, the objective function is
One of my friends likes to remind me that "there is no such thing as a free lunch," which he abbreviates by "TINSTAAFL" (or TANSTAAFL). The TINSTAAFL principle applies to computer programming because you often end up paying a cost (in performance) when you call a convenience function that simplifies
Do you want to bin a numeric variable into a small number of discrete groups? This article compiles a dozen resources and examples related to binning a continuous variable. The examples show both equal-width binning and quantile binning. In addition to standard one-dimensional techniques, this article also discusses various techniques
Binning transforms a continuous numerical variable into a discrete variable with a small number of values. When you bin univariate data, you define cut point that define discrete groups. I've previously shown how to use PROC FORMAT in SAS to bin numerical variables and give each group a meaningful name
I recently showed how to create an annotation data set that will overlay cell counts or percentages on a mosaic plot. A mosaic plot is a visual representation of a cross-tabulation of observed frequencies for two categorical variables. The mosaic plot with cell counts is shown to the right. The
SAS/STAT software contains a number of so-called HP procedures for training and evaluating predictive models. ("HP" stands for "high performance.") A popular HP procedure is HPLOGISTIC, which enables you to fit logistic models on Big Data. A goal of the HP procedures is to fit models quickly. Inferential statistics such
When fitting a least squares regression model to data, it is often useful to create diagnostic plots of the residuals versus the explanatory variables. If the model fits the data well, the plots of the residuals should not display any patterns. Systematic patterns can indicate that you need to include
A previous article describes the DFBETAS statistics for detecting influential observations, where "influential" means that if you delete the observation and refit the model, the estimates for the regression coefficients change substantially. Of course, there are other statistics that you could use to measure influence. Two popular ones are the
My article about deletion diagnostics investigated how influential an observation is to a least squares regression model. In other words, if you delete the i_th observation and refit the model, what happens to the statistics for the model? SAS regression procedures provide many tables and graphs that enable you to
For linear regression models, there is a class of statistics that I call deletion diagnostics or leave-one-out statistics. These observation-wise statistics address the question, "If I delete the i_th observation and refit the model, what happens to the statistics for the model?" For example: The PRESS statistic is similar to
