{"id":100,"date":"2023-06-16T22:06:43","date_gmt":"2023-06-16T13:06:43","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/regression-line-and-confidence-interval-of-poisson-regression-in-r\/"},"modified":"2024-08-29T21:42:37","modified_gmt":"2024-08-29T12:42:37","slug":"regression-line-and-confidence-interval-of-poisson-regression-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/regression-line-and-confidence-interval-of-poisson-regression-in-r\/","title":{"rendered":"R \u3067\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u306e 95 \uff05 \u4fe1\u983c\u533a\u9593\u4ed8\u304d\u56de\u5e30\u76f4\u7dda\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u65b9\u6cd5"},"content":{"rendered":"\n

\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf\u306e\u6563\u5e03\u56f3\u306b\u3001\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u306e\u56de\u5e30\u76f4\u7dda\u3068\u4e88\u6e2c\u5024\u306e 95 \uff05 \u4fe1\u983c\u533a\u9593\u3092\u66f8\u304d\u5165\u308c\u305f\u30b0\u30e9\u30d5\u306e\u66f8\u304d\u65b9<\/p>\n\n\n\n\n\n\n\n

\u30dd\u30a2\u30bd\u30f3\u56de\u5e30<\/h2>\n\n\n\n

\u307e\u308c\u306a\u4e8b\u8c61\u304c\u8d77\u304d\u308b\u3053\u3068\u3092\u8868\u73fe\u3057\u305f\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u3092\u793a\u3059\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf\uff08\u767a\u751f\u6570\u306e\u6570\u3092\u6570\u3048\u305f\u30c7\u30fc\u30bf\uff09\u3092\u4e88\u6e2c\u3059\u308b\u56de\u5e30\u30e2\u30c7\u30eb<\/p>\n\n\n\n

\u3053\u3061\u3089\u3082\u53c2\u7167\u306e\u3053\u3068<\/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\tEZR \u3067\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u5206\u6790\u3092\u884c\u3046\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u3092 EZR \u3067\u884c\u3046\u65b9\u6cd5\u306e\u89e3\u8aac \u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u30fb\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u3068\u306f \u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u3068\u306f\u3001\u307e\u308c\u306b\u3057\u304b\u8d77\u3053\u3089\u306a\u3044\u73fe\u8c61\u3092\u6570\u3048\u305f\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf\u3092\u76ee\u7684\u5909\u6570\u306b\u3057\u305f\u56de\u5e30\u5206\u6790\u306e…<\/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

\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf<\/h2>\n\n\n\n

\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf\u306f\u3001\u690d\u7269\u306e\u4f53\u30b5\u30a4\u30ba x \u3001\u7a2e\u5b50\u6570 y \u306e\u30c7\u30fc\u30bf\u3067\u3042\u308b<\/p>\n\n\n\n

data3a.csv \u3068\u3044\u3046\u30c7\u30fc\u30bf\u3067\u3001data3a \u3068\u3044\u3046\u540d\u524d\u3092\u4ed8\u3051\u3066\u8aad\u307f\u8fbc\u3080<\/p>\n\n\n\n

