[R] lmer or glm with family=binomial : probability variable

[Francesca]

Dear all,
We are dealing with a variable (BA) which indicates the overlap between
small mammal home ranges. It varies between 0 and 1 and it can be
interpreted as "the probability of two home ranges to overlap",
therefore we would have modelled it with the binomial family, also
supported by  the distribution of the variable itself.  However, lmer or
glm require the data to be presented as successes vs failures. In our
case, this is not possible as BA is calculated by GIS on raster maps; in
other words, BA expressess p (probability of success), but it is not
possible to know from how many cases/attempts p came from. 
Therefore, what we get from the analysis is:

       IDAN_IDAN     SESSO   SESSIONE         BA            
1   1D00AD9_1D1421F   F_F        1 	5.909904e-06                
2   1D00AD9_602F513   M_F        1 	5.640469e-03                
3   1D00AD9_602FEAB   M_F        1 	3.715911e-13                
4   1D00AD9_603086B   F_F        1 	2.350365e-17                
5   1D00AD9_60778A4   M_F        1 	1.589195e-08                
6   1D00AD9_60779D7   F_F        1 	7.343189e-22                
7   1D00AD9_6723D30   M_F        1 	8.725496e-01                
8   1D1421F_602F513   M_F        1 	6.757339e-02                
9   1D1421F_602FEAB   M_F        1 	7.612337e-01                
10  1D1421F_603086B   F_F        1 	4.623883e-06                
11  1D1421F_60778A4   M_F        1 	2.856006e-01                
12  1D1421F_60779D7   F_F        1 	9.752100e-11                
13  1D1421F_6723D30   M_F        1 	8.921498e-08                
14  602F513_602FEAB   M_M        1 	2.127866e-02                
15  602F513_603086B   M_F        1 	6.695516e-05                
16  1D00AD9_671ED61   M_F        2 	3.873126e-01                
17  1D00AD9_6723D30   M_F        2 	2.080799e-01                
18  1D00AD9_672594F   M_F        2 	3.983634e-15                
19  1D1421F_602FEAB   M_F        2 	2.956002e-01                
20  1D1421F_603086B   F_F        2 	2.150006e-06                
21  1D1421F_60314C4   F_F        2 	1.947681e-21                
22  1D1421F_6033E53   M_F        2 	1.855792e-01                
23  1D1421F_60655F4   F_F        2 	1.242808e-02                
24  1D1421F_60778A4   M_F        2 	1.398984e-02                

> SESSIONE1<-factor(SESSIONE)
> model<-lmer(BA~ SESSO + (1|SESSIONE1:IDAN_IDAN) + (1|SESSIONE1),
data=foglio1, family=binomial)

Warning messages:
1: #non integer successes in glm binomial model! in: eval(expr, envir,
enclos) 
2: nlminb returned message singular convergence (7) 
 in: LMEopt(x = mer, value = cv) 
3: nlminb returned message false convergence (8) 
 in: LMEopt(x = mer, value = cv) 
4: nlminb returned message singular convergence (7) 
 in: LMEopt(x = mer, value = cv) 
5: nlminb returned message false convergence (8) 
 in: LMEopt(x = mer, value = cv) 
6: nlminb returned message false convergence (8) 
 in: LMEopt(x = mer, value = cv) 
7: IRLS iterations for PQL did not converge 

Is there any possibility to model p vs q=1-p without passing by
successes vs failures frequencies?

Thank you very much for helping!!!

Best regards

Francesca Cagnacci


Francesca Cagnacci, PhD
****************************************
Centro di Ecologia Alpina
Viote del Monte Bondone
38040 Trento
Tel. +393388668767 or +393397481073
Email cagnacci at cealp.it or frcagnac at tin.it