@@ -45,6 +45,7 @@ <h2>bootlm</h2>
4545 -- Function File: [STATS, BOOTSTAT] = bootlm (...)
4646 -- Function File: [STATS, BOOTSTAT, AOVSTAT] = bootlm (...)
4747 -- Function File: [STATS, BOOTSTAT, AOVSTAT, PRED_ERR] = bootlm (...)
48+ -- Function File: [STATS, BOOTSTAT, AOVSTAT, PRED_ERR, X] = bootlm (...)
4849
4950 Fits a linear model with categorical and/or continuous predictors (i.e.
5051 independent variables) on a continuous outcome (i.e. dependent variable)
@@ -57,7 +58,7 @@ <h2>bootlm</h2>
5758 By default, confidence intervals and Null Hypothesis Significance Tests
5859 (NHSTs) for the regression coefficients (H0 = 0) are calculated by wild
5960 bootstrap-t and are robust when normality and homoscedasticity cannot be
60- assumed.
61+ assumed [1] .
6162
6263 Usage of this function is very similar to that of 'anovan'. Data (Y)
6364 is a numeric variable, and the predictor(s) are specified in GROUP (a.k.a.
@@ -136,11 +137,11 @@ <h2>bootlm</h2>
136137
137138 o 'wild' (default): Wild bootstrap-t, using the 'bootwild'
138139 function. Please see the help documentation below and in the
139- function 'bootwild' for more information about this method.
140+ function 'bootwild' for more information about this method [1] .
140141
141142 o 'bayesian': Bayesian bootstrap, using the 'bootbayes' function.
142143 Please see the help documentation below and in the function
143- 'bootbayes' for more information about this method.
144+ 'bootbayes' for more information about this method [2] .
144145
145146 Note that p-values are a frequentist concept and are only computed
146147 and returned from bootlm when the METHOD is 'wild'. Since the wild
@@ -165,7 +166,7 @@ <h2>bootlm</h2>
165166
166167 o 'auto': Sets a value for PRIOR that effectively incorporates
167168 Bessel's correction a priori such that the variance of the
168- posterior (i.e. the rows of BOOTSTAT) becomes an unbiased
169+ posterior (i.e. of the rows of BOOTSTAT) becomes an unbiased
169170 estimator of the sampling variance*. The calculation used for
170171 'auto' is as follows:
171172
@@ -187,7 +188,7 @@ <h2>bootlm</h2>
187188 to Bayes rule: a uniform (or flat) Dirichlet distribution
188189 (over all points in its support). Please see the help
189190 documentation for the function 'bootbayes' for more information
190- about the prior.
191+ about the prior [2] .
191192
192193 '[...] = bootlm (Y, GROUP, ..., 'alpha', ALPHA)'
193194
@@ -198,16 +199,16 @@ <h2>bootlm</h2>
198199 o scalar: Set the central mass of the intervals to 100*(1-ALPHA)%.
199200 For example, 0.05 for a 95% interval. If METHOD is 'wild',
200201 then the intervals are symmetric bootstrap-t confidence
201- intervals. If METHOD is 'bayesian', then the intervals are
202- shortest probability credible intervals.
202+ intervals [1] . If METHOD is 'bayesian', then the intervals
203+ are shortest probability credible intervals [2] .
203204
204205 o vector: A pair of probabilities defining the lower and upper
205206 and upper bounds of the interval(s) as 100*(ALPHA(1))% and
206207 100*(ALPHA(2))% respectively. For example, [.025, .975] for
207208 a 95% interval. If METHOD is 'wild', then the intervals are
208- asymmetric bootstrap-t confidence intervals. If METHOD is
209+ asymmetric bootstrap-t confidence intervals [1] . If METHOD is
209210 'bayesian', then the intervals are simple percentile credible
210- intervals.
211+ intervals [2] .
211212
212213 The default value of ALPHA is the scalar: 0.05.
213214
@@ -412,7 +413,7 @@ <h2>bootlm</h2>
412413 - 'CI_lower': The lower bound(s) of the confidence/credible interval(s)
413414 - 'CI_upper': The upper bound(s) of the confidence/credible interval(s)
414415 - 'pval': The p-value(s) for the hypothesis that the estimate(s) == 0
415- - 'fpr': The minimum false positive risk (FPR) for each p-value
416+ - 'fpr': The minimum false positive risk (FPR) for each p-value [3].
