\\[
\\int x^2 dx = \\frac{x^3}{3} + C
\\]<\/p>\n\n\n\n
\\( E = mc^2 \\)<\/p>\n\n\n\n
\\[
\\frac{d}{dx} \\left( x^2 \\right) = 2x
\\]<\/p>\n\n\n\n
\\[
x = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}
\\]<\/p>\n\n\n\n
<\/p>\n\n\n\n
\\[
\\frac{d}{dx} \\left( x^2 \\right) = 2x
\\]<\/p>\n\n\n\n
\\[
\\int x^2 \\,dx = \\frac{x^3}{3} + C
\\]<\/p>\n\n\n\n
\\[
E = mc^2
\\]<\/p>\n\n\n\n
\\[
\\frac{d}{dx} \\left( x^2 \\right) = 2x
\\]<\/p>\n\n\n\n
\\[
x = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}
\\]<\/p>\n\n\n\n
\\[
\\frac{d}{dx} \\left( x^2 \\right) = 2x
\\]<\/p>\n\n\n\n
\\[
\\text{clr}(x) = (\\text{clr}_1, \\text{clr}_2, \\dots, \\text{clr}_D)
= \\log \\left( \\frac{x_j}{(x_1^{1\/D} x_2^{1\/D} \\dots x_D^{1\/D})} \\right)
= \\log \\left( \\frac{x_j}{\\sqrt[D]{x_1 x_2 \\dots x_D}} \\right) \\quad (2)
\\]<\/p>\n\n\n\n
\\[
\\text{trong \u0111\u00f3: } j = 1, \\dots, D
\\]<\/p>\n\n\n\n### 3.2. L\u1ef1a ch\u1ecdn bi\u1ebfn s\u1ed1\n\nD\u1ef1a theo m\u1ee5c ti\u00eau nghi\u00ean c\u1ee9u \u0111\u00e3 \u0111\u1ec1 ra, c\u00e1c ch\u1ec9 s\u1ed1 (t\u1ef7 s\u1ed1) t\u00e0i ch\u00ednh li\u00ean quan \u0111\u1ebfn kh\u1ea3 n\u0103ng thanh to\u00e1n v\u00e0 c\u00e1c t\u1ef7 l\u1ec7 th\u00e0nh ph\u1ea7n trong ph\u00e2n t\u00edch DuPont \u0111\u01b0\u1ee3c l\u1ef1a ch\u1ecdn. Nh\u01b0 \u0111\u00e3 tr\u00ecnh b\u00e0y \u1edf ph\u1ea7n c\u01a1 s\u1edf l\u00fd thuy\u1ebft, c\u00e1c d\u1eef li\u1ec7u th\u00f4ng tin t\u00e0i ch\u00ednh \u0111\u01b0\u1ee3c thu th\u1eadp d\u1ef1a theo c\u00e1c y\u1ebfu t\u1ed1 c\u00f3 t\u00e1c \u0111\u1ed9ng \u0111\u1ebfn vi\u1ec7c ph\u00e2n lo\u1ea1i doanh nghi\u1ec7p, bao g\u1ed3m t\u00ednh thanh kho\u1ea3n, c\u1ea5u tr\u00fac n\u1ee3 v\u00e0 kh\u1ea3 n\u0103ng sinh l\u1eddi. C\u00e1c ch\u1ec9 s\u1ed1 t\u00e0i ch\u00ednh \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n l\u00e0 c\u00e1c ch\u1ec9 s\u1ed1 th\u00f4ng d\u1ee5ng \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong r\u1ea5t nhi\u1ec1u nghi\u00ean c\u1ee9u \u0111\u1ec3 \u0111\u1ea1i di\u1ec7n cho c\u00e1c nh\u00f3m \u0111\u1eb7c \u0111i\u1ec3m n\u00e0y (du Jardin v\u00e0 c.s., 2019; Veganzones & Severin, 2021).