Hi !
 
We study the effect of several variables on fruit set for 44 individuals
(plants). For each individual, we have the number of fruits, the number
of flowers and a value for each variable.
 
Here is our first model in R :
 
y <- cbind(indnbfruits,indnbflowers);
model1
<-glm(y~red*yellow+I(red^2)+I(yellow^2)+densite8+I(densite8^2)+freq8_4+I
(freq8_4^2), quasibinomial);
 
-        We have used a quasibinomial error because there is
overdispersion. How to know if it is OK?
 
-        Glm does not take account of the correlation between the
flowers of a unique individual. So we would like to add a random effect
‘individual’ but the model2 (here after) gives an output similar to the
one of model1 for estimated coefficients and p-values. 
 
model2 <-
glmmPQL(y~red*yellow+I(red^2)+I(yellow^2)+densite8+I(densite8^2)+freq8_4
+I(freq8_4^2), random=~1|num, quasibinomial);
 
      Does it mean that there is no individual effect or is my model not
good (number of groups (individuals)=number of observations, is it
possible?). 
 
Thank you by advance for your help
 
Emmanuelle TASTARD
 
 
Output model1 :
 
Call:
glm(formula = y ~ red * yellow + I(red^2) + I(yellow^2) + densite8 + 
    I(densite8^2) + freq8_4 + I(freq8_4^2), family = quasibinomial)
 
Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.4978  -1.5396  -0.1700   0.5210   4.5302  
 
Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)     2.8076     2.4489   1.146 0.262042    
red            -1.9290     0.8498  -2.270 0.031738 *  
yellow         -0.3415     1.5189  -0.225 0.823848    
I(red^2)        0.3250     0.1229   2.644 0.013700 *  
I(yellow^2)    -0.1776     0.4129  -0.430 0.670573    
densite8       -8.2691     4.6140  -1.792 0.084750 .  
I(densite8^2)   6.0005     3.4666   1.731 0.095318 .  
freq8_4         9.0044     2.5358   3.551 0.001490 ** 
I(freq8_4^2)  -14.3066     3.8049  -3.760 0.000871 ***
red:yellow      0.2320     0.1893   1.226 0.231315    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
 
(Dispersion parameter for quasibinomial family taken to be 5.374839)
 
    Null deviance: 404.64  on 35  degrees of freedom
Residual deviance: 137.20  on 26  degrees of freedom
AIC: NA
 
Number of Fisher Scoring iterations: 4
 
 
Output model2 :
 
Linear mixed-effects model fit by maximum likelihood
 Data: NULL 
       AIC      BIC    logLik
  112.5895 131.5917 -44.29476
 
Random effects:
 Formula: ~1 | num
        (Intercept) Residual
StdDev:  0.02253235 1.968849
 
Variance function:
 Structure: fixed weights
 Formula: ~invwt 
Fixed effects: y ~ red * yellow + I(red^2) + I(yellow^2) + densite8 +
I(densite8^2) +      freq8_4 + I(freq8_4^2) 
                   Value Std.Error DF   t-value p-value
(Intercept)     2.805933  2.449548 26  1.145490  0.2624
red            -1.927214  0.850055 26 -2.267164  0.0319
yellow         -0.343353  1.519357 26 -0.225986  0.8230
I(red^2)        0.324676  0.122961 26  2.640481  0.0138
I(yellow^2)    -0.177084  0.412955 26 -0.428820  0.6716
densite8       -8.265473  4.615384 26 -1.790853  0.0850
I(densite8^2)   5.997720  3.467743 26  1.729574  0.0956
freq8_4         9.006669  2.535929 26  3.551625  0.0015
I(freq8_4^2)  -14.309852  3.804955 26 -3.760847  0.0009
red:yellow      0.231987  0.189296 26  1.225523  0.2314
 Correlation: 
              (Intr) red    yellow I(r^2) I(y^2) denst8 I(8^2) frq8_4
I(8_4^
red           -0.562

yellow        -0.581 -0.179

I(red^2)       0.467 -0.934  0.248

I(yellow^2)    0.240  0.481 -0.896 -0.451

densite8      -0.764  0.369  0.196 -0.338  0.075

I(densite8^2)  0.743 -0.326 -0.208  0.327 -0.038 -0.987

freq8_4       -0.100 -0.112  0.171 -0.041 -0.254 -0.016 -0.086

I(freq8_4^2)   0.141  0.001 -0.061  0.140  0.095 -0.150  0.240 -0.938

red:yellow     0.585 -0.634 -0.113  0.355 -0.308 -0.468  0.383  0.375
-0.237
 
Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max 
-1.66511749 -0.59215881 -0.08635717  0.26740423  2.75720770 
 
Number of Observations: 36
Number of Groups: 36
 
 
Emmanuelle TASTARD
UMR 5174 'Evolution et Diversité Biologique'  
Université Paul Sabatier Bat 4R3
31062 TOULOUSE CEDEX 9 France
tel : 05 61 55 67 59
 

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