Procedures

Computes the adjusted R-squared value for a data set.

Performs an analysis of variance (ANOVA) on the supplied data set.

Copy every component of a glm_options object.

Defines deep-copy table assignment and shared view assignment.

Computes Bartlett's test statistic and associated probability.

Computes the beta function.

Performs a bootstrap calculation on the supplied data set for the given statistic. The default implementation utlizes a random resampling with replacement. Other resampling methods may be defined by specifying an appropriate routine by means of the method input. The module provides another option, random_resample, which is a parametric Gaussian bootstrap based on the sample mean and standard deviation. It assumes normally distributed observations. The confidence limits are percentile intervals calculated from the bootstrap replicates.

Utilizes the Box-Muller transformation approach to generate the requested number of random samples from a normal distribution of the specified mean and standard deviation.

Computes statistics for the quality of fit for a regression model.

Generates a central composite design in coded variables.

Computes the size of a central composite design.

Copies a column to a work array for the existing array algorithms.

Computes the confidence interval for the specified distribution.

Computes the sample correlation coefficient (an estimate to the population Pearson correlation) as follows.

Computes the covariance matrix $C$ where $C = \left( X^{T} X \right)^{-1}$ and $X$ is computed by design_matrix. Uses an SVD of X, without forming X**T * X. Rank-deficient inputs give the Moore-Penrose covariance; use regression_covariance for rank diagnostics.

Converts coded variable values (-1, +1) to natural scale.

Computes the design matrix $X$ for the linear least-squares regression problem of $X \beta = y$, where $X$ is the matrix computed here, $\beta$ is the vector of coefficients to be determined, and $y$ is the vector of measured dependent variables.

Computes the difference between elements in an array.

Computes the digamma function.

Compares two DOE models using the same data set.

Evaluates the model terms (columns of the design matrix) included in a model at each of the supplied factor values.

Fits a Taylor series model to the provided data.

Computes an analysis of variance (ANOVA) table for a DOE model.

Computes the unscaled parameter covariance matrix $\left( X^{T} X \right)^{-1}$ for a model, where $X$ is the design matrix constructed from the supplied factor values. Only the parameters included in the model (map = true) are represented.

Computes model diagnostics and goodness-of-fit metrics.

Optimizes a fitted response surface within a box of factor bounds.

Computes predictions with confidence and prediction intervals.

Computes predictions with confidence and prediction intervals using a user-supplied residual mean squared error. This is equivalent to doe_predict, and is retained for convenience when the residual mean squared error is computed by the caller.

Computes residual analysis data for model diagnostics.

Computes the stationary point of a quadratic (nway <= 2) response surface in coded variables and classifies its nature.

Employs the expectation-maximization (EM) algorithm to compute the maximum-likelihood estimates of the mean vector and covariance matrix of a multivariate normal population from a data set containing missing values. The missing values are then replaced by their conditional expectations given the observed values and the converged parameter estimates.

Converts natural variable values to coded (-1, +1) scale.

Computes the F-test and returns the probability (two-tailed) that the variances of two data sets are not significantly different.

Computes the factorial of X.

Generates a 2-level fractional factorial design.

Computes the size of a fractional factorial design.

Computes a table with values scaled from 1 to N describing a full-factorial design.

Computes a full-factorial design in coded variables on the range [-1, +1]. Each factor with L levels is assigned L evenly spaced values from -1 to +1 (inclusive). A factor with a single level is assigned a value of 0. For a 2-level factor, the levels are -1 and +1.

Performs a gauge repeatability and reproducibility (gauge R&R) study by means of the analysis of variance (ANOVA) method.

Computes the appropriate size for a full-factorial design table.

Evaluate the logistic inverse link without exponent overflow.

Invert the reciprocal Gamma link g(mu) = 1 / mu.

Invert the Poisson log link with bounded exponentiation.

Computes the incomplete beta function.

Computes the lower incomplete gamma function.

Computes the upper incomplete gamma function.

Fit a GLM from initial coefficients. The working response and weights are z = eta + (y - mu) * g'(mu) and W = 1 / (g'(mu)**2 * V(mu)). The implementation solves the equivalent increment problem sqrt(W) X delta = sqrt(W) (z - eta), using column-scaled, pivoted QR rather than normal equations. Weights and right-hand sides are normalized in log space to avoid overflow.

Determines if the supplied value represents a missing observation.

Computes the Jacobian matrix for a nonlinear regression problem.

Imputes missing values by means of a k-nearest neighbors approach.