data3a <-<\/span> read.csv<\/span>(<\/span>\"data3a.csv\"<\/span>)<\/span>\nhead<\/span>(<\/span>data3a)<\/span>\n<\/code><\/pre>\n\n\n\n
\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u5148\u982d\u90e8\u5206\u3092\u793a\u3059<\/p>\n\n\n\n
\u4eca\u56de\u30b0\u30eb\u30fc\u30d7\u5909\u6570\u306e f \u306f\u4f7f\u308f\u306a\u3044<\/p>\n\n\n\n
><\/span> head<\/span>(<\/span>data3a)<\/span>\ny     x f\n1<\/span>  6<\/span>  8.31<\/span> C\n2<\/span>  6<\/span>  9.44<\/span> C\n3<\/span>  6<\/span>  9.50<\/span> C\n4<\/span> 12<\/span>  9.07<\/span> C\n5<\/span> 10<\/span> 10.16<\/span> C\n6<\/span>  4<\/span>  8.32<\/span> C\n<\/code><\/pre>\n\n\n\n
\u6563\u5e03\u56f3\u3092\u898b\u3066\u307f\u308b<\/p>\n\n\n\n
### Scattergram<\/span>\nlibrary<\/span>(<\/span>ggplot2)<\/span>\nggplot<\/span>(<\/span>data=<\/span>data3a,<\/span> aes<\/span>(<\/span>x=<\/span>x,<\/span> y=<\/span>y))<\/span>+<\/span>\ngeom_point<\/span>(<\/span>size=<\/span>3<\/span>)<\/span>+<\/span>\ntheme_classic<\/span>()<\/span>\n<\/code><\/pre>\n\n\n\n
\u6563\u5e03\u56f3\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u306a\u3093\u3068\u306a\u304f\u53f3\u80a9\u4e0a\u304c\u308a\u306e\u5206\u5e03\u306e\u3088\u3046\u306a\u3001\u305d\u3046\u3067\u3082\u306a\u3044\u3088\u3046\u306a\u30fb\u30fb\u30fb<\/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>
\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\uff1a\u504f\u56de\u5e30\u4fc2\u6570\u63a8\u5b9a\u3068\u4e88\u6e2c\u5024\u8a08\u7b97<\/h2>\n\n\n\n
\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u3092\u5b9f\u969b\u306b\u884c\u3063\u3066\u307f\u308b<\/p>\n\n\n\n
R \u3067\u306f\u3001glm() \u3092\u4f7f\u3046<\/p>\n\n\n\n
family=poisson(link='log')<\/code><\/pre>\n\n\n\n
\u3053\u306e\u6307\u5b9a\u304c\u91cd\u8981\u3067\u3042\u308b<\/p>\n\n\n\n
\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a<\/p>\n\n\n\n
glm.fit1 <-<\/span> glm<\/span>(<\/span>y~<\/span>x,<\/span> family=<\/span>poisson<\/span>(<\/span>link=<\/span>'log'<\/span>),<\/span> data=<\/span>data3a)<\/span>\nsummary<\/span>(<\/span>glm.fit1)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u51fa\u529b\u3055\u308c\u308b<\/p>\n\n\n\n
