Blossom Statistical Package for R

Blossom is an R package with functions for making statistical comparisons with distance-function based permutation tests developed by P.W. Mielke, Jr. and colleagues at Colorado State University, and for testing parameters estimated in linear models with permutation procedures developed by B. S. Cade and colleagues at the U.S. Geological Survey' Fort Collins Science Center, U.S. Geological Survey. This implementation in R has allowed for numerous improvements not supported by the Cade and Richards Fortran implementation, including use of categorical predictor variables in most routines.

Statistical procedures available include:

• A permutation testing version of ordinary least squares (OLS) regression that parallels the least absolute deviation (LAD) and quantile regression permutation tests;
• A permutation and asymptotic chi-square approximation of P-values for a rank score statistic for regression quantiles;
• Double permutation (hypothesis.test with double.permutation) procedures for linear model tests (OLS, LAD regression, and quantile rank score tests) when null models are either implicitly or explicitly constrained through the origin, that is, no intercept models;
• Dropping all but a single zero residual in LAD and quantile regression permutation tests of subsets of variables in multiple regression models;
• Computation of all quantile regression estimates (lad with the option all.quants = TRUE);
• Empirical coverage tests for univariate goodness-of-fit and g-sample comparisons that are extensions of the Kolmogorov-Smirnov family of statistics for comparing cumulative distribution functions, including an option for testing goodness-of-fit for a random uniform distribution on a circle;
• The multiresponse permutation procedures (MRPP) family of statistics including two options for standardizing multiple dependent variables (average Euclidean distance or Hotelling's commensuration based on variance/covariance);
• Computing exact probabilities by complete enumeration of all possible combinations for small block and treatment designs in MRPP and multiresponse randomized block permutation procedures (MRBP);
• A Monte Carlo resampling approximation alternative for all the MRPP family of statistics (the mrpp commands with options number.perms); and
• Multivariate medians and distance quantiles (MEDQ) to be used as descriptive statistics with MRPP analyses. In addition, we offer the option to store (save.test = TRUE) the vector of permuted test statistic values from Monte Carlo resampling approximations of probabilities.