{"id":414,"date":"2019-09-11T21:25:00","date_gmt":"2019-09-11T12:25:00","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/multiple-comparison-for-glm-results-in-r\/"},"modified":"2025-02-19T22:24:47","modified_gmt":"2025-02-19T13:24:47","slug":"multiple-comparison-for-glm-results-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/multiple-comparison-for-glm-results-in-r\/","title":{"rendered":"R \u3067\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790\u3068\u50be\u5411\u691c\u5b9a\u30fb\u591a\u91cd\u6bd4\u8f03\u3092\u884c\u3046\u65b9\u6cd5"},"content":{"rendered":"\n

R \u306b\u7d44\u307f\u8fbc\u307f\u306e\u30bf\u30a4\u30bf\u30cb\u30c3\u30af\u53f7\u306e\u751f\u5b58\u30fb\u6b7b\u4ea1\u30c7\u30fc\u30bf\u3067\u3001\u751f\u5b58\u30fb\u6b7b\u4ea1\u306b\u95a2\u3059\u308b\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790\u3068\u3001\u72ec\u7acb\u5909\u6570\u306e\u591a\u91cd\u6bd4\u8f03\u3092\u5b9f\u884c\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n\n\n\n\n

\u89e3\u6790\u3059\u308b\u30bf\u30a4\u30bf\u30cb\u30c3\u30af\u53f7\u306e\u751f\u5b58\u30fb\u6b7b\u4ea1\u30c7\u30fc\u30bf\u306e\u78ba\u8a8d<\/h2>\n\n\n\n

\u89e3\u6790\u3059\u308b\u30c7\u30fc\u30bf\u306f\u3001carData \u30d1\u30c3\u30b1\u30fc\u30b8\u306e TitanicSurvival \u3068\u3044\u3046\u30c7\u30fc\u30bf\u3002<\/p>\n\n\n\n

carData \u30d1\u30c3\u30b1\u30fc\u30b8\u306f\u6700\u521d\u304b\u3089\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3001library() \u3067\u547c\u3073\u51fa\u3059\u3060\u3051\u3067\u4f7f\u3048\u308b\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n

library<\/span>(<\/span>carData)<\/span>\nstr<\/span>(<\/span>TitanicSurvival)<\/span>\nsummary<\/span>(<\/span>TitanicSurvival)<\/span>\n<\/code><\/pre>\n\n\n\n
\u30bf\u30a4\u30bf\u30cb\u30c3\u30af\u53f7\u304c\u6c88\u6ca1\u3057\u305f\u3068\u304d\u306e\u751f\u5b58\u30fb\u6b7b\u4ea1\uff08survived\uff09\u3001\u4e57\u5ba2\u306e\u6027\u5225\uff08sex\uff09\u3001\u5e74\uff08age\uff09\u3001\u5ba2\u5ba4\u30af\u30e9\u30b9\uff08passengerClass\uff09\u306e\u30c7\u30fc\u30bf\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
><\/span> str<\/span>(<\/span>TitanicSurvival)<\/span>\n'data.frame'<\/span>:<\/span>   1309<\/span> obs. of  4<\/span> variables:<\/span>\n$<\/span> survived      :<\/span> Factor w\/<\/span> 2<\/span> levels \"no\"<\/span>,<\/span>\"yes\"<\/span>:<\/span> 2<\/span> 2<\/span> 1<\/span> 1<\/span> 1<\/span> 2<\/span> 2<\/span> 1<\/span> 2<\/span> 1<\/span> ...\n$<\/span> sex           :<\/span> Factor w\/<\/span> 2<\/span> levels \"female\"<\/span>,<\/span>\"male\"<\/span>:<\/span> 1<\/span> 2<\/span> 1<\/span> 2<\/span> 1<\/span> 2<\/span> 1<\/span> 2<\/span> 1<\/span> 2<\/span> ...\n$<\/span> age           :<\/span> num  29<\/span> 0.917<\/span> 2<\/span> 30<\/span> 25<\/span> ...\n$<\/span> passengerClass:<\/span> Factor w\/<\/span> 3<\/span> levels \"1st\"<\/span>,<\/span>\"2nd\"<\/span>,<\/span>\"3rd\"<\/span>:<\/span> 1<\/span> 1<\/span> 1<\/span> 1<\/span> 1<\/span> 1<\/span> 1<\/span> 1<\/span> 1<\/span> 1<\/span> ...\n><\/span> summary<\/span>(<\/span>TitanicSurvival)<\/span>\nsurvived      sex           age          passengerClass\nno :<\/span>809<\/span>   female:<\/span>466<\/span>   Min.   :<\/span> 0.1667<\/span>   1st:<\/span>323<\/span>\nyes:<\/span>500<\/span>   male  :<\/span>843<\/span>   1st Qu.:<\/span>21.0000<\/span>   2nd:<\/span>277<\/span>\nMedian :<\/span>28.0000<\/span>   3rd:<\/span>709<\/span>\nMean   :<\/span>29.8811<\/span>\n3rd Qu.:<\/span>39.0000<\/span>\nMax.   :<\/span>80.0000<\/span>\nNA's   :263                     <\/span>\n<\/code><\/pre>\n\n\n\n
\u5ba2\u5ba4\u30af\u30e9\u30b9\u9593\u306e\u751f\u5b58\u30fb\u6b7b\u4ea1\u306e\u50be\u5411\uff08\u30c8\u30ec\u30f3\u30c9\uff09<\/h2>\n\n\n\n
