{"id":25538,"date":"2024-01-22T16:59:27","date_gmt":"2024-01-22T08:59:27","guid":{"rendered":"http:\/\/www.biocloudservice.com\/wordpress\/?p=25538"},"modified":"2024-01-22T16:59:28","modified_gmt":"2024-01-22T08:59:28","slug":"%e4%ba%94%e5%88%86%e9%92%9f%e5%b8%a6%e4%bd%a0%e5%bf%ab%e9%80%9f%e4%bd%bf%e7%94%a8r%e8%af%ad%e8%a8%80%e5%8c%85pbkrtest%e5%ba%94%e7%94%a8%e7%bb%9f%e8%ae%a1%e5%bb%ba%e6%a8%a1","status":"publish","type":"post","link":"http:\/\/www.biocloudservice.com\/wordpress\/?p=25538","title":{"rendered":"\u4e94\u5206\u949f\u5e26\u4f60\u5feb\u901f\u4f7f\u7528R\u8bed\u8a00\u5305pbkrtest\u5e94\u7528\u7edf\u8ba1\u5efa\u6a21"},"content":{"rendered":"<p>pbkrtest\u5305\u7684\u4e3b\u8981\u529f\u80fd\u662f\u63d0\u4f9b\u6709\u6548\u7684\u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\uff0c\u7528\u4e8e\u8bc4\u4f30\u6df7\u5408\u6548\u5e94\u6a21\u578b\u4e2d\u56fa\u5b9a\u6548\u5e94\u7684\u663e\u8457\u6027\u3002\u5b83\u901a\u8fc7\u8ba1\u7b97\u8fd1\u4f3c\u7684p\u503c\uff0c\u5229\u7528\u53c2\u6570\u4f30\u8ba1\u7684\u6e10\u8fd1\u5206\u5e03\uff0c\u6765\u8fdb\u884c\u7edf\u8ba1\u63a8\u65ad\u3002\u8fd9\u79cd\u8fd1\u4f3c\u65b9\u6cd5\u5bf9\u4e8e\u5927\u578b\u6570\u636e\u96c6\u548c\u590d\u6742\u7684\u6a21\u578b\u7ed3\u6784\u5c24\u5176\u6709\u7528\uff0c\u56e0\u4e3a\u5b83\u53ef\u4ee5\u663e\u8457\u964d\u4f4e\u8ba1\u7b97\u7684\u590d\u6742\u6027\u3002<\/p>\n<p>\u5728\u4f7f\u7528pbkrtest\u5305\u65f6\uff0c\u7528\u6237\u53ef\u4ee5\u6307\u5b9a\u6df7\u5408\u6548\u5e94\u6a21\u578b\uff0c\u5e76\u4f7f\u7528\u9002\u5f53\u7684\u51fd\u6570\u8fdb\u884c\u62df\u5408\u3002\u7136\u540e\uff0c\u53ef\u4ee5\u4f7f\u7528summary()\u51fd\u6570\u6765\u67e5\u770b\u6a21\u578b\u7684\u6458\u8981\u4fe1\u606f\uff0c\u5305\u62ec\u56fa\u5b9a\u6548\u5e94\u7684\u4f30\u8ba1\u503c\u3001\u6807\u51c6\u8bef\u5dee\u548c\u7f6e\u4fe1\u533a\u95f4\u3002\u540c\u65f6\uff0cpbkrtest\u5305\u8fd8\u63d0\u4f9b\u4e86anova()\u51fd\u6570\uff0c\u7528\u4e8e\u6bd4\u8f83\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u663e\u8457\u6027\u5dee\u5f02\u3002<\/p>\n<p>\u4e0e\u4f20\u7edf\u7684\u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\u76f8\u6bd4\uff0cpbkrtest\u5305\u7684\u4f18\u52bf\u5728\u4e8e\u5b83\u80fd\u591f\u8003\u8651\u5230\u6df7\u5408\u6548\u5e94\u6a21\u578b\u7684\u7279\u6b8a\u7ed3\u6784\uff0c\u5e76\u63d0\u4f9b\u4e86\u66f4\u51c6\u786e\u7684\u5047\u8bbe\u68c0\u9a8c\u7ed3\u679c\u3002\u4f20\u7edf\u7684\u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\u901a\u5e38\u5047\u8bbe\u6570\u636e\u72ec\u7acb\u540c\u5206\u5e03\uff0c\u800c\u6df7\u5408\u6548\u5e94\u6a21\u578b\u5219\u80fd\u591f\u5904\u7406\u6570\u636e\u4e2d\u5b58\u5728\u7684\u5c42\u7ea7\u7ed3\u6784\u548c\u76f8\u5173\u6027\u3002\u6b64\u5916\uff0cpbkrtest\u5305\u8fd8\u63d0\u4f9b\u4e86\u6a21\u578b\u8bca\u65ad\u7684\u529f\u80fd\uff0c\u53ef\u4ee5\u5e2e\u52a9\u7528\u6237\u8bc4\u4f30\u6a21\u578b\u7684\u62df\u5408\u7a0b\u5ea6\u548c\u5047\u8bbe\u7684\u5408\u7406\u6027\u3002<\/p>\n<p>pbkrtest\u5305\u7684\u5e94\u7528\u8303\u56f4\u975e\u5e38\u5e7f\u6cdb\uff0c\u9002\u7528\u4e8e\u8bb8\u591a\u9886\u57df\u7684\u6570\u636e\u5206\u6790\u548c\u7814\u7a76\u3002\u4f8b\u5982\uff0c\u5728\u793e\u4f1a\u79d1\u5b66\u4e2d\uff0c\u7814\u7a76\u4eba\u5458\u53ef\u4ee5\u4f7f\u7528\u6df