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
[[alternative HTML version deleted]]