\u5272\u5408\u306e\u30b0\u30e9\u30d5\u3067\u30c8\u30ec\u30f3\u30c9\u3092\u773a\u3081\u308b<\/h3>\n\n\n\n
\u751f\u5b58\u304c\u3001\u5ba2\u5ba4\u30af\u30e9\u30b9\u306e\u9055\u3044\u3067\u50be\u5411\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u898b\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
(<\/span>tab <-<\/span> with<\/span>(<\/span>TitanicSurvival,<\/span> table<\/span>(<\/span>passengerClass,<\/span> survived)))<\/span>\nprop.table<\/span>(<\/span>tab,<\/span>1<\/span>)<\/span>\nprop.table<\/span>(<\/span>tab,<\/span>1<\/span>)[,<\/span>2<\/span>]<\/span>*<\/span>100<\/span>\nbarplot<\/span>(<\/span>prop.table<\/span>(<\/span>tab,<\/span>1<\/span>)[,<\/span>2<\/span>]<\/span>*<\/span>100<\/span>,<\/span> xlab=<\/span>\"Passenger Class\"<\/span>,<\/span> ylab=<\/span>\"Survived (%)\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
1309\u540d\u4e2d\u3001\u5ba2\u5ba4\u30af\u30e9\u30b9\u5225\u4e57\u5ba2\u306f\u4e00\u7b49\u304c323\u540d\u3001\u4e8c\u7b49\u304c277\u540d\u3001\u4e09\u7b49\u304c709\u540d\u3060\u3063\u305f\u3002<\/p>\n\n\n\n
\u751f\u5b58\u3057\u305f\u306e\u306f500\u540d\u3060\u3063\u305f\u3002<\/p>\n\n\n\n
\u4e00\u7b49\u304c62%\u3001\u4e8c\u7b49\u304c43%\u3001\u4e09\u7b49\u304c26%\u3060\u3063\u305f\u3002<\/p>\n\n\n\n
><\/span> (<\/span>tab <-<\/span> with<\/span>(<\/span>TitanicSurvival,<\/span> table<\/span>(<\/span>passengerClass,<\/span> survived)))<\/span>\nsurvived\npassengerClass  no yes\n1st 123<\/span> 200<\/span>\n2nd 158<\/span> 119<\/span>\n3rd 528<\/span> 181<\/span>\n><\/span>\n><\/span> prop.table<\/span>(<\/span>tab,<\/span>1<\/span>)<\/span>\nsurvived\npassengerClass        no       yes\n1st 0.3808050<\/span> 0.6191950<\/span>\n2nd 0.5703971<\/span> 0.4296029<\/span>\n3rd 0.7447109<\/span> 0.2552891<\/span>\n><\/span>\n><\/span> prop.table<\/span>(<\/span>tab,<\/span>1<\/span>)[,<\/span>2<\/span>]<\/span>*<\/span>100<\/span>\n1st      2nd      3rd\n61.91950<\/span> 42.96029<\/span> 25.52891<\/span>\n<\/code><\/pre>\n\n\n\n
\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\u898b\u4e8b\u306b\u50be\u5411\uff08\u30c8\u30ec\u30f3\u30c9\uff09\u304c\u307f\u3089\u308c\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u5358\u5909\u91cf\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790<\/h3>\n\n\n\n
\u307e\u305a\u3001glm()\u3068family=binomial\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790\u3092\u884c\u3046\u3002<\/p>\n\n\n\n
glm.res <-<\/span> glm<\/span>(<\/span>survived ~<\/span> passengerClass,<\/span> family=<\/span>binomial<\/span>(),<\/span> data=<\/span>TitanicSurvival)<\/span>\nsummary<\/span>(<\/span>glm.res)<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e8c\u7b49\uff08passengerClass2nd\uff09\u3082\u4e09\u7b49\uff08passengerClass3rd\uff09\u3082\u751f\u5b58\u30aa\u30c3\u30ba\u6bd4\u306f\u4e00\u7b49\u306b\u6bd4\u3079\u4f4e\u3044\uff08\u30ed\u30b0\u30aa\u30c3\u30ba\u3067\u30de\u30a4\u30ca\u30b9\uff09\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
><\/span> summary<\/span>(<\/span>glm.res)<\/span>\nCall:<\/span>\nglm<\/span>(<\/span>formula =<\/span> survived ~<\/span> passengerClass,<\/span> family =<\/span> binomial<\/span>(),<\/span>\ndata =<\/span> TitanicSurvival)<\/span>\nDeviance Residuals:<\/span>\nMin       1Q   Median       3Q      Max\n-<\/span>1.3896<\/span>  -<\/span>0.7678<\/span>  -<\/span>0.7678<\/span>   0.9791<\/span>   1.6525<\/span>\nCoefficients:<\/span>\nEstimate Std. Error z value Pr<\/span>(<\/span>>|<\/span>z|<\/span>)<\/span>\n(<\/span>Intercept)<\/span>         0.4861<\/span>     0.1146<\/span>   4.242<\/span> 2.21e-05<\/span> ***<\/span>\npassengerClass2nd  -<\/span>0.7696<\/span>     0.1669<\/span>  -<\/span>4.611<\/span> 4.02e-06<\/span> ***<\/span>\npassengerClass3rd  -<\/span>1.5567<\/span>     0.1433<\/span> -<\/span>10.860<\/span>  <<\/span> 2e-16<\/span> ***<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n(<\/span>Dispersion parameter for<\/span> binomial family taken to be 1<\/span>)<\/span>\nNull deviance:<\/span> 1741.0<\/span>  on 1308<\/span>  degrees of freedom\nResidual deviance:<\/span> 1613.3<\/span>  on 1306<\/span>  degrees of freedom\nAIC:<\/span> 1619.3<\/span>\nNumber of Fisher Scoring iterations:<\/span> 4<\/span>\n<\/code><\/pre>\n\n\n\n
\u5bfe\u6570\u3092\u771f\u6570\u306b\u76f4\u3059\u3068\u3088\u308a\u308f\u304b\u308a\u3084\u3059\u3044\u3002<\/p>\n\n\n\n
\u81ea\u524d\u306err.95ci()\u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n
rr.95ci <-<\/span> function<\/span>(<\/span>x){<\/span>\nres <-<\/span> exp<\/span>(<\/span>cbind<\/span>(<\/span>coef<\/span>(<\/span>x),<\/span>confint<\/span>(<\/span>x)))<\/span>\ncolnames<\/span>(<\/span>res)<\/span> <-<\/span> c<\/span>(<\/span>\"RR\"<\/span>,<\/span>\"LL(2.5%)\"<\/span>,<\/span>\"UL(97.5%)\"<\/span>)<\/span>\nround<\/span>(<\/span>res,<\/span>2<\/span>)<\/span>\n}<\/span>\nrr.95ci<\/span>(<\/span>glm.res)<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e8c\u7b49\u306f\u751f\u5b58\u30aa\u30c3\u30ba\u6bd4 0.46\u3001\u4e09\u7b49\u306f\u751f\u5b58\u30aa\u30c3\u30ba\u6bd4 0.21\u3067\u3042\u3063\u305f\u3002<\/p>\n\n\n\n
\uff11\u3088\u308a\u4f4e\u3044\u5024\u306f\u3001\u751f\u304d\u6b8b\u308c\u306a\u304b\u3063\u305f\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002<\/p>\n\n\n\n
><\/span> rr.95ci<\/span>(<\/span>glm.res)<\/span>\nWaiting for<\/span> profiling to be done...\nRR LL<\/span>(<\/span>2.5<\/span>%)<\/span> UL<\/span>(<\/span>97.5<\/span>%)<\/span>\n(<\/span>Intercept)<\/span>       1.63<\/span>     1.30<\/span>      2.04<\/span>\npassengerClass2nd 0.46<\/span>     0.33<\/span>      0.64<\/span>\npassengerClass3rd 0.21<\/span>     0.16<\/span>      0.28<\/span>\n<\/code><\/pre>\n\n\n\n
\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\uff08\u50be\u5411\u6027\u306e\u691c\u5b9a\uff09\u3092\u3057\u3066\u307f\u308b<\/h3>\n\n\n\n
glm()\u306e\u7d50\u679c\u3092\u5229\u7528\u3057\u3066\u3001\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u3092\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
multcomp \u30d1\u30c3\u30b1\u30fc\u30b8\u306eglht()\u3092\u4f7f\u3063\u3066\u884c\u3046\u3002<\/p>\n\n\n\n
multcomp \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u3046\u306b\u306f\u3001\u4e8b\u524d\u306b\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u3066\u304a\u304f\u3002<\/p>\n\n\n\n
glht \u306f genral linear hypothesis\u306e\u7565\u3002<\/p>\n\n\n\n
install.packages<\/span>(<\/span>\"multcomp\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u4f7f\u3046\u3068\u304d\u306flibrary()\u3067\u547c\u3073\u51fa\u3057\u3066\u4f7f\u3046\u3002<\/p>\n\n\n\n
library<\/span>(<\/span>multcomp)<\/span>\n<\/code><\/pre>\n\n\n\n
\u30c8\u30ec\u30f3\u30c9\u306e\u5bfe\u6bd4\uff08\u30b3\u30f3\u30c8\u30e9\u30b9\u30c8 Contrast\uff09\u3092\u4f5c\u6210\u3057\u3066\u304a\u304f\u3002<\/p>\n\n\n\n
\u7279\u6bb5\u601d\u3046\u3068\u3053\u308d\u304c\u306a\u3051\u308c\u3070\u7dda\u5f62\u306b\u3002<\/p>\n\n\n\n
\u4eca\u56de\u306e\u3088\u3046\u306b\u3001\u4e00\u7b49\u3001\u4e8c\u7b49\u3001\u4e09\u7b49\u306a\u3069\u306e3\u3064\u306e\u30ab\u30c6\u30b4\u30ea\u306a\u3089\uff081,0,-1\uff09\u304c\u3044\u3044\u3002<\/p>\n\n\n\n
