"O Christmas tree, O Christmas tree, how lovely are your branches!" The idealized image of a Christmas tree is a perfectly straight conical tree with lush branches and no bare spots. Although this ideal exists only on Christmas cards, forest researchers are always trying to develop trees that approach the
I previously showed how to create a decile calibration plot for a logistic regression model in SAS. A decile calibration plot (or "decile plot," for short) is used in some fields to visualize agreement between the data and a regression model. It can be used to diagnose an incorrectly specified
To help visualize regression models, SAS provides the EFFECTPLOT statement in several regression procedures and in PROC PLM, which is a general-purpose procedure for post-fitting analysis of linear models. When scoring and visualizing a model, it is important to use reasonable combinations of the explanatory variables for the visualization. When
Intuitively, the skewness of a unimodal distribution indicates whether a distribution is symmetric or not. If the right tail has more mass than the left tail, the distribution is "right skewed." If the left tail has more mass, the distribution is "left skewed." Thus, estimating skewness requires some estimates about
The expected value of a random variable is essentially a weighted mean over all possible values. You can compute it by summing (or integrating) a probability-weighted quantity over all possible values of the random variable. The expected value is a measure of the "center" of a probability distribution. You can
The skewness of a distribution indicates whether a distribution is symmetric or not. The Wikipedia article about skewness discusses two common definitions for the sample skewness, including the definition used by SAS. In the middle of the article, you will discover the following sentence: In general, the [estimators]are both biased
A fundamental principle of data analysis is that a statistic is an estimate of a parameter for the population. A statistic is calculated from a random sample. This leads to uncertainty in the estimate: a different random sample would have produced a different statistic. To quantify the uncertainty, SAS procedures
I previously wrote about the RAS algorithm, which is a simple algorithm that performs matrix balancing. Matrix balancing refers to adjusting the cells of a frequency table to match known values of the row and column sums. Ideally, the balanced matrix will reflect the structural relationships in the original matrix.
A common operation in statistical data analysis is to center and scale a numerical variable. This operation is conceptually easy: you subtract the mean of the variable and divide by the variable's standard deviation. Recently, I wanted to perform a slight variation of the usual standardization: Perform a different standardization
I recently showed how to compute within-group multivariate statistics by using the SAS/IML language. However, a principal of good software design is to encapsulate functionality and write self-contained functions that compute and return the results. What is the best way to return multiple statistics from a SAS/IML module? A convenient
