8

The interpretation is the same as for a generalised linear model, except that the estimates of the fixed effects are conditional on the random effects. Since this is a generalized linear mixed model, the coefficient estimates are not interpreted in the same way as for a linear model. In this case you have a binary outcome with a logit link, so the raw ...


5

I agree that this can be a little confusing. Some authors avoid setting it up in this way. The important point is that the $\alpha_{i}$ are not estimated individually, instead they are subsumed into a general model and the usual assumption is that they are normally distributed, with an unknown variance, which is to be estimated. Focusing on the main point: ...


5

A couple of extra notes on top of what @RobertLong already answered: As Robert also noted, the interpretation of the coefficients from generalized linear mixed models are conditional on the random effects. Most often this is not the interpretation you are looking for. For more info on this check here. You have fitted the model with the default Laplace ...


3

The point that is made in this paper is with regard to the conditional versus marginal interpretation of the regression coefficients. Namely, because of the nonlinear link function used in the mixed effects logistic regression, the fixed effects coefficients have an interpretation conditional on the random effects. Most often this is not the desirable ...


3

Assuming you want to visualize how the binomial approaches the normal as n grows I'd do it as follows: Choose some value for the second parameter, $p$ (like say 0.5 or 0.2) draw a standard normal cdf and compute and plot the cdf of a standardized binomial at some $n=n_1$ draw a standard normal cdf and compute and plot the cdf of a standardized binomial at ...


2

Overdispersion is a phenomenon that often applies to binomial-like data ($y$ successes out of $n$ cases with $n>1$), but it cannot apply to binary data. If $y$ is binary (1/0) and $E(y)=p$ then it must be that var$(y)=p(1-p)$. There is no mathematical possibility that the variance can be any greater or less than that given $E(y)$. If your response ...


1

For modelling count data in regression settings, the negative binomial GLM is far preferable to the Poisson GLM. Indeed, I would go so far as to say that the latter is a bad model that should almost never be used (see discussion here). Generally speaking, the residual values from a Poisson model will not identify problems with overdispersion. What usually ...


1

Since AIC is not defined for quasi-models, and anyhow your two models in this case would not be nested, AIC should not be used for comparison. I would go for model visualization, see for instance Dealing with Overdispersed Negative Binomial using glmmTMB for examples of use of simulated residuals for model checking (well, simulated residuals cannot be ...


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