我有一个没有交互作用的简单模型，它对所有解释变量（连续变量 rok 和分类变量 obdobi（水平 hn 和 nehn）和 kraj 都有显着影响：
Call:
glm(formula = cbind(ml, ad) ~ rok + obdobi + kraj, family = "quasibinomial")
Deviance Residuals:
Min 1Q Median 3Q Max
-3.8007 -1.1716 -0.5117 1.0864 4.2184
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -107.60761 53.96993 -1.994 0.04674 *
rok 0.05381 0.02686 2.003 0.04576 *
obdobinehn -0.26962 0.11646 -2.315 0.02104 *
krajJHC 0.68869 0.31009 2.221 0.02683 *
krajJHM -0.26607 0.32166 -0.827 0.40855
krajLBK -1.11305 0.61942 -1.797 0.07298 .
krajMSK -0.61390 0.41828 -1.468 0.14285
krajOLK -0.49704 0.36981 -1.344 0.17958
krajPAK -1.18444 0.39401 -3.006 0.00279 **
krajPLK -1.28668 0.49672 -2.590 0.00988 **
krajSTC 0.01872 0.31222 0.060 0.95220
krajULKV -0.41950 0.69220 -0.606 0.54478
krajVYS -1.17290 0.44614 -2.629 0.00884 **
krajZLK -0.38170 0.40969 -0.932 0.35198
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for quasibinomial family taken to be 1.645035)
Null deviance: 1136.22 on 489 degrees of freedom
Residual deviance: 938.02 on 476 degrees of freedom
AIC: NA
Number of Fisher Scoring iterations: 4
然后我添加了交互 obdobi:kraj:
Call:
glm(formula = cbind(ml, ad) ~ rok + obdobi + kraj + obdobi:kraj,
family = "quasibinomial")
Deviance Residuals:
Min 1Q Median 3Q Max
-3.4635 -1.1706 -0.4597 1.0275 4.6829
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -101.49501 54.53576 -1.861 0.06336 .
rok 0.05102 0.02715 1.879 0.06086 .
obdobinehn -1.11653 0.62058 -1.799 0.07264 .
krajJHC -0.16805 0.51957 -0.323 0.74651
krajJHM -0.77451 0.53738 -1.441 0.15018
krajLBK -3.29567 1.42164 -2.318 0.02087 *
krajMSK -0.73640 0.67267 -1.095 0.27420
krajOLK -0.41582 0.68758 -0.605 0.54564
krajPAK -1.50156 0.63871 -2.351 0.01914 *
krajPLK -1.48611 0.75745 -1.962 0.05036 .
krajSTC -0.34170 0.52059 -0.656 0.51191
krajULKV -1.72550 1.02726 -1.680 0.09369 .
krajVYS -1.93603 0.65862 -2.940 0.00345 **
krajZLK -0.71065 0.65791 -1.080 0.28063
obdobinehn:krajJHC 1.44638 0.65507 2.208 0.02773 *
obdobinehn:krajJHM 0.82070 0.67910 1.209 0.22746
obdobinehn:krajLBK 3.31340 1.61026 2.058 0.04018 *
obdobinehn:krajMSK 0.12470 0.87281 0.143 0.88645
obdobinehn:krajOLK 0.04528 0.82529 0.055 0.95627
obdobinehn:krajPAK 0.48978 0.81921 0.598 0.55022
obdobinehn:krajPLK 0.23075 1.02316 0.226 0.82167
obdobinehn:krajSTC 0.50339 0.65976 0.763 0.44585
obdobinehn:krajULKV 2.49157 1.43679 1.734 0.08356 .
obdobinehn:krajVYS 1.48201 0.92082 1.609 0.10820
obdobinehn:krajZLK 0.49357 0.85087 0.580 0.56214
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for quasibinomial family taken to be 1.613648)
Null deviance: 1136.22 on 489 degrees of freedom
Residual deviance: 899.28 on 465 degrees of freedom
AIC: NA
Number of Fisher Scoring iterations: 4
奇怪的事情发生了 - 主要影响 rok 和 obdobi 不再显着！这怎么可能发生？如何解释这个事实？如果相互作用obdobi:kraj有显着影响，那么obdobi也有显着影响，对吧？
请注意，第二个模型显着不同（由 测试anova(..., test = "Chi")）。
提前致谢！
编辑：添加了模型的 anova 表（但由于这glm不是简单lm的，所以缺少平方和和 p 值的平均值，我不知道如何解释它......）
> anova(model1)
Analysis of Deviance Table
Model: quasibinomial, link: logit
Response: cbind(ml, ad)
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev
NULL 489 1136.22
rok 1 3.06 488 1133.16
obdobi 1 11.20 487 1121.96
kraj 11 183.94 476 938.02
> anova(model2)
Analysis of Deviance Table
Model: quasibinomial, link: logit
Response: cbind(ml, ad)
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev
NULL 489 1136.22
rok 1 3.06 488 1133.16
obdobi 1 11.20 487 1121.96
kraj 11 183.94 476 938.02
obdobi:kraj 11 38.74 465 899.28