When you fit nonlinear fixed-effect or mixed models, it is difficult to guess the model parameters that fit the data. Yet, most nonlinear regression procedures (such as PROC NLIN and PROC NLMIXED in SAS) require that you provide a good guess! If your guess is not good, the fitting algorithm,
A previous article showed how to use a calibration plot to visualize the goodness-of-fit for a logistic regression model. It is common to overlay a scatter plot of the binary response on a predicted probability plot (below, left) and on a calibration plot (below, right): The SAS program that creates
A SAS programmer asked how to label multiple regression lines that are overlaid on a single scatter plot. Specifically, he asked to label the curves that are produced by using the REG statement with the GROUP= option in PROC SGPLOT. He wanted the labels to be the slope and intercept
I previously showed an easy way to visualize a regression model that has several continuous explanatory variables: use the SLICEFIT option in the EFFECTPLOT statement in SAS to create a sliced fit plot. The EFFECTPLOT statement is directly supported by the syntax of the GENMOD, LOGISTIC, and ORTHOREG procedures in
Slice, slice, baby! You've got to slice, slice, baby! When you fit a regression model that has multiple explanatory variables, it is a challenge to effectively visualize the predicted values. This article describes how to visualize the regression model by slicing the explanatory variables. In SAS, you can use the
If you use SAS regression procedures, you are probably familiar with the "stars and bars" notation, which enables you to construct interaction effects in regression models. Although you can construct many regression models by using that classical notation, a friend recently reminded me that the EFFECT statement in SAS provides
Restricted cubic splines are a powerful technique for modeling nonlinear relationships by using linear regression models. I have attended multiple SAS Global Forum presentations that show how to use restricted cubic splines in SAS regression procedures. However, the presenters have all used the %RCSPLINE macro (Frank Harrell, 1988) to generate
Most regression models try to model a response variable by using a smooth function of the explanatory variables. However, if the data are generated from some nonsmooth process, then it makes sense to use a regression function that is not smooth. A simple way to model a discontinuous process in
Today's post illustrates the REG, PBSPLINE, LOESS, SERIES, and SPLINE statements in PROC SGPLOT. The GROUP= and BREAK options in the SERIES statement are also discussed.
A previous post discusses how the loess regression algorithm is implemented in SAS. The LOESS procedure in SAS/STAT software provides the data analyst with options to control the loess algorithm and fit nonparametric smoothing curves through points in a scatter plot. Although PROC LOESS satisfies 99.99% of SAS users who
Loess regression is a nonparametric technique that uses local weighted regression to fit a smooth curve through points in a scatter plot. Loess curves are can reveal trends and cycles in data that might be difficult to model with a parametric curve. Loess regression is one of several algorithms in
What is weighted regression? How does it differ from ordinary (unweighted) regression? This article describes how to compute and score weighted regression models. Visualize a weighted regression Technically, an "unweighted" regression should be called an "equally weighted " regression since each ordinary least squares (OLS) regression weights each observation equally.
Last week I read an interesting paper by Bob Rodriguez: "Statistical Model Building for Large, Complex Data: Five New Directions in SAS/STAT Software." In it, Rodriguez summarizes five modern techniques for building predictive models and highlights recent SAS/STAT procedures that implement those techniques. The paper discusses the following high-performance (HP)
Graphs enable you to visualize how the predicted values for a regression model depend on the model effects. You can gain an intuitive understanding of a model by using the EFFECTPLOT statement in SAS to create graphs like the one shown at the top of this article. Many SAS regression
I got several positive comments about a recent tip, "How to fit a variety of logistic regression models in SAS." A reader asked if I knew any other similar resources about statistical analysis in SAS. Absolutely! One gem that comes to mind is "Examples of writing CONTRAST and ESTIMATE statements."
SAS software can fit many different kinds of regression models. In fact a common question on the SAS Support Communities is "how do I fit a <name> regression model in SAS?" And within that category, the most frequent questions involve how to fit various logistic regression models in SAS. There
My previous blog post shows how to use PROC LOGISTIC and spline effects to predict the probability that an NBA player scores from various locations on a court. The LOGISTIC procedure fits parametric models, which means that the procedure estimates parameters for every explanatory effect in the model. Spline bases
Most SAS regression procedures support the "stars and bars" operators, which enable you to create models that include main effects and all higher-order interaction effects. You can also easily create models that include all n-way interactions up to a specified value of n. However, it can be a challenge to
Last week I discussed ordinary least squares (OLS) regression models and showed how to illustrate the assumptions about the conditional distribution of the response variable. For a single continuous explanatory variable, the illustration is a scatter plot with a regression line and several normal probability distributions along the line. The
A friend who teaches courses about statistical regression asked me how to create a graph in SAS that illustrates an important concept: the conditional distribution of the response variable. The basic idea is to draw a scatter plot with a regression line, then overlay several probability distributions along the line,
Last week's post about odds ratio plots in SAS made me think about a similar plot that visualizes the parameter estimates for a regression analysis. The so-called regression coefficient plot is a scatter plot of the estimates for each effect in the model, with lines that indicate the width of
My last blog post showed how to simulate data for a logistic regression model with two continuous variables. To keep the discussion simple, I simulated a single sample with N observations. However, to obtain the sampling distribution of statistics, you need to generate many samples from the same logistic model.
In my book Simulating Data with SAS, I show how to use the SAS DATA step to simulate data from a logistic regression model. Recently there have been discussions on the SAS/IML Support Community about simulating logistic data by using the SAS/IML language. This article describes how to efficiently simulate
My previous post described how to use the "missing response trick" to score a regression model. As I said in that article, there are other ways to score a regression model. This article describes using the SCORE procedure, a SCORE statement, the relatively new PLM procedure, and the CODE statement.
A fundamental operation in statistical data analysis is to fit a statistical regression model on one set of data and then evaluate the model on another set of data. The act of evaluating the model on the second set of data is called scoring. One of first "tricks" that I
This week I read an interesting blog post that led to a discussion about specifying the frequencies of observations in a regression model. In SAS software, many of the analysis procedures contain a FREQ statement for specifying frequencies and a WEIGHT statement for specifying weights in a weighted regression. Theis
I often see variations of the following question posted on statistical discussion forums: I want to bin the X variable into a small number of values. For each bin, I want to draw the quartiles of the Y variable for that bin. Then I want to connect the corresponding quartile
Someone recently asked a question on the SAS Support Communities about estimating parameters in ridge regression. I answered the question by pointing to a matrix formula in the SAS documentation. One of the advantages of the SAS/IML language is that you can implement matrix formulas in a natural way. The
In my previous post, I blogged about how to sample from a finite mixture distribution. I showed how to simulate variables from populations that are composed of two or more subpopulations. Modeling a response variable as a mixture distribution is an active area of statistics, as judged by many talks
In a previous post, I discussed computing regression coefficients in different polynomial bases and showed how the coefficients change when you change the basis functions. In particular, I showed how to convert the coefficients computed in one basis to coefficients computed with respect to a different basis. It turns out