Generates a Latin hypercube design for factor space exploration.

Computes Levene's test statistic and associated probability.

Computes a linear least-squares regression to fit a set of data.

Log regularized beta; invalid inputs or nonconvergence return NaN. The leading factor and complementary branch are evaluated in log space.

Log lower gamma ratio; invalid inputs or nonconvergence return NaN.

Log upper gamma ratio; invalid inputs or nonconvergence return NaN.

Computes the smoothing of a data set using a robust locally weighted scatterplot smoothing (LOWESS) algorithm. Fitted values are computed at each of the supplied x values.

Computes the mean of a set of data.

Returns the value used to flag a missing observation. The value is an IEEE quiet NaN.

Generates multiple completed copies of a data set containing missing values by means of Bayesian data augmentation under a multivariate normal model with the noninformative Jeffreys prior.

Performs a nonlinear regression to fit a model using a version of the Levenberg-Marquardt algorithm.

Combines the results of the analyses of multiply-imputed data sets by means of Rubin's rules.

Computes the pooled estimate of variance.

Computes a log density or probability with explicit zero handling.

Computes the R-squared value for a data set.

Parametric Gaussian resampling using the sample mean and standard deviation. This assumes the observations are normally distributed; it is not the nonparametric bootstrap.

Resamples a time series using a circular moving-block bootstrap. The block length is floor(sqrt(n)), with a minimum of two when possible. Define a custom callback to use a domain-specific block length.

Resamples balanced clusters with replacement. The input stores contiguous records as [cluster_id, value], with every cluster having the same number of records. The statistic routine should use the value fields and ignore the cluster identifiers.

Resamples paired observations with replacement. The input stores each pair as adjacent values: [x1, y1, x2, y2, ...].

Random resampling with replacement from the supplied sample.

Reads a delimited text file into a data_table.

Computes the unscaled regression covariance using an SVD of X itself. Singular directions below MAX(M, N) * EPSILON * largest singular value are discarded, giving the Moore-Penrose covariance on identifiable directions. Rank-deficient fits require care: a zero pseudocovariance along a discarded direction does not imply that the corresponding parameter is known exactly.

Computes the regularized beta function.

Computes the regularized lower incomplete gamma function.

Computes the regularized upper incomplete gamma function.

Uses rejection sampling to randomly sample a target distribution.

Samples independent chains concurrently using OpenMP. Initialize each target independently, with no shared mutable state in distributions, models, proposals, or sampler callbacks. The compiler runtime must provide thread-safe RANDOM_NUMBER (as GNU Fortran does). Random streams and reproducibility depend on the compiler runtime and thread scheduling; no per-chain seed guarantee is provided.

Samples a multivariate normal distribution such that $\vec{x} = \vec{mu} + L \vec{u}$, where $L$ is the lower form of the Cholesky factorization of the covariance matrix, and $\vec{u}$ is a randomly generated vector that exists on the set $[-1 1]$

Estimates the sample size required to achieve an experiment with the desired power and significance levels to ascertain the desired difference in parameter.

Computes log(1 + exp(value)) without overflowing the exponential.

Computes exp(x) - 1 without subtractive cancellation near zero.

Computes log(1 + x) accurately when x is near zero.

Computes the 2-tailed Student's T-Test for two data sets of assumed equivalent variances.

Computes the 2-tailed Student's T-Test for two paired data sets.

Computes the 2-tailed Student's T-Test for two data sets of assumed non-equivalent variances.

Computes Tukey's biweight IRLS weight for a standardized residual. The positive tuning constant k defaults to 4.685. $$w(u) = \begin{cases} \left[1 - \left(\frac{u}{k}\right)^2\right]^2, & |u| \le k, \\ 0, & |u| > k. \end{cases}$$

Computes Tukey's biweight score function for a standardized residual. The positive tuning constant k defaults to 4.685. $$\psi(u) = \begin{cases} u \left[1 - \left(\frac{u}{k}\right)^2\right]^2, & |u| \le k, \\ 0, & |u| > k. \end{cases}$$

Computes Tukey's biweight rho loss for a standardized residual. The positive tuning constant k defaults to 4.685. $$\rho(u) = \begin{cases} \frac{k^2}{6} \left\{1 - \left[1 - \left(\frac{u}{k}\right)^2\right]^3\right\}, & |u| \le k, \\ \frac{k^2}{6}, & |u| > k. \end{cases}$$

Writes a data_table to a delimited text file, replacing any existing file.