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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {[@var{pval}, @var{t}, @var{df}] =} t_test_regression (@var{y}, @var{x}, @var{R}, @var{r}, @var{alt}) |
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19 ## Perform an t test for the null hypothesis @code{@var{R} * @var{b} = |
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20 ## @var{r}} in a classical normal regression model @code{@var{y} = |
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21 ## @var{X} * @var{b} + @var{e}}. Under the null, the test statistic @var{t} |
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22 ## follows a @var{t} distribution with @var{df} degrees of freedom. |
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23 ## |
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24 ## If @var{r} is omitted, a value of 0 is assumed. |
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25 ## |
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26 ## With the optional argument string @var{alt}, the alternative of |
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27 ## interest can be selected. If @var{alt} is @code{"!="} or |
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28 ## @code{"<>"}, the null is tested against the two-sided alternative |
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29 ## @code{@var{R} * @var{b} != @var{r}}. If @var{alt} is @code{">"}, the |
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30 ## one-sided alternative @code{@var{R} * @var{b} > @var{r}} is used. |
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31 ## Similarly for @var{"<"}. The default is the two-sided case. |
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32 ## |
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33 ## The p-value of the test is returned in @var{pval}. |
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34 ## |
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35 ## If no output argument is given, the p-value of the test is displayed. |
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36 ## @end deftypefn |
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37 |
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38 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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39 ## Description: Test one linear hypothesis in linear regression model |
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40 |
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41 function [pval, t, df] = t_test_regression (y, X, R, r, alt) |
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42 |
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43 if (nargin == 3) |
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44 r = 0; |
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45 alt = "!="; |
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46 elseif (nargin == 4) |
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47 if (isstr (r)) |
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48 alt = r; |
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49 r = 0; |
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50 else |
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51 alt = "!="; |
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52 endif |
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53 elseif !(nargin == 5) |
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54 usage (["[pval, t, df] ", ... |
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55 "= t_test_regression (y, X, R [, r] [, alt]"]); |
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56 endif |
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57 |
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58 if (! is_scalar (r)) |
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59 error ("t_test_regression: r must be a scalar"); |
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60 elseif (! isstr (alt)) |
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61 error ("t_test_regression: alt must be a string"); |
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62 endif |
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63 |
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64 [T, k] = size (X); |
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65 if !(is_vector (y) && (length (y) == T)) |
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66 error (["t_test_regression: ", ... |
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67 "y must be a vector of length rows (X)"]); |
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68 endif |
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69 s = size (R); |
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70 if !((max (s) == k) && (min (s) == 1)) |
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71 error (["t_test_regression: ", ... |
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72 "R must be a vector of length columns (X)"]); |
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73 endif |
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74 |
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75 R = reshape (R, 1, k); |
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76 y = reshape (y, T, 1); |
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77 [b, v] = ols (y, X); |
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78 df = T - k; |
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79 t = (R * b - r) / sqrt (v * R * inv (X' * X) * R'); |
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80 cdf = t_cdf (t, df); |
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81 |
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82 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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83 pval = 2 * min (cdf, 1 - cdf); |
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84 elseif strcmp (alt, ">") |
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85 pval = 1 - cdf; |
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86 elseif strcmp (alt, "<") |
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87 pval = cdf; |
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88 else |
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89 error ("t_test_regression: the value `%s' for alt is not possible", alt); |
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90 endif |
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91 |
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92 if (nargout == 0) |
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93 printf ("pval: %g\n", pval); |
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94 endif |
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95 |
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96 endfunction |