\u30c8\u30ec\u30f3\u30c9\u5bfe\u6bd4\u306e\u30b3\u30f3\u30c8\u30e9\u30b9\u30c8\u306f\u3001\u5408\u8a08\u3092\u30bc\u30ed\u306b\u3059\u308b\u306e\u304c\u6761\u4ef6\u3067\u3001\u306a\u308b\u3079\u304f\u6063\u610f\u6027\uff08\u3057\u3044\u305b\u3044\uff09\u3092\u306a\u304f\u3057\u305f\u5bfe\u6bd4\u306b\u3059\u308b\u306a\u3089\u3001\u30ab\u30c6\u30b4\u30ea\u9593\u306e\u9593\u9694\u304c\u7b49\u3057\u3044\uff08\u4eca\u56de\u306f1\uff09\u3082\u306e\u304c\u3088\u3044\u3002<\/p>\n\n\n\n
4\u3064\u306e\u5834\u5408\u306f (-3, -1, 1, 3)\u30015\u3064\u306e\u5834\u5408\u306f (-2, -1, 0, 1, 2) \u306a\u3069\u304c\u3088\u3044\u3002<\/p>\n\n\n\n
glht()\u306b\u3001glm()\u306e\u7d50\u679c\u3092\u6295\u5165\u3057\u3001\u7dda\u5f62\u95a2\u6570 linear function (linfct) \u306b \u591a\u91cd\u6bd4\u8f03 multiple comparison (mcp) \u3092\u9078\u629e\u3057\u3001\u305d\u306e\u6bd4\u8f03\u5909\u6570\u3068\u30b3\u30f3\u30c8\u30e9\u30b9\u30c8\u3092\u3001mcp(passengerClass = contr) \u3068\u3044\u3046\u3075\u3046\u306b\u6307\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n
contr <- rbind(\"linear trend\" = c(1,0,-1))\nglht.res <- glht(glm.res, linfct = mcp(passengerClass = contr))\nsummary(glht.res)<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u3053\u3061\u3089\u3002<\/p>\n\n\n\n
><\/span> summary<\/span>(<\/span>glht.res)<\/span>\nSimultaneous Tests for<\/span> General Linear Hypotheses\nMultiple Comparisons of Means:<\/span> User-<\/span>defined Contrasts\nFit:<\/span> glm<\/span>(<\/span>formula =<\/span> survived ~<\/span> passengerClass,<\/span> family =<\/span> binomial<\/span>(),<\/span>\ndata =<\/span> TitanicSurvival)<\/span>\nLinear Hypotheses:<\/span>\nEstimate Std. Error z value Pr<\/span>(<\/span>>|<\/span>z|<\/span>)<\/span>\nlinear trend ==<\/span> 0<\/span>   1.5567<\/span>     0.1433<\/span>   10.86<\/span>   <<\/span>2e-16<\/span> ***<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n(<\/span>Adjusted p values reported --<\/span> single-<\/span>step method)<\/span>\n<\/code><\/pre>\n\n\n\n
linear trend==0 \u306e\u884c\u304c\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u306e\u7d50\u679c\u3067\u3001\u53f3\u7aef\u306ep\u5024\u3092\u898b\u308b\u3068\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
Estimate\u3092\u898b\u308b\u3068\u3001\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u306e\u7d50\u679c\u3068\u540c\u3058\u7d76\u5bfe\u5024\u306e 1.5567 \u3060\u3002<\/p>\n\n\n\n
\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u306e\u898b\u308b\u3079\u304d\u884c\u306f\u3001\u4e09\u7b49\u306e\u751f\u5b58\u30aa\u30c3\u30ba\u6bd4\u306eEstimate\u3060\u3002<\/p>\n\n\n\n
\u7b26\u53f7\u304c\u7570\u306a\u308b\u304c\u7d76\u5bfe\u5024\u306f\u540c\u3058\u5024\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
\u3064\u307e\u308a\u3001\u4e09\u7fa4\u306e\u5834\u5408\u306e\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u306f\u3001\u6700\u5c0f\u306e\u7fa4\u3068\u6700\u5927\u306e\u7fa4\u306e\u6bd4\u8f03\u3068\u8a00\u3048\u308b\u308f\u3051\u3060\u3002<\/p>\n\n\n\n
\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n\"\"<\/a>\r\n
\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div>
\u5ba2\u5ba4\u30af\u30e9\u30b9\u306b\u6027\u5225\u3092\u52a0\u3048\u305f\u30e2\u30c7\u30eb\u3067\u591a\u91cd\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790\u3082\u3057\u3066\u307f\u308b<\/h2>\n\n\n\n
2\u3064\u4ee5\u4e0a\u306e\u5909\u6570\u3092\u6295\u5165\u3057\u3066\u3082\u89e3\u6790\u3067\u304d\u308b\u3002glm()\u306b\u300c+\u300d\u3067\u5909\u6570\u3092\u8ffd\u52a0\u3059\u308b\u3060\u3051\u3060\u3002<\/p>\n\n\n\n
