From 2eedd1882b31f80d60bf0ce7f9875d1537c1bb1d Mon Sep 17 00:00:00 2001 From: acp29 Date: Fri, 14 Jun 2024 09:58:20 +0100 Subject: [PATCH] Added Extended Information Criterion to `bootlm` and bumped version number --- DESCRIPTION | 14 +++++----- inst/bootlm.m | 41 ++++++++++++++++++++++++++--- matlab/statistics-resampling.mltbx | Bin 348009 -> 348439 bytes matlab/statistics-resampling.prj | 6 ++--- 4 files changed, 47 insertions(+), 14 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 2287c81..d23bcb1 100755 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,6 +1,6 @@ name: statistics-resampling -version: 5.5.18 -date: 2024-06-04 +version: 5.6.0 +date: 2024-06-14 author: Andrew Penn maintainer: Andrew Penn title: A statistics package with a variety of resampling tools @@ -9,11 +9,11 @@ description: The statistics-resampling package is an Octave variety of statistics tasks using non-parametric resampling methods. In particular, the functions included can be used to estimate bias, uncertainty (standard errors and confidence - intervals), prediction error, and calculate p-values for null - hypothesis significance tests. Variations of the resampling - methods are included that improve the accuracy of the - statistics for small samples and samples with complex - dependence structures. + intervals), prediction error, information criteria, and + calculate p-values for null hypothesis significance tests. + Variations of the resampling methods are included that + improve the accuracy of the statistics for small samples + and samples with complex dependence structures. license: GPLv3+ depends: octave (>= 4.4.0) url: https://github.com/gnu-octave/statistics-resampling diff --git a/inst/bootlm.m b/inst/bootlm.m index cc9dca7..095f49e 100755 --- a/inst/bootlm.m +++ b/inst/bootlm.m @@ -464,6 +464,9 @@ % - 'PE': Bootstrap estimate of prediction error % - 'PRESS': Bootstrap estimate of predicted residual error sum of squares % - 'RSQ_pred': Bootstrap estimate of predicted R-squared +% - 'EIC': Extended (Efron) Information Criterion +% - 'RL': Relative likelihood (compared to the intercept-only model) +% - 'Wt': Prediction error expressed as weights % % The linear models evaluated are the same as for AOVSTAT, except that the % output also includes the statistics for the intercept-only model. Note @@ -2125,6 +2128,20 @@ OPTIM = S_ERR - A_ERR; % Optimism in apparent error PE = cell2mat (RSS) / n + sum (OPTIM, 2) / NBOOT; + % Compute the Extended (Efron) Information Criterion, weights and relative + % liklihood + % See Konishi & Kitagawa, "Bootstrap Information Criterion". In: Information + % Criteria and Statistical Modeling. Springer Series in Statistics. Springer, NY. + LogLik = @(var) -n / 2 * log (2 * pi) - n / 2 * log (var) - n / 2; + S_LL = LogLik (S_ERR); % Simple estimate of expected log-likelihood + A_LL = LogLik (A_ERR); % Apparent estimates of log-likelihood + b = sum (A_LL - S_LL, 2) / NBOOT; % Bootstrap bias estimate of log-likelihood + LL = LogLik (cell2mat (RSS) / n); % Log-likelihood of model on original sample + EIC = -2 * LL + 2 * b; % Extended (Efron) Information Criterion + RL = exp (0.5 * (EIC(1) - EIC)); % Relative likelihood compared to intercept- + % only model: exp (0.5 * (EIC[H0] - EIC[H1])) + Wt = RL / sum (RL); % EIC weights + % Transform prediction errors to predicted R-squared statistics PRESS = PE * n; % Bootstrap estimate of predicted % residual error sum of squares @@ -2133,7 +2150,8 @@ % by refined bootstrap % Prepare output - PRED_ERR = struct ('MODEL', [], 'PE', PE, 'PRESS', PRESS, 'RSQ_pred', PE_RSQ); + PRED_ERR = struct ('MODEL', [], 'PE', PE, 'PRESS', PRESS, ... + 'RSQ_pred', PE_RSQ, 'EIC', EIC, 'RL', RL, 'Wt', Wt); end @@ -2801,8 +2819,9 @@ %!demo %! -%! % Prediction errors of linear models. Data from Table 9.1, on page 107 of -%! % Efron and Tibshirani (1993) An Introduction to the Bootstrap. +%! % Prediction errors and information criteria of linear models. +%! % Data from Table 9.1, on page 107 of Efron and Tibshirani (1993) +%! % An Introduction to the Bootstrap. %! %! amount = [25.8; 20.5; 14.3; 23.2; 20.6; 31.1; 20.9; 20.9; 30.4; ... %! 