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1 Locfit, Matlab 2.01
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2 http://locfit.herine.net/
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3
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4 April 2, 2007
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5
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6
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7
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8 Attaching:
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9
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10 Make sure that you've added this directory recursively (i.e. with
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11 all subdirectories) to your matlab search path.
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12
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13 Basic usage:
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14
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15 (1) To plot of a smooth curve:
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16 load ethanol; % load the dataset.
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17 fit = locfit(E,NOx) % local regression, with x,y vectors.
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18 lfplot(fit) % plot the fitted curve.
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19
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20 (2a) To evaluate smooth at a specified set of points:
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21 load ethanol;
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22 xev = [0.6 0.7 0.8 0.9]'; % note column vector.
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23 fit = locfit(E,NOx,'ev',xev);
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24 yhat = predict(fit)
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25
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26 (2b) Fit and interpolate approximation; may be faster for large datasets.
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27 load ethanol;
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28 xev = [0.6 0.7 0.8 0.9]'; % note column vector.
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29 fit = locfit(E,NOx);
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30 yhat = predict(fit,xev)
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31
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32 (3) Surface smoothing - give matrix as first input.
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33 load ethanol; % load the dataset.
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34 fit = locfit([E C],NOx) % local regression.
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35 lfplot(fit)
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36
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37
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38 Most of the arguments to the S (and R) locfit() function, described
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39 in my book, will also work in the Matlab version. E.g,
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40 fit = locfit(E,NOx,'deg',1,'kern','gauss')
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41 % local linear fit with the gaussian kernel.
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42 Smoothing parameters can be set with 'nn' and 'h', instead of the
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43 alpha vector used in my book. So
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44 fit = locfit(E,NOx,'alpha',[0 0.2])
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45 fit = locfit(E,NOx,'h',0.2)
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46 are equivalent ways to specify a constant bandwidth h=0.2.
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47
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48
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49 The Book subdirectory contains functions to reproduce most of the book
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50 figures. Run them, and look at the source code (many around 5 lines or less)
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51 for more examples.
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52
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53
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54 Some differences with the S/R version (and book documentation).
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55 (1) Minor renaming of functions, mainly because matlab doesn't have
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56 S-style methods. e.g. lfplot() instead of plot() or plot.locfit().
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57 (2) Use lfband() to add confidence bands to a plot.
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58 (3) Functions such as aicplot(), gcvplot() sensitive to order of
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59 arguments. Smoothing parameter matrix must be given first.
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60 (4) For 2-d predictors, lfplot() defaults to producing a surface, rather
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61 than contour, plot.
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62 (5) The predict() function has an optional 'direct' argument, which
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63 causes the fit to be recomputed at each evaluation point, rather
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64 than interpolation of existing points.
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65 (6) A few things aren't implemented yet...
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66
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67
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68 Technical stuff. Here's the layout of the structure returned by
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69 the locfit() function. The first three components (data, evaluation
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70 structure and smoothing parameters) are what you provide, or default
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71 values. The last two (fit points, parametric component) are what
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72 locfit computes. The expected size or format of the entry is
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73 given in parentheses.
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74
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75
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76 fit.data.x (n*d)
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77 fit.data.y (n*1)
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78 fit.data.weights (n*1 or 1*1)
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79 fit.data.censor (n*1 or 1*1)
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80 fit.data.baseline (n*1 or 1*1)
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81 fit.data.style (string length d)
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82 fit.data.scales (1*d)
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83 fit.data.xlim (2*d)
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84
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85 fit.evaluation_structure.type (string)
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86 fit.evaluation_structure.module (string)
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87 fit.evaluation_structure.lower_left (numeric 1*d)
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88 fit.evaluation_structure.upper_right (numeric 1*d)
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89 fit.evaluation_structure.grid (numeric 1*d)
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90 fit.evaluation_structure.cut (numeric 1*d)
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91 fit.evaluation_structure.maxk
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92 fit.evaluation_structure.derivative
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93
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94 fit.smoothing_parameters.alpha = (nn h pen) vector
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95 fit.smoothing_parameters.adaptive_criterion (string)
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96 fit.smoothing_parameters.degree (numeric)
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97 fit.smoothing_parameters.family (string)
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98 fit.smoothing_parameters.link (string)
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99 fit.smoothing_parameters.kernel (string)
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100 fit.smoothing_parameters.kernel_type (string)
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101 fit.smoothing_parameters.deren
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102 fit.smoothing_parameters.deit
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103 fit.smoothing_parameters.demint
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104 fit.smoothing_parameters.debug
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105
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106 fit.fit_points.evaluation_points (d*nv matrix)
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107 fit.fit_points.fitted_values (matrix, nv rows, many columns)
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108 fit.fit_points.evaluation_vectors
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109 fit.fit_points.fit_limits (d*2 matrix)
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110 fit.fit_points.family_link (numeric values)
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111 fit.fit_points.kappa (likelihood, degrees of freedom, etc)
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112
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113 fit.parametric_component
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114
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115
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116
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117
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118
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119 This was the OLD format:
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120
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121 +-{1} data
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122 | +-{1} xdata matrix (n*d)
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123 | +-{2} ydata column vector (n*1)
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124 | +-{3} wdata weight vector (n*1 or 1*1)
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125 | +-{4} cdata censoring vector (n*1 or 1*1)
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126 | +-{5} base baseline vector (n*1 or 1*1)
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127 | +-{6} style vector (string length d)
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128 | +-{7} scales vector (1*d)
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129 | +-{8} xl xlim vector (2*d)
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130 |
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131 +-{2} evaluation structure
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132 | +-{1} structure type (string)
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133 | +-{2} module (string)
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134 | +-{3} ll corner of bounding box (numeric 1*d)
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135 | +-{4} ur corner of bounding box (numeric 1*d)
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136 | +-{5} mg vector for grid (numeric 1*d)
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137 | +-{6} cut parameter for adaptive structures (numeric 1*d)
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138 | +-{7} maxk memory control parameter
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139 | +-{8} derivative vector
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140 |
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141 +-{3} sp smoothing parameters
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142 | +-{1} alpha = (nn h pen) vector
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143 | +-{2} adaptive criterion (string)
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144 | +-{3} local polynomial degree (numeric)
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145 | +-{4} fitting family (string)
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146 | +-{5} link (string)
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147 | +-{6} kernel (string)
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148 | +-{7} kernel type - product, spherical (string)
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149 |
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150 +-{4} fpc fit points
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151 | +-{1} evaluation points, d*nv matrix.
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152 | +-{2} fitted values etc, (matrix, nv rows, many columns)
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153 | +-{3} cell of vectors generated by evaluation structure.
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154 | | +-{1} ce integer vector.
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155 | | +-{2} s integer vector.
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156 | | +-{3} lo integer vector.
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157 | | +-{4} hi integer vector.
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158 | |
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159 | +-{4} fit limits (d*2 matrix)
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160 | +-{5} [family link] (numeric values)
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161 | +-{6} 'kappa' vector. (likelihood, degrees of freedom, etc)
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162 |
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163 +-{5} parametric component vector.
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