7\u5408\u6548\u5e94\u6a21\u578b\u6765\u5206\u6790\u5bb6\u5ead\u3001\u793e\u533a\u6216\u5b66\u6821\u4e4b\u95f4\u7684\u5dee\u5f02\u5bf9\u4e2a\u4f53\u884c\u4e3a\u7684\u5f71\u54cd\u3002\u5728\u751f\u7269\u533b\u5b66\u7814\u7a76\u4e2d\uff0c\u6df7\u5408\u6548\u5e94\u6a21\u578b\u53ef\u4ee5\u7528\u4e8e\u8003\u8651\u5b9e\u9a8c\u8bbe\u8ba1\u7684\u91cd\u590d\u6027\uff0c\u4ece\u800c\u66f4\u51c6\u786e\u5730\u8bc4\u4f30\u6cbb\u7597\u6548\u679c\u3002<\/p>\n<p>\u8981\u4f7f\u7528pbkrtest\u5305\uff0c\u53ef\u4ee5\u5728R\u4e2d\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u8fdb\u884c\u5b89\u88c5\u548c\u52a0\u8f7d\uff1a<\/p>\n<p>&gt; install.packages(&#8220;pbkrtest&#8221;) #\u5b89\u88c5pbkrtest\u8bed\u8a00\u5305<\/p>\n<p>&gt; library(pbkrtest) #\u52a0\u8f7d\u8bed\u8a00\u5305<\/p>\n<p>\u4e0b\u9762\u662f\u4e00\u4e2a\u4f7f\u7528pbkrtest\u5305\u8fdb\u884c\u751f\u7269\u4fe1\u606f\u76f8\u5173\u5b9e\u9645\u6570\u636e\u5206\u6790\u7684\u793a\u4f8b\uff1a<\/p>\n<p>\u5047\u8bbe\u6211\u4eec\u6b63\u5728\u7814\u7a76\u4e00\u79cd\u65b0\u836f\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\u3002\u6211\u4eec\u6709\u4e00\u4e2a\u5b9e\u9a8c\u6570\u636e\u96c6\uff0c\u5176\u4e2d\u5305\u542b\u4e8610\u4e2a\u75c5\u4eba\uff0c\u5728\u7ed9\u4e88\u836f\u7269\u6cbb\u7597\u524d\u540e\uff0c\u6d4b\u91cf\u4e86\u4ed6\u4eec\u7684\u57fa\u56e0\u8868\u8fbe\u6c34\u5e73\u3002\u6b64\u5916\uff0c\u6bcf\u4e2a\u75c5\u4eba\u8fd8\u6709\u4e00\u4e9b\u57fa\u672c\u4fe1\u606f\uff0c\u5982\u6027\u522b\u548c\u5e74\u9f84\u3002\u6211\u4eec\u60f3\u8981\u786e\u5b9a\u836f\u7269\u662f\u5426\u5bf9\u57fa\u56e0\u8868\u8fbe\u4ea7\u751f\u663e\u8457\u5f71\u54cd\uff0c\u5e76\u4e14\u662f\u5426\u5b58\u5728\u4e2a\u4f53\u95f4\u7684\u5dee\u5f02\u3002<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u52a0\u8f7d\u6240\u9700\u7684\u5305\uff0c\u5e76\u5bfc\u5165\u6570\u636e\u96c6\u3002\u5047\u8bbe\u6211\u4eec\u7684\u6570\u636e\u96c6\u547d\u540d\u4e3a&#8221;gene_expression.csv&#8221;\uff0c\u5176\u4e2d\u5305\u542b\u4e86&#8221;PatientID&#8221;\uff08\u75c5\u4ebaID\uff09\u3001&#8221;Treatment&#8221;\uff08\u6cbb\u7597\u524d\u540e\uff09\u3001&#8221;GeneExpression&#8221;\uff08\u57fa\u56e0\u8868\u8fbe\u6c34\u5e73\uff09\u3001&#8221;Gender&#8221;\uff08\u6027\u522b\uff09\u548c&#8221;Age&#8221;\uff08\u5e74\u9f84\uff09\u7b49\u53d8\u91cf\u3002<\/p>\n<p># \u52a0\u8f7d\u6240\u9700\u7684\u5305<\/p>\n<p>&gt; library(lme4)<\/p>\n<p>&gt; library(pbkrtest)<\/p>\n<p># \u5bfc\u5165\u6570\u636e\u96c6<\/p>\n<p>&gt; data &lt;- read.csv(&#8220;gene_expression.csv&#8221;)<\/p>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u6df7\u5408\u6548\u5e94\u6a21\u578b\uff0c\u5176\u4e2d\u57fa\u56e0\u8868\u8fbe\u6c34\u5e73\u662f\u56e0\u53d8\u91cf\uff0c\u6cbb\u7597\u548c\u75c5\u4eba\u662f\u56fa\u5b9a\u6548\u5e94\uff0c\u800c\u75c5\u4eba\u662f\u968f\u673a\u6548\u5e94\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528lmer()\u51fd\u6570\u6765\u62df\u5408\u8be5\u6a21\u578b\u3002<\/p>\n<p># \u6784\u5efa\u6df7\u5408\u6548\u5e94\u6a21\u578b<\/p>\n<p>&gt; model &lt;- lmer(GeneExpression ~ Treatment + (1 | PatientID), data = data)<\/p>\n<p>\u7136\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528pbkrtest\u5305\u63d0\u4f9b\u7684summary()\u51fd\u6570\u6765\u67e5\u770b\u6a21\u578b\u7684\u6458\u8981\u4fe1\u606f\uff0c\u5305\u62ec\u56fa\u5b9a\u6548\u5e94\u7684\u4f30\u8ba1\u503c\u3001\u6807\u51c6\u8bef\u5dee\u548c\u7f6e\u4fe1\u533a\u95f4\u3002<\/p>\n<p># \u67e5\u770b\u6a21\u578b\u6458\u8981\u4fe1\u606f<\/p>\n<p>&gt; summary(model)<\/p>\n<p>\u8f93\u51fa\u7684\u6458\u8981\u4fe1\u606f\u5c06\u63d0\u4f9b\u56fa\u5b9a\u6548\u5e94\u7684\u4f30\u8ba1\u503c\u3001\u6807\u51c6\u8bef\u5dee\u548c\u7f6e\u4fe1\u533a\u95f4\u7b49\u7edf\u8ba1\u91cf\u3002\u901a\u8fc7\u68c0\u67e5\u56fa\u5b9a\u6548\u5e94\u7684p\u503c\uff0c\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u6cbb\u7597\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\u662f\u5426\u663e\u8457\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528anova()\u51fd\u6570\u6765\u6bd4\u8f83\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u663e\u8457\u6027\u5dee\u5f02\u3002\u5047\u8bbe\u6211\u4eec\u8fd8\u60f3\u8003\u8651\u6027\u522b\u548c\u5e74\u9f84\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u4e00\u4e2a\u5305\u542b\u8fd9\u4e9b\u53d8\u91cf\u7684\u6a21\u578b\uff0c\u5e76\u4f7f\u7528anova()\u51fd\u6570\u8fdb\u884c\u6bd4\u8f83\u3002<\/p>\n<p># \u6784\u5efa\u5305\u542b\u6027\u522b\u548c\u5e74\u9f84\u7684\u6a21\u578b<\/p>\n<p>&gt; model_full &lt;- lmer(GeneExpression ~ Treatment + Gender + Age + (1 | PatientID), data = data)<\/p>\n<p># \u6bd4\u8f83\u4e24\u4e2a\u6a21\u578b\u7684\u663e\u8457\u6027\u5dee\u5f02<\/p>\n<p>&gt; anova(model, model_full)<\/p>\n<p>\u901a\u8fc7\u6bd4\u8f83\u6a21\u578b\u7684\u663e\u8457\u6027\u5dee\u5f02\uff0c\u6211\u4eec\u53ef\u4ee5\u786e\u5b9a\u662f\u5426\u6709\u5fc5\u8981\u5c06\u6027\u522b\u548c\u5e74\u9f84\u8003\u8651\u5728\u5185\u3002<\/p>\n<p>\u5728\u8fd9\u4e2a\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u4f7f\u7528pbkrtest\u5305\u6765\u5206\u6790\u751f\u7269\u4fe1\u606f\u76f8\u5173\u7684\u5b9e\u9645\u6570\u636e\u3002\u6211\u4eec\u6784\u5efa\u4e86\u6df7\u5408\u6548\u5e94\u6a21\u578b\uff0c\u8003\u8651\u4e86\u6cbb\u7597\u548c\u4e2a\u4f53\u95f4\u7684\u5dee\u5f02\uff0c\u5e76\u4f7f\u7528summary()\u51fd\u6570\u67e5\u770b\u4e86\u6a21\u578b\u7684\u6458\u8981\u4fe1\u606f\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u4f7f\u7528anova()\u51fd\u6570\u6bd4\u8f83\u4e86\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u663e\u8457\u6027\u5dee\u5f02\u3002\u901a\u8fc7\u8fd9\u4e9b\u5206\u6790\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u5173\u4e8e\u836f\u7269\u5bf9\u57fa\u56e0\u8868\u8fbe\u7684\u5f71\u54cd\u4ee5\u53ca\u5176\u4ed6\u56e0\u7d20\u7684\u7ed3\u8bba\u3002<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" width=\"640\" height=\"378\" class=\"wp-image-25539\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/mm-2.png?resize=640%2C378\" alt=\"mm-2\" srcset=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/mm-2.png?w=1265 1265w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/mm-2.png?resize=300%2C177 300w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/mm-2.png?resize=1024%2C605 1024w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/mm-2.png?resize=768%2C454 768w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/mm-2.png?resize=600%2C354 