# Interpret quasipoisson GLM with interactions

#### Augustus2.0

##### New Member
Hello to all the community, I write this post because I would need a little help with the interpretation of my model's summary.

First, here is the model :

Code:
    glm(formula = Nb_bone_discovery ~ Order * Time, family = "quasipoisson") #I used quasipoisson since I got surdispersion.
Where :

- Order is a discret variable with 3 modalities ["Carnivora","Human","Marsupial"]
- Nb_bone_discovery is a discrete quantitative variables. ex: ["0,1,2..."]
- Time is a continuous quantitative variables ex: ["0.33,0.5,0.8,1,2..."]

To be more precise I try with this model to show that the Order factor will have an effect on the number of bone_discoveries, while removing the effect of Time, since theoretically, the more time passes, the greater the number of bone discoveries is anyway.

SO here are the results:

Code:
 Deviance Residuals:
Min       1Q   Median       3Q      Max
-2.5270  -1.2207  -0.5733   0.6993   2.7131

Coefficients:
Estimate   Std. Error  t value   Pr(>|t|)
(Intercept)      -0.5916    0.1794      -3.297    0.001148 **
Human            1.0946     0.2379       4.600    7.31e-06 ***
Marsupial        0.6850     0.3005       2.280    0.023632 *
Time             12.1964    3.2483       3.755    0.000225 ***
Human:Time       -11.3398   3.6346       -3.120   0.002064 **
Marsupial:Time   -9.0848    4.3548       -2.086   0.038179 *

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for quasipoisson family taken to be 1.446357)

Null deviance: 388.61  on 214  degrees of freedom
Residual deviance: 339.54  on 209  degrees of freedom
(32 observations deleted due to missingness)
AIC: NA

Number of Fisher Scoring iterations: 5
Number of Fisher Scoring iterations: 5

With that summary is it correct to say the following things :

- Having an Human Order predisposes to more discovered bones (if you are Human you have 1.0946 more bones discovered than if you are Carnivora)
- Being Human almost eliminates the Time effect (12.1964 -11.3398 =~0.85: you gain 0.85 bones discoveries per unit of Time when you are Human)
- Being Marsupial does not decrease the Time effect as much (12.1964-9.0848 =~3.11 : you gain 3.11 bones discoveries per unit of Time when you are Marsupial)

I'm correct, and did I miss some other interpretations from that summary ?

Can I say that overall, bones are more discovered in Human order compared to the others, and that number of bones discovered in Human are less affected by Time than others?

Thanks a lot for your help

#### hlsmith

##### Less is more. Stay pure. Stay poor.
If you have interaction terms - it is usually standard not to attempt to interpret the base terms but to solely focus on the interactions. This is because the base terms are conditional on another variable.