glm.res2 <-<\/span> glm<\/span>(<\/span>survived ~<\/span> sex +<\/span> passengerClass,<\/span> data=<\/span>TitanicSurvival,<\/span> family=<\/span>binomial)<\/span>\nglht.res2 <-<\/span> glht<\/span>(<\/span>glm.res2,<\/span> linfct =<\/span> mcp<\/span>(<\/span>passengerClass =<\/span> contr))<\/span>\nsummary<\/span>(<\/span>glm.res2)<\/span>\nsummary<\/span>(<\/span>glht.res2)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7537\u6027\u306e\u751f\u5b58\u30ed\u30b0\u30aa\u30c3\u30ba\u304c\u8a08\u7b97\u3055\u308c\u3066\u3044\u308b\u304c\u3001\u30de\u30a4\u30ca\u30b9\u5024\u3067\u3042\u308a\u3001\u5973\u6027\u306b\u6bd4\u3079\u3066\u751f\u5b58\u3057\u306a\u304b\u3063\u305f\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
\u5ba2\u5ba4\u30af\u30e9\u30b9\u306e\u5024\u306f\u5358\u5909\u91cf\u306e\u3068\u304d\u3068\u5927\u5dee\u306a\u3057\u3002<\/p>\n\n\n\n
\u5ba2\u5ba4\u30af\u30e9\u30b9\u306e\u751f\u5b58\u30aa\u30c3\u30ba\u6bd4\u306e\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u306e\u7d50\u679c\u3082\u5358\u5909\u91cf\u3068\u540c\u69d8\u306b\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3067\u3042\u3063\u305f\u3002<\/p>\n\n\n\n
><\/span> summary<\/span>(<\/span>glm.res2)<\/span>\nCall:<\/span>\nglm<\/span>(<\/span>formula =<\/span> survived ~<\/span> sex +<\/span> passengerClass,<\/span> family =<\/span> binomial,<\/span>\ndata =<\/span> TitanicSurvival)<\/span>\nDeviance Residuals:<\/span>\nMin       1Q   Median       3Q      Max\n-<\/span>2.1089<\/span>  -<\/span>0.6984<\/span>  -<\/span>0.4741<\/span>   0.7167<\/span>   2.1173<\/span>\nCoefficients:<\/span>\nEstimate Std. Error z value Pr<\/span>(<\/span>>|<\/span>z|<\/span>)<\/span>\n(<\/span>Intercept)<\/span>         2.1091<\/span>     0.1728<\/span>  12.203<\/span>  <<\/span> 2e-16<\/span> ***<\/span>\nsexmale            -<\/span>2.5150<\/span>     0.1467<\/span> -<\/span>17.145<\/span>  <<\/span> 2e-16<\/span> ***<\/span>\npassengerClass2nd  -<\/span>0.8808<\/span>     0.1977<\/span>  -<\/span>4.456<\/span> 8.34e-06<\/span> ***<\/span>\npassengerClass3rd  -<\/span>1.7231<\/span>     0.1715<\/span> -<\/span>10.047<\/span>  <<\/span> 2e-16<\/span> ***<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n(<\/span>Dispersion parameter for<\/span> binomial family taken to be 1<\/span>)<\/span>\nNull deviance:<\/span> 1741.0<\/span>  on 1308<\/span>  degrees of freedom\nResidual deviance:<\/span> 1257.2<\/span>  on 1305<\/span>  degrees of freedom\nAIC:<\/span> 1265.2<\/span>\nNumber of Fisher Scoring iterations:<\/span> 4<\/span>\n><\/span> summary<\/span>(<\/span>glht.res2)<\/span>\nSimultaneous Tests for<\/span> General Linear Hypotheses\nMultiple Comparisons of Means:<\/span> User-<\/span>defined Contrasts\nFit:<\/span> glm<\/span>(<\/span>formula =<\/span> survived ~<\/span> sex +<\/span> passengerClass,<\/span> family =<\/span> binomial,<\/span>\ndata =<\/span> TitanicSurvival)<\/span>\nLinear Hypotheses:<\/span>\nEstimate Std. Error z value Pr<\/span>(<\/span>>|<\/span>z|<\/span>)<\/span>\nlinear trend ==<\/span> 0<\/span>   1.7231<\/span>     0.1715<\/span>   10.05<\/span>   <<\/span>2e-16<\/span> ***<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n(<\/span>Adjusted p values reported --<\/span> single-<\/span>step method)<\/span>\n<\/code><\/pre>\n\n\n\n
\u5225\u306e\u30bf\u30a4\u30bf\u30cb\u30c3\u30af\u53f7\u30c7\u30fc\u30bf\u3092\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf\u3068\u3057\u3066\u4f7f\u3046<\/h2>\n\n\n\n
\u30bf\u30a4\u30bf\u30cb\u30c3\u30af\u53f7\u306e\u30c7\u30fc\u30bf\u306f\u3001datasets \u30d1\u30c3\u30b1\u30fc\u30b8\u306b\u3082\u3042\u308b\u3002\u540d\u524d\u306f Titanic \u30c7\u30fc\u30bf\u3002<\/p>\n\n\n\n
\u3053\u3061\u3089\u306e\u8a18\u4e8b\u3082\u53c2\u7167\u3002<\/p>\n\n\n