\n\nC\u00e1c t\u1ef7 l\u1ec7 n\u00e0y \u0111\u01b0\u1ee3c t\u00ednh t\u1eeb d\u1eef li\u1ec7u th\u00f4ng tin k\u1ebf to\u00e1n thu th\u1eadp \u0111\u01b0\u1ee3c. \u0110\u1ea7u ti\u00ean, c\u00e1c bi\u1ebfn cho th\u00f4ng tin k\u1ebf to\u00e1n \u0111\u01b0\u1ee3c g\u00e1n th\u00e0nh c\u00e1c bi\u1ebfn \\( x_j \\), c\u1ee5 th\u1ec3 nh\u01b0 sau:\n\n\\[\nx_1 = \\text{T\u00e0i s\u1ea3n d\u00e0i h\u1ea1n} = \\text{T\u1ed5ng t\u00e0i s\u1ea3n} – \\text{T\u00e0i s\u1ea3n ng\u1eafn h\u1ea1n}\n\\]\n\n\\[\nx_2 = \\text{T\u00e0i s\u1ea3n ng\u1eafn h\u1ea1n}\n\\]\n\n\\[\nx_3 = \\text{N\u1ee3 d\u00e0i h\u1ea1n}\n\\]\n\n\\[\nx_4 = \\text{N\u1ee3 ng\u1eafn h\u1ea1n}\n\\]\n\n\\[\nx_5 = \\text{Doanh thu}\n\\]\n\n\\[\nx_6 = \\text{Chi ph\u00ed} = \\text{Doanh thu} – \\text{L\u1ee3i nhu\u1eadn r\u00f2ng}\n\\]\n\nTi\u1ebfp theo \u0111\u00f3, c\u00e1c ch\u1ec9 s\u1ed1 t\u00e0i ch\u00ednh ti\u00eau chu\u1ea9n s\u1ebd \u0111\u01b0\u1ee3c t\u00ednh t\u1eeb c\u00e1c bi\u1ebfn \\( x \\) \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh \u1edf tr\u00ean. B\u1ea3ng d\u01b0\u1edbi \u0111\u00e2y cung c\u1ea5p gi\u1ea3i th\u00edch cho \u00fd ngh\u0129a c\u1ee7a t\u1eebng ch\u1ec9 s\u1ed1:\n\\[\nx_1 = \\text{T\u00e0i s\u1ea3n d\u00e0i h\u1ea1n} = \\text{T\u1ed5ng t\u00e0i s\u1ea3n} – \\text{T\u00e0i s\u1ea3n ng\u1eafn h\u1ea1n}\n\\]\n\n\\[\nx_2 = \\text{T\u00e0i s\u1ea3n ng\u1eafn h\u1ea1n}\n\\]\n\n\\[\nx_3 = \\text{N\u1ee3 d\u00e0i h\u1ea1n}\n\\]\n\n\\[\nx_4 = \\text{N\u1ee3 ng\u1eafn h\u1ea1n}\n\\]\n\n\\[\nx_5 = \\text{Doanh thu}\n\\]\n\n\\[\nx_6 = \\text{Chi ph\u00ed} = \\text{Doanh thu} – \\text{L\u1ee3i nhu\u1eadn r\u00f2ng}\n\\]\n\nTi\u1ebfp theo \u0111\u00f3, c\u00e1c ch\u1ec9 s\u1ed1 t\u00e0i ch\u00ednh ti\u00eau chu\u1ea9n s\u1ebd \u0111\u01b0\u1ee3c t\u00ednh t\u1eeb c\u00e1c bi\u1ebfn \\( x \\) \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh \u1edf tr\u00ean. B\u1ea3ng d\u01b0\u1edbi \u0111\u00e2y cung c\u1ea5p gi\u1ea3i th\u00edch cho \u00fd ngh\u0129a c\u1ee7a t\u1eebng ch\u1ec9 s\u1ed1:\n\n% Th\u00eam b\u1ea3ng n\u1ebfu c\u1ea7n\n\n\n\n### 3.3.2. Chuy\u1ec3n \u0111\u1ed5i d\u1eef li\u1ec7u \u0111a h\u1ee3p s\u1eed d\u1ee5ng ph\u00e9p chuy\u1ec3n \u0111\u1ed5i logarit c\u1ed9ng t\u00ednh (Additive log-ratios) v\u00e0 logarit trung t\u00e2m (Centered log-ratios) c\u00f3 tr\u1ecdng s\u1ed1.\n\nDo c\u00e1c th\u00e0nh ph\u1ea7n trong vector \u0111a h\u1ee3p lu\u00f4n c\u00f3 t\u1ed5ng b\u1eb1ng 1 (ho\u1eb7c 100%), vi\u1ec7c ph\u00e2n t\u00edch tr\u1ef1c ti\u1ebfp c\u00e1c th\u00e0nh ph\u1ea7n c\u00f3 th\u1ec3 g\u00e2y ra ph\u1ee5 thu\u1ed9c gi\u1ea3. \u0110\u1ec3 thu\u1eadn ti\u1ec7n h\u01a1n trong vi\u1ec7c x\u1eed l\u00fd v\u00e0 ph\u00e2n t\u00edch d\u1eef li\u1ec7u, CoDA s\u1eed d\u1ee5ng c\u00e1c