1 /* PSPP - a program for statistical analysis.
2 Copyright (C) 2005, 2011 Free Software Foundation, Inc. Written by Jason H. Stover.
4 This program is free software: you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation, either version 3 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program. If not, see <http://www.gnu.org/licenses/>. */
20 #include <gsl/gsl_math.h>
21 #include <gsl/gsl_matrix.h>
22 #include <gsl/gsl_vector.h>
27 LINREG_CONDITIONAL_INVERSE
,
35 Options describing what special values should be computed.
37 struct pspp_linreg_opts_struct
39 int get_depvar_mean_std
;
40 int *get_indep_mean_std
; /* Array of booleans
42 independent variables need
43 their means and standard
44 deviations computed within
45 pspp_linreg. This array
47 n_indeps. If element i is
50 variance of indpendent
51 variable i. If element i
52 is 0, it will not compute
54 deviation, and assume the
56 cache->indep_mean[i] is
58 cache->indep_std[i] is the
59 sample standard deviation. */
61 typedef struct pspp_linreg_opts_struct pspp_linreg_opts
;
65 Find the least-squares estimate of b for the linear model:
69 where Y is an n-by-1 column vector, X is an n-by-p matrix of
70 independent variables, b is a p-by-1 vector of regression coefficients,
71 and Z is an n-by-1 normally-distributed random vector with independent
72 identically distributed components with mean 0.
74 This estimate is found via the sweep operator or singular-value
75 decomposition with gsl.
80 1. Matrix Computations, third edition. GH Golub and CF Van Loan.
81 The Johns Hopkins University Press. 1996. ISBN 0-8018-5414-8.
83 2. Numerical Analysis for Statisticians. K Lange. Springer. 1999.
86 3. Numerical Linear Algebra for Applications in Statistics. JE Gentle.
87 Springer. 1998. ISBN 0-387-98542-5.
93 double n_obs
; /* Number of observations. */
94 int n_indeps
; /* Number of independent variables. */
95 int n_coeffs
; /* The intercept is not considered a
99 Pointers to the variables.
101 const struct variable
*depvar
;
102 const struct variable
**indep_vars
;
106 int method
; /* Method to use to estimate parameters. */
108 Means and standard deviations of the variables.
109 If these pointers are null when pspp_linreg() is
110 called, pspp_linreg() will compute their values.
112 Entry i of indep_means is the mean of independent
113 variable i, whose observations are stored in the ith
114 column of the design matrix.
117 gsl_vector
*indep_means
;
118 gsl_vector
*indep_std
;
123 double ssm
; /* Sums of squares for the overall model. */
124 double sst
; /* Sum of squares total. */
125 double sse
; /* Sum of squares error. */
126 double mse
; /* Mean squared error. This is just sse /
127 dfe, but since it is the best unbiased
128 estimate of the population variance, it
129 has its own entry here. */
131 Covariance matrix of the parameter estimates.
141 int dependent_column
; /* Column containing the dependent variable. Defaults to last column. */
145 typedef struct linreg_struct linreg
;
149 linreg
*linreg_alloc (const struct variable
*, const struct variable
**,
152 void linreg_unref (linreg
*);
153 void linreg_ref (linreg
*);
156 Fit the linear model via least squares. All pointers passed to pspp_linreg
157 are assumed to be allocated to the correct size and initialized to the
158 values as indicated by opts.
160 void linreg_fit (const gsl_matrix
*, linreg
*);
162 double linreg_predict (const linreg
*, const double *, size_t);
163 double linreg_residual (const linreg
*, double, const double *, size_t);
164 const struct variable
** linreg_get_vars (const linreg
*);
167 Mean of the independent variable.
169 double linreg_get_indep_variable_mean (const linreg
*, size_t);
170 void linreg_set_indep_variable_mean (linreg
*, size_t, double);
172 double linreg_mse (const linreg
*);
174 double linreg_intercept (const linreg
*);
176 const gsl_matrix
* linreg_cov (const linreg
*);
177 double linreg_coeff (const linreg
*, size_t);
178 const struct variable
* linreg_indep_var (const linreg
*, size_t);
179 size_t linreg_n_coeffs (const linreg
*);
180 double linreg_n_obs (const linreg
*);
181 double linreg_sse (const linreg
*);
182 double linreg_ssreg (const linreg
*);
183 double linreg_dfmodel (const linreg
*);
184 double linreg_sst (const linreg
*);
185 void linreg_set_depvar_mean (linreg
*, double);
186 double linreg_get_depvar_mean (const linreg
*);