\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\tR \u3067\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u3092\u884c\u3046\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t\u30bf\u30a4\u30bf\u30cb\u30c3\u30af\u53f7\u306f\u30011912\u5e744\u670814\u65e5\u306e\u591c\u3001\u6c37\u5c71\u306b\u6fc0\u7a81\u3057\u3001\u5317\u5927\u897f\u6d0b\u306e\u5e95\u306b1,500\u540d\u4ee5\u4e0a\u306e\u547d\u3068\u4e00\u7dd2\u306b\u6c88\u3093\u3060\u3002 \u4e57\u5ba2\u4e57\u54e1\u306e\u751f\u5b58\u30fb\u6b7b\u4ea1\u306e\u30c7\u30fc\u30bf\u3092\u7528\u3044\u3066\u3001\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n
Titanic \u30c7\u30fc\u30bf\u306f\u3001\u4e57\u52d9\u54e1\u306e\u30c7\u30fc\u30bf\u3082\u542b\u307e\u308c\u3066\u3044\u3066\u3001\u30c7\u30fc\u30bf\u884c\u304c\u591a\u3044\u3002<\/p>\n\n\n\n
\u5ba2\u5ba4\u30af\u30e9\u30b9\u306e\u4eba\u6570\u3082\u82e5\u5e72\u7570\u306a\u308b\uff08\u304c\u307b\u3068\u3093\u3069\u540c\u3058\uff09\u3002<\/p>\n\n\n\n
><\/span> rowSums<\/span>(<\/span>apply<\/span>(<\/span>Titanic,<\/span>c<\/span>(<\/span>1<\/span>,<\/span>4<\/span>),<\/span>sum))<\/span>\n1st  2nd  3rd Crew\n325<\/span>  285<\/span>  706<\/span>  885<\/span>\n><\/span> summary<\/span>(<\/span>TitanicSurvival$<\/span>passengerClass)<\/span>\n1st 2nd 3rd\n323<\/span> 277<\/span> 709<\/span>\n<\/code><\/pre>\n\n\n\n
Titanic \u30c7\u30fc\u30bf\u3067 Class \u306e\u751f\u5b58\u30aa\u30c3\u30ba\u6bd4\u306e\u591a\u91cd\u6bd4\u8f03\u3092\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
\u4e57\u52d9\u54e1\u306f\u5e8f\u5217\u304c\u3064\u304b\u305a\u3001\u30c8\u30ec\u30f3\u30c9\u306b\u7d44\u307f\u8fbc\u307f\u306b\u304f\u3044\u3002<\/p>\n\n\n\n
\u3086\u3048\u306b\u3001\u591a\u91cd\u6bd4\u8f03\u30b3\u30f3\u30c8\u30e9\u30b9\u30c8\u306fTukey\u306b\u3059\u308b\u3002<\/p>\n\n\n\n
Tukey\u306f\u7dcf\u5f53\u305f\u308a\u306e\u65b9\u6cd5\u3060\u3002<\/p>\n\n\n\n
Tukey\u306f\u3053\u3061\u3089\u3082\u53c2\u7167\u306e\u3053\u3068\u3002<\/p>\n\n\n
\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\tR \u3067\u30c1\u30e5\u30fc\u30ad\u30fc\u691c\u5b9a\u3092\u884c\u3046\u65b9\u6cd5<\/a>\n\t\t\t\t\t\tTukey HSD\u691c\u5b9a\u3092R\u3067\u884c\u3046\u65b9\u6cd5\u306e\u89e3\u8aac\u3002 Tukey HSD\u691c\u5b9a\u3092R\u3067\u884c\u3046\u65b9\u6cd5 aov()\u3068TukeyHSD()\u3068\u3044\u3046\u4e8c\u3064\u306e\u95a2\u6570\u3092\u4f7f\u3046\u3002 \u30c0\u30cd\u30c3\u30c8\u691c\u5b9a\u306e\u3068\u304d\u3068\u540c\u3058\u3088\u3046\u306b\u3001\u4f8b\u3068\u3057\u3066warpbreaks\u3068…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n\n\n\n\n
Titanic\u30c7\u30fc\u30bf\u306f\u3001as.data.frame()\u3067\u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u306b\u5909\u63db\u3057\u3066\u304b\u3089\u3001\u4eba\u6570\u96c6\u8a08\u30c7\u30fc\u30bf\u3086\u3048\u306eweights=Freq\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u4f7f\u3046\u65b9\u6cd5\u3067\u89e3\u6790\u3059\u308b\u3002<\/p>\n\n\n\n
\u5ba2\u5ba4\u30af\u30e9\u30b9\u30fb\u4e57\u52d9\u54e1\u306e\u7fa4\u5206\u3051\u3068\u751f\u5b58\u30fb\u6b7b\u4ea1\u306e\u591a\u91cd\u6bd4\u8f03\u3092\u3001\u5358\u5909\u91cf\u30e2\u30c7\u30eb\u3068\u6027\u5225\u3001\u5e74\u9f62\uff08\u5927\u4eba\u304b\u5b50\u4f9b\u304b\uff09\u3082\u8003\u616e\u306b\u5165\u308c\u305f\u591a\u5909\u91cf\u3067\u691c\u8a0e\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
dat <-<\/span> as.data.frame<\/span>(<\/span>Titanic)<\/span>\nlogi1 <-<\/span> glm<\/span>(<\/span>Survived~<\/span>Class,<\/span>weights=<\/span>Freq,<\/span>data=<\/span>dat,<\/span>family=<\/span>binomial)<\/span>\nlogi2 <-<\/span> glm<\/span>(<\/span>Survived ~<\/span> Class+<\/span>Sex+<\/span>Age,<\/span> weights=<\/span>Freq,<\/span> family=<\/span>binomial,<\/span> data=<\/span>dat)<\/span>\nsummary<\/span>(<\/span>glht<\/span>(<\/span>logi1,<\/span> linfct =<\/span> mcp <\/span>(<\/span>Class =<\/span> \"Tukey\"<\/span>)))<\/span>\nsummary<\/span>(<\/span>glht<\/span>(<\/span>logi2,<\/span> linfct =<\/span> mcp <\/span>(<\/span>Class =<\/span> \"Tukey\"<\/span>)))<\/span>\n<\/code><\/pre>\n\n\n\n