600w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" width=\"640\" height=\"457\" class=\"wp-image-25540\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/unnamed-chunk-6-1.png?resize=640%2C457\" alt=\"unnamed-chunk-6-1\" srcset=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/unnamed-chunk-6-1.png?w=1344 1344w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/unnamed-chunk-6-1.png?resize=300%2C214 300w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/unnamed-chunk-6-1.png?resize=1024%2C731 1024w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/unnamed-chunk-6-1.png?resize=768%2C549 768w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/unnamed-chunk-6-1.png?resize=600%2C429 600w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/unnamed-chunk-6-1.png?w=1280 1280w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" width=\"640\" height=\"640\" class=\"wp-image-25541\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/0sw01.png?resize=640%2C640\" alt=\"0SW01\" srcset=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/0sw01.png?w=800 800w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/0sw01.png?resize=300%2C300 300w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/0sw01.png?resize=150%2C150 150w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/0sw01.png?resize=768%2C768 768w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/0sw01.png?resize=600%2C600 600w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/0sw01.png?resize=100%2C100 100w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" width=\"500\" height=\"374\" class=\"wp-image-25542\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/tumblr_inline_mlmoj7b1jq1qz4rgp.jpeg?resize=500%2C374\" alt=\"tumblr_inline_mlmoj7B1jq1qz4rgp\" srcset=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/tumblr_inline_mlmoj7b1jq1qz4rgp.jpeg?w=500 500w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/tumblr_inline_mlmoj7b1jq1qz4rgp.jpeg?resize=300%2C224 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" data-recalc-dims=\"1\" \/><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" width=\"640\" height=\"481\" class=\"wp-image-25543\" src=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/anova-residuals.png?resize=640%2C481\" alt=\"anova-residuals\" srcset=\"https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/anova-residuals.png?w=668 668w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/anova-residuals.png?resize=300%2C225 300w, https:\/\/i0.wp.com\/www.biocloudservice.com\/wordpress\/wp-content\/uploads\/2024\/01\/anova-residuals.png?resize=600%2C451 600w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/p>\n<p>\u4ee5\u4e0a\u5c31\u662f\u5bf9R\u8bed\u8a00\u5305pbkrtest\u7684\u7b80\u5355\u4ecb\u7ecd\u5566\uff0cpbkrtest\u5305\u4e3a\u7814\u7a76\u4eba\u5458\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u7528\u4e8e\u5728\u6df7\u5408\u6548\u5e94\u6a21\u578b\u4e2d\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u548c\u53c2\u6570\u4f30\u8ba1\u3002\u5b83\u80fd\u591f\u5904\u7406\u590d\u6742\u7684\u6570\u636e\u7ed3\u6784\u548c\u76f8\u5173\u6027\uff0c\u63d0\u4f9b\u51c6\u786e\u7684\u7edf\u8ba1\u63a8\u65ad\u7ed3\u679c\u3002\u901a\u8fc7\u4f7f\u7528pbkrtest\u5305\uff0c\u7814\u7a76\u4eba\u