Natural language data -sociolinguistic, historical, and other types of corpora -should not be analyzed with fixed-effects regression models, such as VARBRUL and GoldVarb use. This is because tokens of linguistic variables are rarely independent; they are usually grouped and correlated according to factors like speaker (or text) and word.Fixed-effects models can estimate the effects of higher-level "nesting" predictors (like speaker gender or word frequency), but they cannot be accurate if there exist any individual effects of lower-level "nested" predictors (like speaker or word). Mixed-effects models are designed to take these multiple levels of variation into account at the same time. Because many predictors of interest are in a nesting relationship with speaker or word, mixed models give more accurate quantitative estimates of their effect sizes, and especially of their statistical significance. The problems with fixed-effects models are only exacerbated by the token imbalances that exist across speakers and words in naturalistic speech, while mixed-effects models handle these imbalances well. This article demonstrates these and other advantages of mixed models, using data on /t, d/-deletion taken from the Buckeye Corpus as well as other real and simulated data sets.