\u5358\u5909\u91cf\u89e3\u6790\u306e\u7dcf\u5f53\u305f\u308a\u6bd4\u8f03\u306e\u7d50\u679c\u3001\u4e09\u7b49\u5ba2\u5ba4\u306e\u4e57\u5ba2\u3068\u4e57\u52d9\u54e1\u304c\u540c\u3058\u3067\u3001\u3042\u3068\u306f\u3059\u3079\u3066\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u7570\u306a\u308b\u3068\u3044\u3046\u7d50\u679c\u3060\u3063\u305f\u3002<\/p>\n\n\n\n
\u6027\u5225\u3068\u5927\u4eba\u30fb\u5b50\u4f9b\u3092\u8003\u616e\u3059\u308b\u3068\u4e8c\u7b49\u306e\u4e57\u5ba2\u3068\u4e57\u52d9\u54e1\u304c\u540c\u3058\u3068\u3044\u3046\u7d50\u679c\u306b\u5909\u308f\u3063\u305f\u3002<\/p>\n\n\n\n
><\/span> summary<\/span>(<\/span>glht<\/span>(<\/span>logi1,<\/span> linfct =<\/span> mcp <\/span>(<\/span>Class =<\/span> \"Tukey\"<\/span>)))<\/span>\nSimultaneous Tests for<\/span> General Linear Hypotheses\nMultiple Comparisons of Means:<\/span> Tukey Contrasts\nFit:<\/span> glm<\/span>(<\/span>formula =<\/span> Survived ~<\/span> Class,<\/span> family =<\/span> binomial,<\/span> data =<\/span> dat,<\/span>\nweights =<\/span> Freq)<\/span>\nLinear Hypotheses:<\/span>\nEstimate Std. Error z value Pr<\/span>(<\/span>>|<\/span>z|<\/span>)<\/span>\n2nd -<\/span> 1st ==<\/span> 0<\/span>  -<\/span>0.85649<\/span>    0.16609<\/span>  -<\/span>5.157<\/span>   <<\/span>1e-05<\/span> ***<\/span>\n3rd -<\/span> 1st ==<\/span> 0<\/span>  -<\/span>1.59650<\/span>    0.14365<\/span> -<\/span>11.114<\/span>   <<\/span>1e-05<\/span> ***<\/span>\nCrew -<\/span> 1st ==<\/span> 0<\/span> -<\/span>1.66434<\/span>    0.13902<\/span> -<\/span>11.972<\/span>   <<\/span>1e-05<\/span> ***<\/span>\n3rd -<\/span> 2nd ==<\/span> 0<\/span>  -<\/span>0.74000<\/span>    0.14824<\/span>  -<\/span>4.992<\/span>   <<\/span>1e-05<\/span> ***<\/span>\nCrew -<\/span> 2nd ==<\/span> 0<\/span> -<\/span>0.80785<\/span>    0.14375<\/span>  -<\/span>5.620<\/span>   <<\/span>1e-05<\/span> ***<\/span>\nCrew -<\/span> 3rd ==<\/span> 0<\/span> -<\/span>0.06785<\/span>    0.11711<\/span>  -<\/span>0.579<\/span>    0.937<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n(<\/span>Adjusted p values reported --<\/span> single-<\/span>step method)<\/span>\n><\/span> summary<\/span>(<\/span>glht<\/span>(<\/span>logi2,<\/span> linfct =<\/span> mcp <\/span>(<\/span>Class =<\/span> \"Tukey\"<\/span>)))<\/span>\nSimultaneous Tests for<\/span> General Linear Hypotheses\nMultiple Comparisons of Means:<\/span> Tukey Contrasts\nFit:<\/span> glm<\/span>(<\/span>formula =<\/span> Survived ~<\/span> Class +<\/span> Sex +<\/span> Age,<\/span> family =<\/span> binomial,<\/span>\ndata =<\/span> dat,<\/span> weights =<\/span> Freq)<\/span>\nLinear Hypotheses:<\/span>\nEstimate Std. Error z value Pr<\/span>(<\/span>>|<\/span>z|<\/span>)<\/span>\n2nd -<\/span> 1st ==<\/span> 0<\/span>   -<\/span>1.0181<\/span>     0.1960<\/span>  -<\/span>5.194<\/span>   <<\/span>1e-04<\/span> ***<\/span>\n3rd -<\/span> 1st ==<\/span> 0<\/span>   -<\/span>1.7778<\/span>     0.1716<\/span> -<\/span>10.362<\/span>   <<\/span>1e-04<\/span> ***<\/span>\nCrew -<\/span> 1st ==<\/span> 0<\/span>  -<\/span>0.8577<\/span>     0.1573<\/span>  -<\/span>5.451<\/span>   <<\/span>1e-04<\/span> ***<\/span>\n3rd -<\/span> 2nd ==<\/span> 0<\/span>   -<\/span>0.7597<\/span>     0.1764<\/span>  -<\/span>4.308<\/span>   <<\/span>1e-04<\/span> ***<\/span>\nCrew -<\/span> 2nd ==<\/span> 0<\/span>   0.1604<\/span>     0.1738<\/span>   0.923<\/span>    0.791<\/span>\nCrew -<\/span> 3rd ==<\/span> 0<\/span>   0.9201<\/span>     0.1486<\/span>   6.192<\/span>   <<\/span>1e-04<\/span> ***<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n(<\/span>Adjusted p values reported --<\/span> single-<\/span>step method)<\/span>\n<\/code><\/pre>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u30bf\u30a4\u30bf\u30cb\u30c3\u30af\u53f7\u306e\u751f\u5b58\u30fb\u6b7b\u4ea1\u30c7\u30fc\u30bf\u3092\u7528\u3044\u3066\u3001\u5ba2\u5ba4\u30af\u30e9\u30b9\u306e\u9055\u3044\u306b\u3088\u308b\u751f\u5b58\u78ba\u7387\u3092\u691c\u8a0e\u3057\u305f\u3002<\/p>\n\n\n\n
