Quasi-maximum Likelihood

Quasi-maximum likelihood

Classical maximum likelihood assumes the level of variability is approximately as predicted for the distribution being used. Switching to quasi-maximum likelihood instead estimates the observed level of variation in the data as we did earlier with linear models and adjusts the standard errors accordingly. Below is an example of quasi-maximum likelihood:

qml1 <- glm(Species_counts ~ N_deposition, family = quasipoisson, 
    data = Species)

The estimates of the intercept and slope remain the same, but the standard errors change. The changes are small because the level of variation is about what we would expect for a Poisson distribution, but if there were marked overdispersion the changes to the standard errors would be larger:

summary(qml1)

##
## Call:
## glm(formula = Species_counts ~ N_deposition, family = quasipoisson, 
##      data = Species)
##
## Deviance Residuals:
##     Min       1Q   Median       3Q     Max
## -2.1788  -0.6813  -0.1904   0.5825  3.1749
##
## Coefficients:
##               Estimate  Std. Error  t value  Pr(>|t|)
## (Intercept)   3.210340    0.078168    41.07   < 2e-16
## N_deposition -0.029436    0.003853    -7.64  7.18e-11
##
## (Dispersion parameter for quasipoisson family taken to be 0.9392865) 
##
##     Null deviance: 120.778 on 73 degrees of freedom
## Residual deviance:  64.707 on 72 degrees of freedom
## AIC: NA
##
## Number of Fisher Scoring iterations: 4