# Solved – Interaction suppresses the main effect? How to interpret it

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 ``
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#### 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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