5458\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u6570\u636e\uff0c\u5e76\u5f97\u51fa\u66f4\u53ef\u9760\u7684\u7ed3\u8bba\u3002<\/p>\n<p>\u5c0f\u4f19\u4f34\u4eec\uff0c\u4eca\u5929\u6709\u6ca1\u6709\u5b66\u5230\u65b0\u77e5\u8bc6\u5462\uff0c\u60f3\u8981\u7ee7\u7eed\u4e86\u89e3R\u8bed\u8a00\u5185\u5bb9\u53ef\u4ee5\u6301\u7eed\u5173\u6ce8\u5c0f\u679c\u54e6\uff5e\uff5e\u6216\u8005\u4e5f\u53ef\u4ee5\u5173\u6ce8\u6211\u4eec\u7684\u5b98\u7f51\u4e5f\u4f1a\u6301\u7eed\u66f4\u65b0\u7684\u54e6\uff5e <a href=\"http:\/\/www.biocloudservice.com\/home.html\">http:\/\/www.biocloudservice.com\/home.html<\/a><\/p>\n<p>References:<\/p>\n<ol>\n<li><a href=\"https:\/\/ourcodingclub.github.io\/tutorials\/mixed-models\/\">https:\/\/ourcodingclub.github.io\/tutorials\/mixed-models\/<\/a><\/li>\n<li><a href=\"https:\/\/terpconnect.umd.edu\/~egurarie\/teaching\/Biol709\/Topic3\/Lecture16_MixedEffectsModels.html\">https:\/\/terpconnect.umd.edu\/~egurarie\/teaching\/Biol709\/Topic3\/Lecture16_MixedEffectsModels.html<\/a><\/li>\n<li><a href=\"https:\/\/stackoverflow.com\/questions\/40546716\/plotting-mixed-models-regression-coefficients-in-r\">https:\/\/stackoverflow.com\/questions\/40546716\/plotting-mixed-models-regression-coefficients-in-r<\/a><\/li>\n<li><a href=\"http:\/\/www.analyticsforfun.com\/2014\/06\/performing-anova-test-in-r-results-and.html\">http:\/\/www.analyticsforfun.com\/2014\/06\/performing-anova-test-in-r-results-and.html<\/a><\/li>\n<li><a href=\"https:\/\/www.scribbr.com\/statistics\/anova-in-r\/\">https:\/\/www.scribbr.com\/statistics\/anova-in-r\/<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>pbkrtest\u5305\u7684\u4e3b\u8981\u529f\u80fd\u662f\u63d0\u4f9b\u6709\u6548\u7684\u5047\u8bbe\u68c0\u9a8c\u65b9\u6cd5\uff0c\u7528\u4e8e\u8bc4\u4f30\u6df7\u5408\u6548\u5e94\u6a21\u578b\u4e2d\u56fa\u5b9a\u6548\u5e94\u7684\u663e\u8457\u6027\u3002\u5b83\u901a\u8fc7\u8ba1\u7b97\u8fd1\u4f3c\u7684 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":""},"categories":[1],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"http:\/\/www.biocloudservice.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/25538"}],"collection":[{"href":"http:\/\/www.biocloudservice.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.biocloudservice.com\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.biocloudservice.com\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.biocloudservice.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=25538"}],"version-history":[{"count":1,"href":"http:\/\/www.biocloudservice.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/25538\/revisions"}],"predecessor-version":[{"id":25555,"href":"http:\/\/www.biocloudservice.com\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/25538\/revisions\/25555"}],"wp:attachment":[{"href":"http:\/\/www.biocloudservice.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=25538"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.biocloudservice.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=25538"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.biocloudservice.com\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=25538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}