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I am using the glmer function in package "lme4". The results shows that: AIC BIC logLik deviance df.resid 96.7 105.5 -44.4 88.7 62

So the dispersion parameter is deviance/df.resid=1.43, which is approximately equals to 1. But if it is far too smaller or larger than 1, can I just use its results or not? If not, what can I do?

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This informal check holds mainly for GLMs. When you fit generalized linear mixed models you account for (some degree) of over-dispersion but including random effects (typically, when you include something more than random intercepts).

To better check for over-dispersion in GLMMs you could use the simulated residuals provided by the DHARMa package, though you should be careful with these residuals if you have missing data that are something more than missing completely at random (i.e., missing at random or missing not at random).

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