><\/span> summary(<\/span>glm.fit1)<\/span>\nCall:<\/span>\nglm(<\/span>formula =<\/span> y ~<\/span> x,<\/span> family =<\/span> poisson(<\/span>link =<\/span> \"log\"),<\/span> data =<\/span> data3a)<\/span>\nDeviance Residuals:<\/span>\nMin       1Q   Median       3Q      Max\n-2.3679<\/span>  -0.7348<\/span>  -0.1775<\/span>   0.6987<\/span>   2.3760<\/span>\nCoefficients:<\/span>\nEstimate Std. Error z value Pr(>|<\/span>z|)<\/span>\n(<\/span>Intercept)<\/span>  1.29172<\/span>    0.36369<\/span>   3.552<\/span> 0.000383<\/span> ***<\/span>\nx            0.07566<\/span>    0.03560<\/span>   2.125<\/span> 0.033580<\/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> poisson family taken to be 1)<\/span>\nNull deviance:<\/span> 89.507<\/span>  on 99<\/span>  degrees of freedom\nResidual deviance:<\/span> 84.993<\/span>  on 98<\/span>  degrees of freedom\nAIC:<\/span> 474.77<\/span>\nNumber of Fisher Scoring iterations:<\/span> 4<\/span><\/code><\/pre>\n\n\n\n
x \u304c 1 \u5927\u304d\u304f\u306a\u308b\u3068\u3001y \u306f\u30010.07566 \u5927\u304d\u304f\u306a\u308b<\/p>\n\n\n\n
\u771f\u6570\u306b\u623b\u3059\u3068\u500b\u6570\u306b\u306a\u308b<\/p>\n\n\n\n
$ e^{0.07566} = 1.078596 $ \u306a\u306e\u3067\u3001\u7d04 1 \u500b\u5897\u3048\u308b\u3068\u3044\u3046\u3053\u3068\u3060<\/p>\n\n\n\n
\u4e88\u6e2c\u5024\u306e\u8a08\u7b97<\/h2>\n\n\n\n
\u4e88\u6e2c\u5f0f\u3092\u7528\u3044\u3066\u3001\u4e88\u6e2c\u5024\u306e\u8a08\u7b97\u3092\u884c\u3046<\/p>\n\n\n\n
\u4e88\u6e2c\u5f0f\u306f\u3001$ y = e^{(1.29172 + 0.07566 \\times x)} $<\/p>\n\n\n\n
\u4e88\u6e2c\u5024\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308b<\/p>\n\n\n\n
\u4e88\u6e2c\u5024\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u306f\u3001x = new_data \u3092\u6e96\u5099\u3057\u3066\u304a\u304f\u5fc5\u8981\u304c\u3042\u308b<\/p>\n\n\n\n
### Fitted values<\/span>\nnew_data <-<\/span> data.frame(<\/span>x=seq(min(<\/span>data3a$<\/span>x),<\/span> max(<\/span>data3a$<\/span>x),<\/span>\nlength=100))<\/span>\npred.glm.fit1 <-<\/span> predict(<\/span>glm.fit1,<\/span> new_data,<\/span> type='link',<\/span>\nse.fit=TRUE)<\/span>\n### 95% confidence interval limits<\/span>\nalpha <-<\/span> 0.05<\/span>\nci.upper <-<\/span> exp(<\/span>pred.glm.fit1$<\/span>fit +<\/span>\n(qnorm(1-<\/span>alpha\/2)*<\/span>pred.glm.fit1$<\/span>se.fit))<\/span>\nci.lower <-<\/span> exp(<\/span>pred.glm.fit1$<\/span>fit -<\/span>\n(qnorm(1-<\/span>alpha\/2)*<\/span>pred.glm.fit1$<\/span>se.fit))<\/span><\/code><\/pre>\n\n\n\n
ci.upper, ci.lower \u306f\u4e88\u6e2c\u5024\u306e 95 \uff05 \u4fe1\u983c\u533a\u9593\u306e\u4e0a\u9650\u3068\u4e0b\u9650\u3060<\/p>\n\n\n\n
\u5f0f\u3067\u66f8\u3044\u3066\u307f\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b<\/p>\n\n\n\n

