We propose two methods to evaluate the conditional Akaike information (cAI) for mixed-effects models with no restriction on cluster size. Method 1 is designed for continuous data and includes formulae for the derivatives of fixed and random effects estimators with respect to observations. Method 2, compatible with any type of observation, requires modeling the marginal (or prior) distribution of random effects as a multivariate normal distribution. Simulations show that Method 1 performs well with Gaussian data but struggles with skewed continuous distributions, whereas Method 2 consistently performs well across various distributions, including normal, gamma, negative binomial, and Tweedie, with flexible link functions. A case study demonstrates the differences in model selection for real-world data between the conventional AIC and the conditional AIC. Based on our findings, we recommend Method 2 as a distributionally robust cAI criterion for model selection in mixed-effects models.

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