# NAG FL InterfaceG02 (Correg)Correlation and Regression Analysis

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G02 (Correg) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.

Routine
Mark of
Introduction

Purpose
g02aaf 22 nagf_correg_corrmat_nearest
Computes the nearest correlation matrix to a real square matrix, using the method of Qi and Sun
g02abf 23 nagf_correg_corrmat_nearest_bounded
Computes the nearest correlation matrix to a real square matrix, augmenting g02aaf to incorporate weights and bounds
g02aef 23 nagf_correg_corrmat_nearest_kfactor
Computes the nearest correlation matrix with $k$-factor structure to a real square matrix
g02ajf 24 nagf_correg_corrmat_h_weight
Computes the nearest correlation matrix to a real square matrix, using element-wise weighting
g02akf 27 nagf_correg_corrmat_nearest_rank
Computes the rank-constrained nearest correlation matrix to a real square matrix, using the method of Qi and Sun
g02anf 25 nagf_correg_corrmat_shrinking
Computes a correlation matrix from an approximate matrix with fixed submatrix
g02apf 26 nagf_correg_corrmat_target
Computes a correlation matrix from an approximate one using a specified target matrix
g02asf 27 nagf_correg_corrmat_fixed
Computes the nearest correlation matrix to a real square matrix, with fixed elements
g02baf 4 nagf_correg_coeffs_pearson
Pearson product-moment correlation coefficients, all variables, no missing values
g02bbf 4 nagf_correg_coeffs_pearson_miss_case
Pearson product-moment correlation coefficients, all variables, casewise treatment of missing values
g02bcf 4 nagf_correg_coeffs_pearson_miss_pair
Pearson product-moment correlation coefficients, all variables, pairwise treatment of missing values
g02bdf 4 nagf_correg_coeffs_zero
Correlation-like coefficients (about zero), all variables, no missing values
g02bef 4 nagf_correg_coeffs_zero_miss_case
Correlation-like coefficients (about zero), all variables, casewise treatment of missing values
g02bff 4 nagf_correg_coeffs_zero_miss_pair
Correlation-like coefficients (about zero), all variables, pairwise treatment of missing values
g02bgf 4 nagf_correg_coeffs_pearson_subset
Pearson product-moment correlation coefficients, subset of variables, no missing values
g02bhf 4 nagf_correg_coeffs_pearson_subset_miss_case
Pearson product-moment correlation coefficients, subset of variables, casewise treatment of missing values
g02bjf 4 nagf_correg_coeffs_pearson_subset_miss_pair
Pearson product-moment correlation coefficients, subset of variables, pairwise treatment of missing values
g02bkf 4 nagf_correg_coeffs_zero_subset
Correlation-like coefficients (about zero), subset of variables, no missing values
g02blf 4 nagf_correg_coeffs_zero_subset_miss_case
Correlation-like coefficients (about zero), subset of variables, casewise treatment of missing values
g02bmf 4 nagf_correg_coeffs_zero_subset_miss_pair
Correlation-like coefficients (about zero), subset of variables, pairwise treatment of missing values
g02bnf 4 nagf_correg_coeffs_kspearman_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, overwriting input data
g02bpf 4 nagf_correg_coeffs_kspearman_miss_case_overwrite
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, overwriting input data
g02bqf 4 nagf_correg_coeffs_kspearman
Kendall/Spearman non-parametric rank correlation coefficients, no missing values, preserving input data
g02brf 4 nagf_correg_coeffs_kspearman_miss_case
Kendall/Spearman non-parametric rank correlation coefficients, casewise treatment of missing values, preserving input data
g02bsf 4 nagf_correg_coeffs_kspearman_miss_pair
Kendall/Spearman non-parametric rank correlation coefficients, pairwise treatment of missing values
g02btf 14 nagf_correg_ssqmat_update
Update a weighted sum of squares matrix with a new observation
g02buf 14 nagf_correg_ssqmat
Computes a weighted sum of squares matrix
g02bwf 14 nagf_correg_ssqmat_to_corrmat
Computes a correlation matrix from a sum of squares matrix
g02bxf 14 nagf_correg_corrmat
Computes (optionally weighted) correlation and covariance matrices
g02byf 17 nagf_correg_corrmat_partial
Computes partial correlation/variance-covariance matrix from correlation/variance-covariance matrix computed by g02bxf
g02bzf 24 nagf_correg_ssqmat_combine
Combines two sums of squares matrices, for use after g02buf
g02caf 4 nagf_correg_linregs_const
Simple linear regression with constant term, no missing values
g02cbf 4 nagf_correg_linregs_noconst
Simple linear regression without constant term, no missing values
g02ccf 4 nagf_correg_linregs_const_miss
Simple linear regression with constant term, missing values
g02cdf 4 nagf_correg_linregs_noconst_miss
Simple linear regression without constant term, missing values
g02cef 4 nagf_correg_linregm_service_select
Service routine for multiple linear regression, select elements from vectors and matrices
g02cff 4 nagf_correg_linregm_service_reorder
Service routine for multiple linear regression, reorder elements of vectors and matrices
g02cgf 4 nagf_correg_linregm_coeffs_const
Multiple linear regression, from correlation coefficients, with constant term
g02chf 4 nagf_correg_linregm_coeffs_noconst
Multiple linear regression, from correlation-like coefficients, without constant term
g02daf 14 nagf_correg_linregm_fit
