[R] Interpreting GLM coefficients

Pablo Pita Orduna ppita at udc.es
Fri Mar 6 23:04:52 CET 2009

Hi all,

I´m fitting GLM´s and I can´t interprete the coefficients when I run a  
model with interaction terms.

When I run the simpliest model there is no problem:

Model1<-glm (Fishes ~ Year + I(Year^2) + Kind.Geographic +  
Kind.Fishers + Zone.2 + Hours + Fishers + Month, family =  
poisson(log)) # Fishes, Year, Hours, and Fishers are numeric,  
Kind.Geographic, Kind.Fishers, Zone.2 and Month are factors with 4, 3,  
5 and 12 levels respectively.

Model1$coefficients (whith Helmert contrasts):

    (Intercept)             Year           IYear^2 Kind.Geographic1  
Kind.Geographic2 Kind.Geographic3    Kind.Fishers1    Kind.Fishers2     
       Zone.21          Zone.22          Zone.23          Zone.24
  -4.416915e+02     4.758455e-01    -1.270986e-04    -5.436199e-01     
-1.068809e-01    -1.498580e-01     2.958462e-01     1.316589e-01     
-1.328204e-01    -1.605802e-01     5.281869e-03     7.422885e-02
          Hours          Fishers           Month1           Month2      
      Month3           Month4           Month5           Month6         
  Month7           Month8           Month9          Month10
   9.772076e-02    -2.709955e-03    -1.586887e-01    -1.887837e-02     
-5.183241e-03     5.870942e-02     7.075386e-02     2.061223e-02      
7.372268e-03    -1.204835e-02    -5.047994e-03     2.441498e-02

So I can write, for example:

y = -4.416915e+02 + -1.270986e-04*x^2 + 4.758455e-01*x # And add this  
function to a plot(Year,Fishes).

My problem is to understand the coefficients for the model with interaction:

Model2<-glm(Fishes ~ Year + I(Year^2) + Kind.Geographic + Kind.Fishers  
+ Zone.2 + Hours + Fishers + Month + Year:Kind.Geographic +  
Year:Kind.Fishers + Year:Zone.2 + Year:Hours + Year:Fishers +  
Year:Month + Kind.Geographic:Hours + Kind.Fishers:Hours + Zone.2:Hours  
+ Hours:Fishers + Hours:Month +Kind.Geographic:Fishers +  
Zone.2:Fishers + Fishers:Month , poisson (log))

Model2$coefficients (with Helmert contrast):

            (Intercept)                     Year                 
I(Year^2)         Kind.Geographic1         Kind.Geographic2          
Kind.Geographic3            Kind.Fishers1            Kind.Fishers2
           1.641473e+03            -1.748703e+00              
4.664752e-04            -6.721427e+00             1.856033e+01          
  -3.762727e-02             2.903564e+01             9.022858e+01
                Zone.21                  Zone.22                   
Zone.23                  Zone.24                    Hours               
     Fishers                   Month1                   Month2
           8.110814e-02            -1.902803e+01              
8.335792e+00            -3.661641e+00            -7.824623e+00          
   7.088065e-01             2.479387e+03             8.346729e+02
                 Month3                   Month4                    
Month5                   Month6                   Month7                
   Month8                   Month9                  Month10
           4.052680e+02             2.384440e+02              
1.570644e+02             1.032445e+02             7.930499e+01          
   6.487925e+01             5.592869e+01             3.888328e+01
                Month11    Year:Kind.Geographic1     
Year:Kind.Geographic2    Year:Kind.Geographic3        
Year:Kind.Fishers1       Year:Kind.Fishers2             Year:Zone.21    
           4.801656e+01             3.397984e-03             
-9.443234e-03                       NA            -1.449305e-02         
     -4.470212e-02            -6.269309e-05             9.421045e-03
           Year:Zone.23             Year:Zone.24                
Year:Hours             Year:Fishers              Year:Month1            
  Year:Month2              Year:Month3              Year:Month4
          -4.184866e-03             1.854810e-03              
3.257250e-03            -4.103058e-04            -1.264934e+00          
  -4.255907e-01            -2.069909e-01            -1.216459e-01
            Year:Month5              Year:Month6               
Year:Month7              Year:Month8              Year:Month9           
    Year:Month10             Year:Month11   Kind.Geographic1:Hours
          -8.015823e-02            -5.278291e-02             
-4.054404e-02            -3.313487e-02            -2.846036e-02         
     -1.973118e-02            -2.410902e-02             1.341231e-01
  Kind.Geographic2:Hours   Kind.Geographic3:Hours       
Kind.Fishers1:Hours      Kind.Fishers2:Hours            Zone.21:Hours   
           Zone.22:Hours            Zone.23:Hours             
           5.806418e-02                       NA              
1.318444e-02            -1.234521e-01             7.961319e-04          
   1.622411e-02            -5.357266e-04             7.749412e-03
          Hours:Fishers             Hours:Month1              
Hours:Month2             Hours:Month3             Hours:Month4          
   Hours:Month5             Hours:Month6             Hours:Month7
          -6.805803e-03             7.971549e+00              
2.627090e+00             1.403430e+00             7.747360e-01          
   5.163810e-01             3.732549e-01             2.827511e-01
           Hours:Month8             Hours:Month9             
Hours:Month10            Hours:Month11 Kind.Geographic1:Fishers  
Kind.Geographic2:Fishers Kind.Geographic3:Fishers           
           2.091230e-01             1.057001e-01              
1.159929e-01                       NA            -3.422994e-02          
  -3.421851e-03                       NA            -3.802354e-03
        Zone.22:Fishers          Zone.23:Fishers           
Zone.24:Fishers           Fishers:Month1           Fishers:Month2       
      Fishers:Month3           Fishers:Month4           Fishers:Month5
           1.618358e-05             4.197350e-04             
-8.773088e-05             7.806815e-01             2.509529e-01         
      1.280752e-01             7.520139e-02             5.370220e-02
         Fishers:Month6           Fishers:Month7            
Fishers:Month8           Fishers:Month9          Fishers:Month10        
           3.786759e-02             2.936135e-02              
2.381810e-02             2.422438e-02                       NA          

I would like to know if it is possible to extract the intercepts and  
the slopes for Year and Year^2 for this Model2.

Thank you very much for your help.
Pablo Pita Orduna
Grupo de Recursos Marinos y Pesquerías.
Universidade de A Coruña. Campus da Zapateira s/n. E-15071. A Coruña, Spain.
Tel. +34(981) 167000 ext. 2204 Fax. +34(981) 167065.

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