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Correlation & regression

The following methods treat data with heteroscedastic (different for each point) measurement errors which are commonly present in astronomical data:
Linear regression with measurement errors and scatter
    Weighted ordinary least squares line with heteroscedastic measurement errors and homoscedastic intrinsic scatter in the dependent variable. Also includes code in SLOPES. Developed for astronomy by M. Akritas (Penn State) & M. Bershady (Wisconsin).

Partial correlation for censored data
    A test for partial correlation between three variables, any or all of which are subject to censoring, based on a generalized Kendall's tau.  Developed for astronomy by M. Akritas (Penn State) and J. Siebert (MPI). 

Measurement error linear regression
    Three short Fortran programs implementing errors-in-variables bivariate linear regression (York, Fasano & Vio, Ripley methods).  Developed for astronomy by F. Murtagh of University of London. (Look under "Various other programs")

    Orthogonal distance nonlinear regression for data weighted by known measurement errors.  By the National Institute Standards & Technology.

Errors-in-Variables Model
    Least squares linear and nonlinear parameter estimation with errors in the predictor variables and the dependent variable.  Applied Stat Algorithm #286 distributed by Statlib.

Linear regression with measurement errors
    Code calculationg simultaneous confidence bands for linear regression with heteroscedastic errors using bootstrap resampling, based on Faraway & Sun (JASA 1995). Code in LISP-STAT and S+.

    Computes ordinary and symmetrical least-squares regression lines for bivariate data (orthogonal regression, reduced major axis, OLS bisector and mean OLS).  Developed for astronomy by G. J. Babu & E. Feigelson of Penn State.

    Least median of squares regression  and least trimmed squares (LTS) which is highly robust to outliers in the data.  By P. Pousseeuw of University of Antwerp.

Fast Least Trimmed Squares (LTS)
    Robust multivariate regression technique based on the subset of points whose least-squares fit gives the smallest sum of squared residuals.  Efficient method for large datasets. By P. Rousseeuw  of University of Antwerp.

    Programs for nonlinear parameter estimation by least squares, maximum-likelihood and some robust methods.  From NIST's GAMS.

Nonlinear regression
    Large Fortran program for maximum-likelihood and quasi-ML estimation of parameters in nonlienar regression models.  TOMS Algorithm #717.

Least squares codes
    A extensive collection of Fortran 90 codes for unconstrained linear and nonlinear least-squares, ridge regression, fitting ellipses to (x,y) data, logistic regression, and more. From Alan J. Miller (CSIRO).

    Econometrics package for Windows including: variable transformations, kernel density estimation, time series analysis (cross-correlation, stationarity tests, ARIMA & GARCH modeling), linear regression models (Poisson regression, Tobit, 2-stage least squares, user-supplied nonlinear), and more by H. Bierens (Penn State).

Nonlinear Statistical Models
    C++ implementation of least squares estimates for univariate and multivariate nonlinear regression. Associated with the text by A. R. Gallant (1987).

    a Macintosh-based program for linear and non-linear regression, with bootstrap estimation of errors of parameters and other options.  From

Generalized additive models
    Generalized additive models fitting a variety of models (Gaussian, Binomial, Poisson, Gamma, Cox) using cubic smoothing splines.  Distributed by StatLib.

Robust linear regression
    Robust regression by least absolute deviations. Applied Statistics algorithm #132 distributted by Statlib

Confidence intervals for nonlinear regression
    Generates grid of variance ratios to plot confidence regions for two parameters using Halperin's method.  Applied Statisiticss algorithm #290 distributed by Statlib.