416417 - 'N': The number of independent sampling units used to compute CIs
417418 - 'prior': The prior used for Bayesian bootstrap. This will return a
418419 scalar for regression coefficients, or a P x 1 or P x 2
@@ -445,7 +446,7 @@ <h2>bootlm</h2>
445446 - 'MS': Mean-squares
446447 - 'F': F-Statistic
447448 - 'PVAL': p-values
448- - 'FPR': The minimum false positive risk for each p-value
449+ - 'FPR': The minimum false positive risk for each p-value [3]
449450 - 'SSE': Sum-of-Squared Error
450451 - 'DFE': Degrees of Freedom for Error
451452 - 'MSE': Mean Squared Error
@@ -459,8 +460,8 @@ <h2>bootlm</h2>
459460 the method used is 'wild' bootstrap AND when no other statistics are
460461 requested (i.e. estimated marginal means or posthoc tests). The
461462 bootstrap is achieved by wild bootstrap of the residuals from the full
462- model. Computations of the statistics in AOVSTAT are compatible with
463- the 'clustid' and 'blocksz' options.
463+ model [1,4] . Computations of the statistics in AOVSTAT are compatible
464+ with the 'clustid' and 'blocksz' options.
464465
465466 The bootlm function treats all model predictors as fixed effects during
466467 ANOVA tests. While any type of predictor, be it a fixed effect or
@@ -478,13 +479,13 @@ <h2>bootlm</h2>
478479 sample sizes are equal or not.
479480
480481 '[STATS, BOOTSTAT, AOVSTAT, PRED_ERR] = bootlm (...)' also computes
481- refined bootstrap estimates of prediction error* and returns the derived
482- statistics in a structure with the following fields:
482+ refined bootstrap estimates of prediction error* and returns statistics
483+ derived from it in a structure containing the following fields:
483484 - 'MODEL': The formula of the linear model(s) in Wilkinson's notation
484- - 'PE': Bootstrap estimate of prediction error
485+ - 'PE': Bootstrap estimate of prediction error [5]
485486 - 'PRESS': Bootstrap estimate of predicted residual error sum of squares
486487 - 'RSQ_pred': Bootstrap estimate of predicted R-squared
487- - 'EIC': Extended (Efron) Information Criterion
488+ - 'EIC': Extended (Efron) Information Criterion [6]
488489 - 'RL': Relative likelihood (compared to the intercept-only model)
489490 - 'Wt': EIC expressed as weights
490491
@@ -501,7 +502,30 @@ <h2>bootlm</h2>
501502 installed and loaded, then these computations will be automatically
502503 accelerated by parallel processing on platforms with multiple processors
503504
504- bootlm (version 2024.05.17)
505+ '[STATS, BOOTSTAT, AOVSTAT, PRED_ERR, MAT] = bootlm (...)' also returns
506+ a structure containing the design matrix of the predictors (X), the
507+ regression coefficients (b), the hypothesis matrix (L) and the outcome (Y)
508+ for the linear model.
509+
510+ Bibliography:
511+ [1] Penn, A.C. statistics-resampling manual: `bootwild` function reference.
512+ https://gnu-octave.github.io/statistics-resampling/function/bootwild.html
513+ and references therein. Last accessed 02 Sept 2024.
514+ [2] Penn, A.C. statistics-resampling manual: `bootbayes` function reference.
515+ https://gnu-octave.github.io/statistics-resampling/function/bootbayes.html
516+ and references therein. Last accessed 02 Sept 2024.
517+ [3] David Colquhoun (2019) The False Positive Risk: A Proposal Concerning
518+ What to Do About p-Values, The American Statistician, 73:sup1, 192-201
519+ [4] ter Braak (1992) Permutation versus bootstrap significance test in
520+ multiple regression and ANOVA. In Jockel et al (Eds.) Bootstrapping
521+ and Related Techniques. Springer-Verlag, Berlin, pg 79-86
522+ [5] Efron and Tibshirani (1993) An Introduction to the Bootstrap.
523+ New York, NY: Chapman & Hall. pg 247-252
524+ [6] Konishi & Kitagawa (2008), "Bootstrap Information Criterion" In:
525+ Information Criteria and Statistical Modeling. Springer Series in
526+ Statistics. Springer, NY.
527+
528+ bootlm (version 2024.07.08)
505529 Author: Andrew Charles Penn
506530 https://www.researchgate.net/profile/Andrew_Penn/
507531
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