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+/* PSPP - a program for statistical analysis.
+ Copyright (C) 2005 Free Software Foundation, Inc. Written by Jason H. Stover.
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see <http://www.gnu.org/licenses/>. */
+
+#ifndef LINREG_H
+#define LINREG_H
+#include <stdbool.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+
+struct variable;
+struct pspp_coeff;
+union value;
+
+enum
+{
+ PSPP_LINREG_CONDITIONAL_INVERSE,
+ PSPP_LINREG_QR,
+ PSPP_LINREG_SWEEP,
+};
+
+
+
+/*
+ Options describing what special values should be computed.
+ */
+struct pspp_linreg_opts_struct
+{
+ int get_depvar_mean_std;
+ int *get_indep_mean_std; /* Array of booleans
+ dictating which
+ independent variables need
+ their means and standard
+ deviations computed within
+ pspp_linreg. This array
+ MUST be of length
+ n_indeps. If element i is
+ 1, pspp_linreg will
+ compute the mean and
+ variance of indpendent
+ variable i. If element i
+ is 0, it will not compute
+ the mean and standard
+ deviation, and assume the
+ values are stored.
+ cache->indep_mean[i] is
+ the mean and
+ cache->indep_std[i] is the
+ sample standard deviation. */
+};
+typedef struct pspp_linreg_opts_struct pspp_linreg_opts;
+
+
+/*
+ Find the least-squares estimate of b for the linear model:
+
+ Y = Xb + Z
+
+ where Y is an n-by-1 column vector, X is an n-by-p matrix of
+ independent variables, b is a p-by-1 vector of regression coefficients,
+ and Z is an n-by-1 normally-distributed random vector with independent
+ identically distributed components with mean 0.
+
+ This estimate is found via the sweep operator or singular-value
+ decomposition with gsl.
+
+
+ References:
+
+ 1. Matrix Computations, third edition. GH Golub and CF Van Loan.
+ The Johns Hopkins University Press. 1996. ISBN 0-8018-5414-8.
+
+ 2. Numerical Analysis for Statisticians. K Lange. Springer. 1999.
+ ISBN 0-387-94979-8.
+
+ 3. Numerical Linear Algebra for Applications in Statistics. JE Gentle.
+ Springer. 1998. ISBN 0-387-98542-5.
+*/
+
+
+struct pspp_linreg_cache_struct
+{
+ int n_obs; /* Number of observations. */
+ int n_indeps; /* Number of independent variables. */
+ int n_coeffs; /* The intercept is not considered a
+ coefficient here. */
+
+ /*
+ The variable struct is ignored during estimation. It is here so
+ the calling procedure can find the variable used in the model.
+ */
+ const struct variable *depvar;
+
+ gsl_vector *residuals;
+ struct pspp_coeff **coeff;
+ double intercept;
+ int method; /* Method to use to estimate parameters. */
+ /*
+ Means and standard deviations of the variables.
+ If these pointers are null when pspp_linreg() is
+ called, pspp_linreg() will compute their values.
+
+ Entry i of indep_means is the mean of independent
+ variable i, whose observations are stored in the ith
+ column of the design matrix.
+ */
+ double depvar_mean;
+ double depvar_std;
+ gsl_vector *indep_means;
+ gsl_vector *indep_std;
+
+ /*
+ Sums of squares.
+ */
+ double ssm; /* Sums of squares for the overall model. */
+ gsl_vector *ss_indeps; /* Sums of squares from each
+ independent variable. */
+ double sst; /* Sum of squares total. */
+ double sse; /* Sum of squares error. */
+ double mse; /* Mean squared error. This is just sse /
+ dfe, but since it is the best unbiased
+ estimate of the population variance, it
+ has its own entry here. */
+ gsl_vector *ssx; /* Centered sums of squares for independent
+ variables, i.e. \sum (x[i] - mean(x))^2. */
+ double ssy; /* Centered sums of squares for dependent
+ variable.
+ */
+ /*
+ Covariance matrix of the parameter estimates.
+ */
+ gsl_matrix *cov;
+ /*
+ Degrees of freedom.
+ */
+ double dft;
+ double dfe;
+ double dfm;
+
+ /*
+ 'Hat' or Hessian matrix, i.e. (X'X)^{-1}, where X is our
+ design matrix.
+ */
+ gsl_matrix *hat;
+
+ double (*predict) (const struct variable **, const union value **,
+ const void *, int);
+ double (*residual) (const struct variable **,
+ const union value **,
+ const union value *, const void *, int);
+ /*
+ Returns pointers to the variables used in the model.
+ */
+ int (*get_vars) (const void *, const struct variable **);
+ struct variable *resid;
+ struct variable *pred;
+
+};
+
+typedef struct pspp_linreg_cache_struct pspp_linreg_cache;
+
+
+
+/*
+ Allocate a pspp_linreg_cache and return a pointer
+ to it. n is the number of cases, p is the number of
+ independent variables.
+ */
+pspp_linreg_cache *pspp_linreg_cache_alloc (size_t n, size_t p);
+
+bool pspp_linreg_cache_free (void *);
+
+/*
+ Fit the linear model via least squares. All pointers passed to pspp_linreg
+ are assumed to be allocated to the correct size and initialized to the
+ values as indicated by opts.
+ */
+int
+pspp_linreg (const gsl_vector * Y, const gsl_matrix * X,
+ const pspp_linreg_opts * opts, pspp_linreg_cache * cache);
+
+double
+pspp_linreg_predict (const struct variable **, const union value **,
+ const void *, int);
+double
+pspp_linreg_residual (const struct variable **, const union value **,
+ const union value *, const void *, int);
+/*
+ All variables used in the model.
+ */
+int pspp_linreg_get_vars (const void *, const struct variable **);
+
+const struct pspp_coeff *pspp_linreg_get_coeff (const pspp_linreg_cache
+ *,
+ const struct variable
+ *,
+ const union value *);
+#endif
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