ph\u00e9p bi\u1ebfn \u0111\u1ed5i logarit \u0111\u1ec3 x\u1eed l\u00fd vector \u0111a h\u1ee3p, nh\u01b0 ph\u01b0\u01a1ng ph\u00e1p \u0111\u00e3 \u0111\u01b0\u1ee3c gi\u1edbi thi\u1ec7u b\u1edfi Aitchison v\u00e0o n\u0103m 1986. Trong nghi\u00ean c\u1ee9u n\u00e0y, t\u1ef7 l\u1ec7 logarit c\u1ed9ng t\u00ednh (ALR) v\u00e0 t\u1ef7 l\u1ec7 logarit trung t\u00e2m (CLR) \u0111\u01b0\u1ee3c ch\u1ecdn \u0111\u1ec3 s\u1eed d\u1ee5ng. Sau khi th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p chuy\u1ec3n \u0111\u1ed5i log-ratio, vector \u0111a h\u1ee3p ban \u0111\u1ea7u s\u1ebd \u0111\u01b0\u1ee3c \u0111\u01b0a v\u00e0o kh\u00f4ng gian Euclid m\u00e0 \u1edf \u0111\u00f3 c\u00e1c ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea th\u00f4ng th\u01b0\u1eddng (nh\u01b0 h\u1ed3i quy, ph\u00e2n c\u1ee5m, PCA) c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c v\u00e0 kh\u00f4ng t\u1ea1o ra c\u00e1c m\u1ed1i ph\u1ee5 thu\u1ed9c gi\u1ea3.\n\n\u0110\u1ed1i v\u1edbi m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c \\( D \\) lo\u1ea1i t\u00e0i kho\u1ea3n k\u1ebf to\u00e1n thu \u0111\u01b0\u1ee3c t\u1eeb b\u00e1o c\u00e1o t\u00e0i ch\u00ednh (c\u00e1c ch\u1ec9 s\u1ed1 t\u00e0i ch\u00ednh \u0111\u01b0\u1ee3c g\u00e1n l\u00e0 \\( x_j \\)), ph\u00e9p bi\u1ebfn \u0111\u1ed5i ALR \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n nh\u01b0 sau:\n\n\\[\n\\text{alr}(x) = (\\text{alr}_1, \\text{alr}_2, \\dots, \\text{alr}_{D-1}) = \\left(\\log \\frac{x_1}{x_D}, \\dots, \\log \\frac{x_{D-1}}{x_D} \\right) \\quad (1)\n\\]\n\nPh\u00e9p bi\u1ebfn \u0111\u1ed5i logarit c\u1ed9ng t\u00ednh (ALR) chuy\u1ec3n \u0111\u1ed5i c\u00e1c bi\u1ec3u di\u1ec5n trong \u0111\u01a1n h\u00ecnh (simplex) th\u00e0nh bi\u1ec3u di\u1ec5n trong kh\u00f4ng gian vector th\u1eadt. ALR chuy\u1ec3n \u0111\u1ed5i d\u1eef li\u1ec7u \u0111a h\u1ee3p b\u1eb1ng c\u00e1ch ch\u1ecdn m\u1ed9t th\u00e0nh ph\u1ea7n chu\u1ea9n v\u00e0 t\u00ednh log-ratio gi\u1eefa c\u00e1c th\u00e0nh ph\u1ea7n c\u00f2n l\u1ea1i v\u1edbi th\u00e0nh ph\u1ea7n chu\u1ea9n n\u00e0y. Nh\u01b0 \u0111\u00e3 th\u1ea5y t\u1eeb c\u00f4ng th\u1ee9c bi\u1ec3u di\u1ec5n, vector ALR sau ph\u00e9p bi\u1ebfn \u0111\u1ed5i s\u1ebd c\u00f3 \\( D-1 \\) ph\u1ea7n t\u1eed.