16.3; 11.6; 11.8; 32.5; 32.0; 18.0; 24.1; 26.5; 25.8; ... @@ -2828,6 +2847,17 @@ %! % Efron and Tibhirani (1993) using the same refined bootstrap procedure, %! % because they have used case resampling whereas we have used wild bootstrap %! % resampling. The equivalent value of Cp (eq. to AIC) statistic is 2.96. +%! +%! PRED_ERR +%! +%! % The results from the bootstrap are broadly consistent to the results +%! % obtained for Akaike's Information Criterion (AIC, computed in R with the +%! % AIC function from the 'stats' package): +%! % +%! % MODEL AIC EIC +%! % amount ~ 1 180.17 178.41 +%! % amount ~ 1 + hrs 127.33 125.00 +%! % amount ~ 1 + hrs + lot 107.85 106.36 %!demo %! @@ -2884,12 +2914,15 @@ %! % The results from the bootstrap are broadly consistent to the results %! % obtained for PE, PRESS and RSQ_pred using cross-validation: %! % -%! % MODEL PE-CV PRESS-CV RSQ_pred-CV +%! % MODEL PE-CV PRESS-CV RSQ_pred-CV %! % sr ~ 1 20.48 1024.186 -0.041 %! % sr ~ 1 + pop15 16.88 843.910 +0.142 %! % sr ~ 1 + pop15 + pop75 16.62 830.879 +0.155 %! % sr ~ 1 + pop15 + pop75 + dpi 16.54 827.168 +0.159 %! % sr ~ 1 + pop15 + pop75 + dpi + ddpi 15.98 798.939 +0.188 +%! +%! % Relative likelihood of the nested models (exluding intercept-only model) +%! PRED_ERR.RL(2:end) ./ PRED_ERR.RL(1:end-1) %!test %! diff --git a/matlab/statistics-resampling.mltbx b/matlab/statistics-resampling.mltbx index a7d342da8240c912115b7c3d7a050e9efc27c033..18cea725014c575a97f406012c1c3469a14492b5 100644 GIT binary patch delta 34968 zcmV)RK(oK;o)wp(6%9~J0|XQR000O8@J`OL4aorm@lMXO*#RyO1MyDIvkDPO83XZ7 z&a+l3$rKLoPR>}X`VbYu6953{OOs(L7_&t`&l3aiPR_FzQ?MHY@lMXO%5IYO1MyDI zw_jxeTPFkYPR_Tzi~)@r1MyDIw@s%3JO~5vPR_TCuK~{|1Mp7Hw_eu)>?{NDPR_SY z1OoL61Mp7Hw?z*EfJ1-qPR>}*9hba2hX4Q=PyzrC0001Hb8>HQbT49WZ***JE^X|+ z>3Z8pk|_G$PmyQQkgOtUl9H^g-DhN(Dr>B*MY+lzx7!~?LJ}+zU=g5}@p!)T>%7DL zdtc@Lyl-)zqMyW<(IAZbp@`xvoZJS(R8)g_AjS>&JPp&DxJ)J@yAGeMh)H-g3DY!6Vt6pT zyo~x$7-y-toFpR=h+!0m!9m)qf{I>?t%xgdwlZqZu7|sKx#C^{xt4q z2x>nXhTGJ^;Yfc}-_^z2+Pph{Iy-rDy4YQH(QG#B;&}I{TNgj?9=_==^;~5TjVg8V z^5AH>#{jWe6i<_B3QzBy9G@Q?zd3o+TMh_e5}rRgdD%TYe|NfM*V7CpA(#xJe+vOf z?|k?8FMG|Mbz4Ike z8RHM|`075@eIS&`Zq<@qC8$ABv@MQ0G?_ZaDe4L~(kA0l7 zlO9mP-jaW$9ERBQUbkD)ZJ_S+o_MYSz+?U!-_xBi3P2!!{P38EfO<}T{`#kpe!DL} 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zsxW?F`G_&VwE%bbvg|GoBSIcZW`F_l-h~Ct*+GK@1SB3IEE+@&5Dd=BC)f-uj=PGtI4hDW@`h(Djk)%2LZch56XAcWahbXMfG@ ze5|%wDKGi*kg}(^PIkOV|?h3 zhy5AJ@d0k|UAz4LE~qv;6B<}(d06pY<;s!8n$g;rTLDNi|&nIEN8oTG*xIGthHS= zF)YJh_V77dhSnM(n9zEhBtJo8jqY3#B)L#%Bm}ytQ56brvHKV94~6a2crgriP(v05 zfz&vzHwN@W8^U#*o#Eh5In{ckKOFohVjTg#+Bgw9a%F^W=oUe&iD+D}!w-L6FGt8M z65B+AXEBSZoDlizI6~XrL5SRFBWsAXi=(C}O_`UIlkb^KF4;LLsUF#}G86JKu_43s zoDdfxu27Hg5pqm2c0Vv{;I7QiJ80xCBJ!`cPGo-UfY4}~v4189{}u@%F`MN6gz>6Y zK*-GsAxoMZLfRzl9I;pm^qhcqNP#h(c?Iv40zIbSA{JQi!u3)R(Pz^`0M42Z2cLL@ zV~hWm0zGQrRhDOyfcY{V&re2xf3k6$48+v2hy{iUalIb+mIZq1@GmluP{t|?d~+W2 zqjWC*QABH{m4kz3ICl78luoOdg?l?F%)^~guwKH>aO$Sn0DrQM-i z=2WzfI;YlzY$X*)ml;zpO;M@?mPhN<5~7J3v#eF~`f%$OA2b|{L97b3b51 - + statistics-resampling Andrew Penn andy.c.penn@gmail.com University of Sussex, UK Statistical analysis using resampling methods - The statistics-resampling package is an Octave package and Matlab toolbox that can be used to perform a wide variety of statistics tasks using non-parametric resampling methods. In particular, the functions included can be used to estimate bias, uncertainty (standard errors and confidence intervals), prediction error, and calculate p-values for null hypothesis significance tests. Variations of the resampling methods are included that improve the accuracy of the statistics for small samples and samples with complex dependence structures. + The statistics-resampling package is an Octave package and Matlab toolbox that can be used to perform a wide variety of statistics tasks using non-parametric resampling methods. In particular, the functions included can be used to estimate bias, uncertainty (standard errors and confidence intervals), prediction error, information criteria, and calculate p-values for null hypothesis significance tests. Variations of the resampling methods are included that improve the accuracy of the statistics for small samples and samples with complex dependence structures. Y:\Documents\GitHub\statistics-resampling\doc\icon.png - 5.5.18 + 5.6.0 ${PROJECT_ROOT}\statistics-resampling.mltbx