Contents
What does Underdispersion mean?
Underdispersion exists when data exhibit less variation than you would expect based on a binomial distribution (for defectives) or a Poisson distribution (for defects). Underdispersion can occur when adjacent subgroups are correlated with each other, also known as autocorrelation.
What does family binomial mean?
quasibinomial family
Binomial or quasibinomial family: binary data like 0 and 1, or proportion like survival number vs death number, positive frequency vs negative frequency, winning times vs the number of failtures, et al… Gamma family : usually describe time data like the time or duration of the occurrence of the event.
How do you detect Overdispersion?
Overdispersion can be detected by dividing the residual deviance by the degrees of freedom. If this quotient is much greater than one, the negative binomial distribution should be used. There is no hard cut off of “much larger than one”, but a rule of thumb is 1.10 or greater is considered large.
Is the interpretation of GLMMs the same as GLMs?
The interpretation of GLMMs is similar to GLMs; however, there is an added complexity because of the random effects. On the linearized metric (after taking the link function), interpretation continues as usual. However, it is often easier to back transform the results to the original metric.
Is the GLMMs an extension of generalized linear regression?
Alternatively, you could think of GLMMs as an extension of generalized linear models (e.g., logistic regression) to include both fixed and random effects (hence mixed models). The general form of the model (in matrix notation) is:
Why does the line appear to wiggle in GLMM?
In the graphical representation, the line appears to wiggle because the number of patients per doctor varies. In order to see the structure in more detail, we could also zoom in on just the first 10 doctors.
How are random effect complements modeled in GLMM?
Because we directly estimated the fixed effects, including the fixed effect intercept, random effect complements are modeled as deviations from the fixed effect, so they have mean zero. The random effects are just deviations around the value in β, which is the mean. So what is left to estimate is the variance.