I have a simple model without interaction and it stated significant effect for all the explanatory variables (continuous variable rok and categorical variables obdobi (levels hn and nehn) and kraj:
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
Then I added interaction 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
Strange thing happened – the main effects rok and obdobi are no longer significant! How can this happen? How to interpret this fact? If the interaction obdobi:kraj
has significant effect, then the obdobi
also has significant effect, right?
Note that the second model differs significantly (tested by anova(..., test = "Chi")
).
Thanks in advance!
EDIT: added anova tables of the models (but since this is glm
and not simple lm
, mean sum of squares and p-values are missing and I don't know how to interpret it…)
> 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
Best Answer
The main effects went from "significant" to "not", but the evidence really didn't change all that much. For example, p=0.047 to p=0.063 for rok
isn't, to me, a remarkable change. And a lack of evidence for a coefficient being non-zero isn't the same as saying it is 0.
In considering the coefficient for obdobinehn
when the interaction is included, you need to pay careful attention to the factor contrasts that are being used, as the meaning of the coefficient changes and depends on those contrasts.
Note also that if a covariate is involved in an important interaction, then it does have an effect on the outcome, even if it shows no main effect.
I agree with John's comment that it's useful, with factor covariates, to look at an ANOVA table.
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