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While these problems commonly appear together, researchers tend to treat them individually by (a) finding an optimal model based on the conditional Akaike information criterion (<jats:italic>cAIC<\/jats:italic>) and (b) applying transformations on the dependent variable. However, the optimal model depends on the transformation and vice versa. In this paper, we aim to solve both problems simultaneously. In particular, we propose an adjusted <jats:italic>cAIC<\/jats:italic> by using the Jacobian of the particular transformation such that various model candidates with differently transformed data can be compared. From a computational perspective, we propose a step-wise selection approach based on the introduced adjusted <jats:italic>cAIC<\/jats:italic>. Model-based simulations are used to compare the proposed selection approach to alternative approaches. Finally, the introduced approach is applied to Mexican data to estimate poverty and inequality indicators for 81 municipalities.<\/jats:p>","DOI":"10.1007\/s11222-022-10198-9","type":"journal-article","created":{"date-parts":[[2022,12,26]],"date-time":"2022-12-26T09:10:36Z","timestamp":1672045836000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Variable selection using conditional AIC for linear mixed models with data-driven transformations"],"prefix":"10.1007","volume":"33","author":[{"given":"Yeonjoo","family":"Lee","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Natalia","family":"Rojas-Perilla","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4897-4464","authenticated-orcid":false,"given":"Marina","family":"Runge","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7217-2501","authenticated-orcid":false,"given":"Timo","family":"Schmid","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,12,26]]},"reference":[{"key":"10198_CR1","unstructured":"Akaike, H.: Information theory and an extension of the maximum likelihood principle, In Information Theory: Proceedings of the 2nd International Symposium, eds. 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