164 lines
5.2 KiB
Mathematica
164 lines
5.2 KiB
Mathematica
(All default values mentioned here are set by loess_setup().)
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struct loess_struct *lo;
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in
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n: number of observations.
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p: number of numeric predictors.
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y: vector of response (length n).
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x: vector of predictors, of length (n * p).
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The j-th coordinate of the i-th point is in x[i+n*j],
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where 0<=j<p, 0<=i<n.
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weights: vector of weights to be given to individual
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observations in the sum of squared residuals that
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forms the local fitting criterion.
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By default, an unweighted fit is carried out.
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If supplied, weights should be a non-negative
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numeric vector. If the different observations
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have non-equal variances, weights should be
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inversely proportional to the variances.
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model
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span: smoothing parameter. Default is 0.75.
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degree: overall degree of locally-fitted polynomial. 1 is
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locally-linear fitting and 2 is locally-quadratic
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fitting. Default is 2.
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normalize: logical that determines if numeric predictors should
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be normalized. If TRUE (1) - the default - the
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standard normalization is used. If FALSE (0), no
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normalization is carried out.
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parametric: for two or more numeric predictors, this argument
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specifies those variables that should be
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conditionally-parametric. The argument should be a
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logical vector of length p, specified in the order
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of the predictor group ordered in x.
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Default is a vector of 0's of length p.
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drop_square: for cases with degree = 2, and with two or more
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numeric predictors, this argument specifies those
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numeric predictors whose squares should be dropped
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from the set of fitting variables. The method of
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specification is the same as for parametric.
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Default is a vector of 0's of length p.
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family: the assumed distribution of the errors. The values
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are "gaussian" or "symmetric". The first value is
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the default. If the second value is specified,
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a robust fitting procedure is used.
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control
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surface: determines whether the fitted surface is computed
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directly at all points ("direct") or whether an
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interpolation method is used ("interpolate").
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The latter, the default, is what most users should
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use unless special circumstances warrant.
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statistics: determines whether the statistical quantities are
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computed exactly ("exact") or approximately
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("approximate"). The latter is the default. The former
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should only be used for testing the approximation in
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statistical development and is not meant for routine
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usage because computation time can be horrendous.
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cell: if interpolation is used to compute the surface, this
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argument specifies the maximum cell size of the k-d
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tree. Suppose k = floor(n*cell*span) where n is the
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number of observations. Then a cell is further
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divided if the number of observations within it
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is greater than or equal to k.
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trace_hat: when surface is "approximate", determines the
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computational method used to compute the trace of
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the hat matrix, which is used in the computation of
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the statistical quantities. If "exact", an exact
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computation is done; normally this goes quite fast
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on the fastest machines until n, the number of
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observations is 1000 or more, but for very slow
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machines, things can slow down at n = 300.
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If "wait.to.decide" is selected, then a default
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is chosen in loess(); the default is "exact" for
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n < 500 and "approximate" otherwise. If surface
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is "exact", an exact computation is always done
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for the trace. Set trace_hat to "approximate" for
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large dataset will substantially reduce the
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computation time.
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iterations: if family is "symmetric", the number of iterations
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of the robust fitting method. Default is 0 for
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family being "gaussian" by default.
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kd_tree: k-d tree, an output of loess().
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out
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fitted_values: fitted values of the local regression model
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fitted_residuals: residuals of the local regression fit
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enp: equivalent number of parameters.
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s: estimate of the scale of the residuals.
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one_delta: a statistical parameter used in the computation of
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standard errors.
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two_delta: a statistical parameter used in the computation of
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standard errors.
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pseudovalues: adjusted values of the response when robust
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estimation is used.
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trace_hat: trace of the operator hat matrix.
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diagonal: diagonal of the operator hat matrix.
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robust: robustness weights for robust fitting.
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divisor: normalization divisor for numeric predictors.
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struct pred_struct *pre;
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fit: the evaluated loess surface at eval.
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se_fit: estimates of the standard errors of the surface values.
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residual_scale: estimate of the scale of the residuals.
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df: the degrees of freedom of the t-distribution used to
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compute pointwise confidence intervals for the
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evaluated surface.
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struct anova_struct *aov;
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dfn: degrees of freedom of the numerator.
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dfd: degrees of freedom of the denominator.
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F_values: F statistic.
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Pr_F: probability F_value is exceeded if null hypothesis
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is true.
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struct ci_struct *ci;
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fit: the evaluated loess surface at eval (see pred_struct).
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upper: upper limits of pointwise confidence intervals.
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lower: lower limits of pointwise confidence intervals.
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