Fits a general (multiple) linear regression model
g02dcf 14 nagf_correg_linregm_obs_edit
Add/delete an observation to/from a general linear regression model
g02ddf 14 nagf_correg_linregm_update
Estimates of linear parameters and general linear regression model from updated model
Add a new independent variable to a general linear regression model
g02dff 14 nagf_correg_linregm_var_del
Delete an independent variable from a general linear regression model
g02dgf 14 nagf_correg_linregm_fit_newvar
Fits a general linear regression model to new dependent variable
g02dkf 14 nagf_correg_linregm_constrain
Estimates and standard errors of parameters of a general linear regression model for given constraints
g02dnf 14 nagf_correg_linregm_estfunc
Computes estimable function of a general linear regression model and its standard error
Computes residual sums of squares for all possible linear regressions for a set of independent variables
Calculates ${R}^{2}$ and ${C}_{P}$ values from residual sums of squares
g02eef 14 nagf_correg_linregm_fit_onestep
Fits a linear regression model by forward selection
g02eff 21 nagf_correg_linregm_fit_stepwise
Stepwise linear regression
g02faf 14 nagf_correg_linregm_stat_resinf
Calculates standardized residuals and influence statistics
g02fcf 15 nagf_correg_linregm_stat_durbwat
Computes Durbin–Watson test statistic
g02gaf 14 nagf_correg_glm_normal
Fits a generalized linear model with Normal errors
g02gbf 14 nagf_correg_glm_binomial
Fits a generalized linear model with binomial errors
g02gcf 14 nagf_correg_glm_poisson
Fits a generalized linear model with Poisson errors
g02gdf 14 nagf_correg_glm_gamma
Fits a generalized linear model with gamma errors
g02gkf 14 nagf_correg_glm_constrain
Estimates and standard errors of parameters of a general linear model for given constraints
g02gnf 14 nagf_correg_glm_estfunc
Computes estimable function of a generalized linear model and its standard error
g02gpf 22 nagf_correg_glm_predict
Computes a predicted value and its associated standard error based on a previously fitted generalized linear model
g02haf 13 nagf_correg_robustm
Robust regression, standard $M$-estimates
g02hbf 13 nagf_correg_robustm_wts
Robust regression, compute weights for use with g02hdf
g02hdf 13 nagf_correg_robustm_user
Robust regression, compute regression with user-supplied functions and weights
g02hff 13 nagf_correg_robustm_user_varmat
Robust regression, variance-covariance matrix following g02hdf
g02hkf 14 nagf_correg_robustm_corr_huber
Calculates a robust estimation of a covariance matrix, Huber's weight function
g02hlf 14 nagf_correg_robustm_corr_user_deriv
Calculates a robust estimation of a covariance matrix, user-supplied weight function plus derivatives
g02hmf 14 nagf_correg_robustm_corr_user
Calculates a robust estimation of a covariance matrix, user-supplied weight function
g02jff 27 nagf_correg_lmm_init
Linear mixed effects regression, initialization routine for g02jhf
g02jgf 27 nagf_correg_lmm_init_combine
Linear mixed effects regression, initialization routine for g02jgf and g02jhf
g02jhf 27 nagf_correg_lmm_fit
Linear mixed effects regression using either Restricted Maximum Likelihood (REML) or Maximum Likelihood (ML)
g02kaf 22 nagf_correg_ridge_opt
Ridge regression, optimizing a ridge regression parameter
g02kbf 22 nagf_correg_ridge
Ridge regression using a number of supplied ridge regression parameters
g02laf 22 nagf_correg_pls_svd
Partial least squares (PLS) regression using singular value decomposition
g02lbf 22 nagf_correg_pls_wold
Partial least squares (PLS) regression using Wold's iterative method
g02lcf 22 nagf_correg_pls_fit
PLS parameter estimates following partial least squares regression by g02laf or g02lbf
g02ldf 22 nagf_correg_pls_pred
PLS predictions based on parameter estimates from g02lcf
g02maf 25 nagf_correg_lars
Least angle regression (LARS), least absolute shrinkage and selection operator (LASSO) and forward stagewise regression
g02mbf 25 nagf_correg_lars_xtx
Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) and forward stagewise regression using the cross-products matrix
g02mcf 25 nagf_correg_lars_param
Calculates additional parameter estimates following Least Angle Regression (LARS), Least Absolute Shrinkage and Selection Operator (LASSO) or forward stagewise regression
g02qff 23 nagf_correg_quantile_linreg_easy
Linear quantile regression, simple interface, independent, identically distributed (IID) errors
g02qgf 23 nagf_correg_quantile_linreg
Linear quantile regression, comprehensive interface
g02zkf 23 nagf_correg_optset
Option setting routine for g02qgf
g02zlf 23 nagf_correg_optget
Option getting routine for g02qgf
g02jaf 21 (Deprecated) nagf_correg_mixeff_reml
Linear mixed effects regression using Restricted Maximum Likelihood (REML)
g02jbf 21 (Deprecated) nagf_correg_mixeff_ml
Linear mixed effects regression using Maximum Likelihood (ML)
g02jcf 23 (Deprecated) nagf_correg_mixeff_hier_init
Hierarchical mixed effects regression, initialization routine for g02jdf and g02jef
g02jdf 23 (Deprecated) nagf_correg_mixeff_hier_reml
Hierarchical mixed effects regression using Restricted Maximum Likelihood (REML)
g02jef 23 (Deprecated) nagf_correg_mixeff_hier_ml
Hierarchical mixed effects regression using Maximum Likelihood (ML)