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1 ## Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2006, |
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2 ## 2007 Kurt Hornik |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{pval}, @var{t}, @var{df}] =} t_test_regression (@var{y}, @var{x}, @var{rr}, @var{r}, @var{alt}) |
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22 ## Perform an t test for the null hypothesis @code{@var{rr} * @var{b} = |
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23 ## @var{r}} in a classical normal regression model @code{@var{y} = |
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24 ## @var{x} * @var{b} + @var{e}}. Under the null, the test statistic @var{t} |
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25 ## follows a @var{t} distribution with @var{df} degrees of freedom. |
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26 ## |
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27 ## If @var{r} is omitted, a value of 0 is assumed. |
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28 ## |
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29 ## With the optional argument string @var{alt}, the alternative of |
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30 ## interest can be selected. If @var{alt} is @code{"!="} or |
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31 ## @code{"<>"}, the null is tested against the two-sided alternative |
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32 ## @code{@var{rr} * @var{b} != @var{r}}. If @var{alt} is @code{">"}, the |
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33 ## one-sided alternative @code{@var{rr} * @var{b} > @var{r}} is used. |
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34 ## Similarly for @var{"<"}, the one-sided alternative @code{@var{rr} * |
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35 ## @var{b} < @var{r}} is used. The default is the two-sided case. |
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36 ## |
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37 ## The p-value of the test is returned in @var{pval}. |
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38 ## |
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39 ## If no output argument is given, the p-value of the test is displayed. |
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40 ## @end deftypefn |
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41 |
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42 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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43 ## Description: Test one linear hypothesis in linear regression model |
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44 |
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45 function [pval, t, df] = t_test_regression (y, X, R, r, alt) |
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46 |
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47 if (nargin == 3) |
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48 r = 0; |
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49 alt = "!="; |
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50 elseif (nargin == 4) |
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51 if (ischar (r)) |
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52 alt = r; |
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53 r = 0; |
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54 else |
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55 alt = "!="; |
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56 endif |
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57 elseif (! (nargin == 5)) |
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58 print_usage (); |
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59 endif |
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60 |
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61 if (! isscalar (r)) |
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62 error ("t_test_regression: r must be a scalar"); |
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63 elseif (! ischar (alt)) |
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64 error ("t_test_regression: alt must be a string"); |
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65 endif |
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66 |
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67 [T, k] = size (X); |
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68 if (! (isvector (y) && (length (y) == T))) |
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69 error ("t_test_regression: y must be a vector of length rows (X)"); |
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70 endif |
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71 s = size (R); |
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72 if (! ((max (s) == k) && (min (s) == 1))) |
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73 error ("t_test_regression: R must be a vector of length columns (X)"); |
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74 endif |
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75 |
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76 R = reshape (R, 1, k); |
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77 y = reshape (y, T, 1); |
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78 [b, v] = ols (y, X); |
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79 df = T - k; |
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80 t = (R * b - r) / sqrt (v * R * inv (X' * X) * R'); |
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81 cdf = t_cdf (t, df); |
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82 |
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83 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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84 pval = 2 * min (cdf, 1 - cdf); |
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85 elseif strcmp (alt, ">") |
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86 pval = 1 - cdf; |
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87 elseif strcmp (alt, "<") |
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88 pval = cdf; |
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89 else |
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90 error ("t_test_regression: the value `%s' for alt is not possible", alt); |
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91 endif |
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92 |
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93 if (nargout == 0) |
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94 printf ("pval: %g\n", pval); |
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95 endif |
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96 |
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97 endfunction |