$$ \\displaystyle e^{(log(\\hat{y}) \\pm Z_{\\alpha\/2} \\times SE)} $$
<\/p>\n\n\n\n
\u6563\u5e03\u56f3\u3068\u56de\u5e30\u76f4\u7dda<\/h2>\n\n\n\n
\u5148\u307b\u3069\u306e\u6563\u5e03\u56f3\u306b\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u3067\u5f97\u305f\u56de\u5e30\u76f4\u7dda\u3092\u66f8\u304d\u5165\u308c\u3066\u307f\u308b<\/p>\n\n\n\n
# 1\u3064\u76ee\u306e\u6563\u5e03\u56f3<\/span>\ngraph1 <-<\/span> ggplot<\/span>(<\/span>data =<\/span> data3a,<\/span> aes<\/span>(<\/span>x =<\/span> x,<\/span> y =<\/span> y))<\/span> +<\/span>\ngeom_point<\/span>(<\/span>size =<\/span> 3<\/span>)<\/span> +<\/span>\ntheme_classic<\/span>()<\/span>\n# \u56de\u5e30\u66f2\u7dda\u3092\u91cd\u306d\u308b<\/span>\ngraph1 +<\/span>\ngeom_line<\/span>(<\/span>data=<\/span>data.frame<\/span>(<\/span>x=<\/span>new_data,<\/span> y=<\/span>exp<\/span>(<\/span>pred.glm.fit1$<\/span>fit)),<\/span>\naes<\/span>(<\/span>x =<\/span> x,<\/span> y =<\/span> y),<\/span> linewidth =<\/span> 2<\/span>)<\/span>+<\/span>\ngeom_line<\/span>(<\/span>data =<\/span> data.frame<\/span>(<\/span>x =<\/span> new_data,<\/span> y =<\/span> ci.upper),<\/span>\naes<\/span>(<\/span>x=<\/span>x,<\/span> y=<\/span>y),<\/span> linewidth=<\/span>1<\/span>,<\/span> linetype=<\/span>2<\/span>)<\/span>+<\/span>\ngeom_line<\/span>(<\/span>data=<\/span>data.frame<\/span>(<\/span>x=<\/span>new_data,<\/span> y=<\/span>ci.lower),<\/span>\naes<\/span>(<\/span>x=<\/span>x,<\/span> y=<\/span>y),<\/span> linewidth=<\/span>1<\/span>,<\/span> linetype=<\/span>2<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u6700\u521d\u306e ggplot() \u3067\u6563\u5e03\u56f3\u3092\u66f8\u304d\u3001graph1 + geom_line() \u3067\u3001\u56de\u5e30\u76f4\u7dda\u3068\u4fe1\u983c\u533a\u9593\u3092\u66f8\u304d\u5165\u308c\u308b<\/p>\n\n\n\n
\u3067\u304d\u3042\u304c\u308a\u306e\u56f3\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a<\/p>\n\n\n\n
\u5b9f\u7dda\u304c\u4e88\u6e2c\u5024\u3067\u3001\u7834\u7dda\u304c\u4fe1\u983c\u533a\u9593\u306e\u4e0a\u9650\u3068\u4e0b\u9650\u3067\u3042\u308b<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u4eca\u56de\u306e\u30c7\u30fc\u30bf\u3092\u76f4\u7dda\u3067\u4e88\u6e2c\u3059\u308b\u3068\u3044\u3046\u306e\u306f\u3057\u3087\u305b\u3093\u7121\u7406\u304c\u3042\u308b\u306a\u3068\u3044\u3063\u305f\u3068\u3053\u308d<\/p>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u30dd\u30a2\u30bd\u30f3\u56de\u5e30\u5206\u6790\u304b\u3089\u5f97\u3089\u308c\u305f\u3001\u4e88\u6e2c\u5024\u3068 95 \uff05 \u4fe1\u983c\u533a\u9593\u3092\u3001\u5143\u306e\u6563\u5e03\u56f3\u306b\u66f8\u304d\u5165\u308c\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u305f<\/p>\n\n\n\n
\u53c2\u8003\u306b\u306a\u308c\u3070<\/p>\n\n\n\n
\u53c2\u8003\u30b5\u30a4\u30c8<\/h2>\n\n\n\n
\u30dd\u30a2\u30bd\u30f3\u56de\u5e30 | R glm \u95a2\u6570\u3092\u5229\u7528\u3057\u3066\u30ab\u30a6\u30f3\u30c8\u30c7\u30fc\u30bf\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u4f5c\u6210<\/a><\/p>\n\n\n\n
\u53c2\u8003\u66f8\u7c4d\u30fb\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf<\/h2>\n\n\n\n
\u30c7\u30fc\u30bf\u89e3\u6790\u306e\u305f\u3081\u306e\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u5165\u9580<\/p>\n\n\n\n
\"\u30c7\u30fc\u30bf\u89e3\u6790\u306e\u305f\u3081\u306e\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u5165\u9580\u2015\u2015\u4e00\u822c\u5316\u7dda\u5f62\u30e2\u30c7\u30eb\u30fb\u968e\u5c64\u30d9\u30a4\u30ba\u30e2\u30c7\u30eb\u30fbMCMC<\/a>\n
\n
\u30c7\u30fc\u30bf\u89e3\u6790\u306e\u305f\u3081\u306e\u7d71\u8a08\u30e2\u30c7\u30ea\u30f3\u30b0\u5165\u9580\u2015\u2015\u4e00\u822c\u5316\u7dda\u5f62\u30e2\u30c7\u30eb\u30fb\u968e\u5c64\u30d9\u30a4\u30ba\u30e2\u30c7\u30eb\u30fbMCMC (\u78ba\u7387\u3068\u60c5\u5831\u306e\u79d1\u5b66)<\/a><\/p>\n