\u4e00\u7b49\u3001\u4e8c\u7b49\u3001\u4e09\u7b49\u306e\u9806\u306b\u751f\u5b58\u3067\u304d\u306a\u304b\u3063\u305f\u30c8\u30ec\u30f3\u30c9\u304c\u898b\u3089\u308c\u305f\u3002<\/p>\n\n\n\n
\u751f\u5b58\u30fb\u6b7b\u4ea1\u306a\u3069\u4e8c\u5024\u306e\u30c7\u30fc\u30bf\u3092\u6271\u3046\u56de\u5e30\u5206\u6790\u306f\u3001\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790\u3067\u3001R \u3067\u306fglm()\u3092\u4f7f\u3044\u3001familiy=binomial\u3068\u3044\u3046\u6307\u5b9a\u3092\u5165\u308c\u308b\u3002<\/p>\n\n\n\n
\u307e\u305f\u3001\u30e2\u30c7\u30eb\u4e2d\u306e\u4e09\u7fa4\u4ee5\u4e0a\u306e\u30c8\u30ec\u30f3\u30c9\u691c\u5b9a\u3092\u884c\u3044\u305f\u3044\u3068\u304d\u306f\u3001glm()\u306e\u7d50\u679c\u3092\u7528\u3044\u3066\u3001multcomp \u30d1\u30c3\u30b1\u30fc\u30b8\u306eglht()\u3092\u4f7f\u3046\u3068\u3088\u3044\u3002<\/p>\n\n\n\n
\u30c8\u30ec\u30f3\u30c9\u5bfe\u6bd4\u306f (-1, 0, 1), (-3, -1, 1, 3), (-2, -1, 0, 1, 2) \u306a\u3069\u3092\u4f7f\u3046\u3002<\/p>\n\n\n\n
\u3082\u3046\u4e00\u3064\u306e\u30bf\u30a4\u30bf\u30cb\u30c3\u30af\u53f7\u306e\u30c7\u30fc\u30bf Titanic \u3067\u3001\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790\uff06\u591a\u91cd\u6bd4\u8f03\u3092\u884c\u3063\u3066\u307f\u305f\u3002<\/p>\n\n\n\n
multcomp \u30d1\u30c3\u30b1\u30fc\u30b8\u306e glht()\u3092\u4f7f\u3046\u3068\u3001\u591a\u5909\u91cf\u8abf\u6574\u306e\u30e2\u30c7\u30eb\u4e2d\u306e\u30b0\u30eb\u30fc\u30d7\u5909\u6570\u306b\u304a\u3051\u308b\u4e09\u7fa4\u4ee5\u4e0a\u306e\u591a\u91cd\u6bd4\u8f03\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u304a\u3059\u3059\u3081\u66f8\u7c4d<\/h2>\n\n\n\n
\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790: SAS\u3092\u5229\u7528\u3057\u305f\u7d71\u8a08\u89e3\u6790\u306e\u5b9f\u969b (\u7d71\u8a08\u30e9\u30a4\u30d6\u30e9\u30ea\u30fc)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
R \u306b\u7d44\u307f\u8fbc\u307f\u306e\u30bf\u30a4\u30bf\u30cb\u30c3\u30af\u53f7\u306e\u751f\u5b58\u30fb\u6b7b\u4ea1\u30c7\u30fc\u30bf\u3067\u3001\u751f\u5b58\u30fb\u6b7b\u4ea1\u306b\u95a2\u3059\u308b\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u5206\u6790\u3068\u3001\u72ec\u7acb\u5909\u6570\u306e\u591a\u91cd\u6bd4\u8f03\u3092\u5b9f\u884c\u3057\u3066\u307f\u308b\u3002<\/p>\n","protected":false},"author":2,"featured_media":2419,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[5,47,24,49],"tags":[],"class_list":["post-414","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-r","category-47","category-24","category-49"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2019\/09\/20190911190826.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/414","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=414"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/414\/revisions"}],"predecessor-version":[{"id":3526,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/414\/revisions\/3526"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/2419"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=414"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=414"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=414"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}