added references to bootlm help documentation and function reference

inst/bootlm.m

@@ -36,7 +36,7 @@
 %        By default, confidence intervals and Null Hypothesis Significance Tests
 %     (NHSTs) for the regression coefficients (H0 = 0) are calculated by wild
 %     bootstrap-t and are robust when normality and homoscedasticity cannot be
-%     assumed.
+%     assumed [1].
 %
 %        Usage of this function is very similar to that of 'anovan'. Data (Y)
 %     is a numeric variable, and the predictor(s) are specified in GROUP (a.k.a.
@@ -115,11 +115,11 @@
 %
 %             o 'wild' (default): Wild bootstrap-t, using the 'bootwild'
 %               function. Please see the help documentation below and in the
-%               function 'bootwild' for more information about this method.
+%               function 'bootwild' for more information about this method [1].
 %
 %             o 'bayesian': Bayesian bootstrap, using the 'bootbayes' function.
 %                Please see the help documentation below and in the function
-%               'bootbayes' for more information about this method.
+%               'bootbayes' for more information about this method [2].
 %
 %             Note that p-values are a frequentist concept and are only computed
 %             and returned from bootlm when the METHOD is 'wild'. Since the wild
@@ -144,7 +144,7 @@
 %
 %             o 'auto': Sets a value for PRIOR that effectively incorporates
 %                  Bessel's correction a priori such that the variance of the
-%                  posterior (i.e. the rows of BOOTSTAT) becomes an unbiased
+%                  posterior (i.e. of the rows of BOOTSTAT) becomes an unbiased
 %                  estimator of the sampling variance*. The calculation used for
 %                  'auto' is as follows:
 % 
@@ -166,7 +166,7 @@
 %               to Bayes rule: a uniform (or flat) Dirichlet distribution
 %               (over all points in its support). Please see the help
 %               documentation for the function 'bootbayes' for more information
-%               about the prior.
+%               about the prior [2].
 %
 %     '[...] = bootlm (Y, GROUP, ..., 'alpha', ALPHA)'
 %
@@ -177,16 +177,16 @@
 %             o scalar: Set the central mass of the intervals to 100*(1-ALPHA)%.
 %                  For example, 0.05 for a 95% interval. If METHOD is 'wild',
 %                  then the intervals are symmetric bootstrap-t confidence
-%                  intervals. If METHOD is 'bayesian', then the intervals are
-%                  shortest probability credible intervals.
+%                  intervals [1]. If METHOD is 'bayesian', then the intervals
+%                  are shortest probability credible intervals [2].
 %
 %             o vector: A pair of probabilities defining the lower and upper
 %                  and upper bounds of the interval(s) as 100*(ALPHA(1))% and 
 %                  100*(ALPHA(2))% respectively. For example, [.025, .975] for
 %                  a 95% interval. If METHOD is 'wild', then the intervals are
-%                  asymmetric bootstrap-t confidence intervals. If METHOD is
+%                  asymmetric bootstrap-t confidence intervals [1]. If METHOD is
 %                  'bayesian', then the intervals are simple percentile credible
-%                  intervals.
+%                  intervals [2].
 %
 %               The default value of ALPHA is the scalar: 0.05.
 %
@@ -391,7 +391,7 @@
 %       - 'CI_lower': The lower bound(s) of the confidence/credible interval(s)
 %       - 'CI_upper': The upper bound(s) of the confidence/credible interval(s)
 %       - 'pval': The p-value(s) for the hypothesis that the estimate(s) == 0
-%       - 'fpr': The minimum false positive risk (FPR) for each p-value
+%       - 'fpr': The minimum false positive risk (FPR) for each p-value [3].
 %       - 'N': The number of independent sampling units used to compute CIs
 %       - 'prior': The prior used for Bayesian bootstrap. This will return a
 %                  scalar for regression coefficients, or a P x 1 or P x 2
@@ -424,7 +424,7 @@
 %       - 'MS': Mean-squares
 %       - 'F': F-Statistic
 %       - 'PVAL': p-values
-%       - 'FPR': The minimum false positive risk for each p-value
+%       - 'FPR': The minimum false positive risk for each p-value [3]
 %       - 'SSE': Sum-of-Squared Error
 %       - 'DFE': Degrees of Freedom for Error
 %       - 'MSE': Mean Squared Error
@@ -438,8 +438,8 @@
 %       the method used is 'wild' bootstrap AND when no other statistics are
 %       requested (i.e. estimated marginal means or posthoc tests). The
 %       bootstrap is achieved by wild bootstrap of the residuals from the full
-%       model. Computations of the statistics in AOVSTAT are compatible with
-%       the 'clustid' and 'blocksz' options.
+%       model [1,4]. Computations of the statistics in AOVSTAT are compatible
+%       with the 'clustid' and 'blocksz' options.
 %
 %       The bootlm function treats all model predictors as fixed effects during
 %       ANOVA tests. While any type of predictor, be it a fixed effect or
@@ -457,13 +457,13 @@
 %          sample sizes are equal or not.
 %
 %     '[STATS, BOOTSTAT, AOVSTAT, PRED_ERR] = bootlm (...)' also computes
-%     refined bootstrap estimates of prediction error* and returns the derived
-%     statistics in a structure with the following fields:
+%     refined bootstrap estimates of prediction error* and returns statistics
+%     derived from it in a structure containing the following fields:
 %       - 'MODEL': The formula of the linear model(s) in Wilkinson's notation
-%       - 'PE': Bootstrap estimate of prediction error
+%       - 'PE': Bootstrap estimate of prediction error [5]
 %       - 'PRESS': Bootstrap estimate of predicted residual error sum of squares
 %       - 'RSQ_pred': Bootstrap estimate of predicted R-squared
-%       - 'EIC': Extended (Efron) Information Criterion
+%       - 'EIC': Extended (Efron) Information Criterion [6]
 %       - 'RL': Relative likelihood (compared to the intercept-only model)
 %       - 'Wt': EIC expressed as weights
 %
@@ -485,6 +485,24 @@
 %     regression coefficients (b), the hypothesis matrix (L) and the outcome (Y)
 %     for the linear model.
 %
+%  Bibliography:
+%  [1] Penn, A.C. statistics-resampling manual: `bootwild` function reference.
+%        https://gnu-octave.github.io/statistics-resampling/function/bootwild.html 
+%        and references therein. Last accessed 02 Sept 2024.
+%  [2] Penn, A.C. statistics-resampling manual: `bootbayes` function reference.
+%        https://gnu-octave.github.io/statistics-resampling/function/bootbayes.html
+%        and references therein. Last accessed 02 Sept 2024.
+%  [3] David Colquhoun (2019) The False Positive Risk: A Proposal Concerning
+%        What to Do About p-Values, The American Statistician, 73:sup1, 192-201
+%  [4] ter Braak (1992) Permutation versus bootstrap significance test in
+%        multiple regression and ANOVA. In Jockel et al (Eds.) Bootstrapping
+%        and Related Techniques. Springer-Verlag, Berlin, pg 79-86
+%  [5] Efron and Tibshirani (1993) An Introduction to the Bootstrap. 
+%        New York, NY: Chapman & Hall. pg 247-252
+%  [6] Konishi & Kitagawa (2008), "Bootstrap Information Criterion" In: 
+%        Information Criteria and Statistical Modeling. Springer Series in
+%        Statistics. Springer, NY.
+%
 %  bootlm (version 2024.07.08)
 %  Author: Andrew Charles Penn
 %  https://www.researchgate.net/profile/Andrew_Penn/