\n\nV\u1edbi m\u1ed9t t\u1eadp h\u1ee3p g\u1ed3m \\( D \\) lo\u1ea1i t\u00e0i kho\u1ea3n k\u1ebf to\u00e1n t\u01b0\u01a1ng t\u1ef1, ph\u00e9p bi\u1ebfn \u0111\u1ed5i logarit trung t\u00e2m (CLR) c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n nh\u01b0 sau:\n\n\\[\n\\text{clr}(x) = (\\text{clr}_1, \\text{clr}_2, \\dots, \\text{clr}_D) = \\log \\left( \\frac{x_j}{(x_1^{1\/D} x_2^{1\/D} \\dots x_D^{1\/D})} \\right) = \\log \\left( \\frac{x_j}{\\sqrt[D]{x_1 x_2 \\dots x_D}} \\right) \\quad (2)\n\\]\n\ntrong \u0111\u00f3: \\( j = 1, \\dots, D \\)\n\nT\u01b0\u01a1ng t\u1ef1 nh\u01b0 ALR, ph\u00e9p bi\u1ebfn \u0111\u1ed5i CLR chuy\u1ec3n \u0111\u1ed5i bi\u1ec3u di\u1ec5n \u0111\u01a1n h\u00ecnh th\u00e0nh bi\u1ec3u di\u1ec5n kh\u00f4ng gian vector. CLR chuy\u1ec3n \u0111\u1ed5i t\u1ea5t c\u1ea3 c\u00e1c th\u00e0nh ph\u1ea7n trong vector \u0111a h\u1ee3p b\u1eb1ng c\u00e1ch so s\u00e1nh v\u1edbi trung b\u00ecnh h\u00ecnh h\u1ecdc c\u1ee7a to\u00e0n b\u1ed9 c\u00e1c th\u00e0nh ph\u1ea7n. Vector CLR sau ph\u00e9p bi\u1ebfn \u0111\u1ed5i s\u1ebd c\u00f3 \\( D \\) ph\u1ea7n t\u1eed. Sau khi bi\u1ebfn \u0111\u1ed5i CLR, kho\u1ea3ng c\u00e1ch Euclid gi\u1eefa hai vector trong kh\u00f4ng gian log-ratio ph\u1ea3n \u00e1nh \u0111\u00fang s\u1ef1 kh\u00e1c bi\u1ec7t t\u01b0\u01a1ng \u0111\u1ed1i gi\u1eefa c\u00e1c th\u00e0nh ph\u1ea7n c\u1ee7a hai vector \u0111a h\u1ee3p (hay c\u00f2n g\u1ecdi l\u00e0 kho\u1ea3ng c\u00e1ch Aitchison).\n\nV\u1edbi thu\u1ed9c t\u00ednh b\u1ea3o to\u00e0n kho\u1ea3ng c\u00e1ch, CLR th\u01b0\u1eddng \u0111\u01b0\u1ee3c \u01b0u ti\u00ean s\u1eed d\u1ee5ng h\u01a1n ALR trong c\u00e1c ph\u00e2n t\u00edch ph\u00e2n c\u1ee5m. Tuy nhi\u00ean, trong c\u00e1c \u1ee9ng d\u1ee5ng th\u00f4ng th\u01b0\u1eddng c\u1ee7a ph\u00e2n t\u00edch d\u1eef li\u1ec7u \u0111a h\u1ee3p, m\u1ed9t s\u1ed1 nh\u00f3m d\u1eef li\u1ec7u t\u00e0i ch\u00ednh nh\u1ea5t \u0111\u1ecbnh c\u00f3 gi\u00e1 tr\u1ecb th\u01b0\u1eddng th\u1ea5p c\u00f3 th\u1ec3 b\u1ed9c l\u1ed9 ra gi\u00e1 tr\u1ecb ph\u01b0\u01a1ng sai CLR r\u1ea5t l\u1edbn, g\u00e2y \u1ea3nh h\u01b0\u1edfng \u0111\u00e1ng k\u1ec3 \u0111\u1ebfn k\u1ebft qu\u1ea3 ph\u00e2n lo\u1ea1i (Egozcue & Pawlowsky-Glahn, 2016; Greenacre & Lewi, 2009; Jofre-Campuzano & Coenders, 2022). \u0110i\u1ec3m h\u1ea1n ch\u1ebf n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i quy\u1ebft b\u1eb1ng c\u00e1ch t\u00ednh to\u00e1n m\u1ed9t bi\u1ebfn th\u1ec3 c\u00f3 tr\u1ecdng s\u1ed1 c\u1ee7a ph\u00e9p bi\u1ebfn \u0111\u1ed5i CLR, trong \u0111\u00f3 tr\u1ecdng s\u1ed1 \\( w_j \\), v\u1edbi t\u1ed5ng t\u1ea5t c\u1ea3 tr\u1ecdng s\u1ed1 b\u1eb1ng 1, t\u1ef7 l\u1ec7 thu\u1eadn v\u1edbi gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a \\( x_j \\):\n\n\\[\n\\text{wclr}_j = \\sqrt{w_j} \\cdot \\log \\left( \\frac{x_j}{x_1^{w_1} x_2^{w_2} \\dots x_D^{w_D}} \\right) \\quad (3)\n\\]\n\n\n\n\\[\n\\text{Cho d\u00e3y s\u1ed1 } (u_n)_{n \\geq 1}, \\text{ x\u00e1c \u0111\u1ecbnh b\u1edfi: } u_1 = 3, \\quad u_2 = 5 \\text{ v\u00e0}\n\\]\n\\[\nu_{n+2} = u_{n+1} + 2u_n, \\quad \\forall n \\geq 1.\n\\]\n\\[\n\\text{Khi \u0111\u00f3, ta c\u00f3: }\n\\]\n\\[\n9u_{n+1}^2 + (-1)^{n+1} \\cdot 2^{n+5} \\text{ l\u00e0 m\u1ed9t s\u1ed1 ch\u00ednh ph\u01b0\u01a1ng,} \\quad \\forall n \\geq 1.\n\\]\n","protected":false},"excerpt":{"rendered":"
\\[\\int x^2 dx = \\frac{x^3}{3} + C\\] \\( E = mc^2 \\) \\[\\frac{d}{dx} \\left( x^2 \\right) = 2x\\] \\[x = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}\\] \\[\\frac{d}{dx} \\left( x^2 \\right) = 2x\\] \\[\\int x^2 \\,dx = \\frac{x^3}{3} + C\\] \\[E = mc^2\\] \\[\\frac{d}{dx} \\left( x^2 \\right) = 2x\\] \\[x = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}\\] \\[\\frac{d}{dx} \\left( x^2 […]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_eb_attr":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-613","post","type-post","status-publish","format-standard","hentry","category-others"],"blocksy_meta":[],"_links":{"self":[{"href":"https:\/\/nbvps.anhtuanlqd.com\/index.php?rest_route=\/wp\/v2\/posts\/613","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nbvps.anhtuanlqd.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/nbvps.anhtuanlqd.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/nbvps.anhtuanlqd.com\/index.php?rest_route=\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/nbvps.anhtuanlqd.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=613"}],"version-history":[{"count":31,"href":"https:\/\/nbvps.anhtuanlqd.com\/index.php?rest_route=\/wp\/v2\/posts\/613\/revisions"}],"predecessor-version":[{"id":650,"href":"https:\/\/nbvps.anhtuanlqd.com\/index.php?rest_route=\/wp\/v2\/posts\/613\/revisions\/650"}],"wp:attachment":[{"href":"https:\/\/nbvps.anhtuanlqd.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=613"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nbvps.anhtuanlqd.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=613"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nbvps.anhtuanlqd.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=613"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}