What mechanisms underlie linguistic generalization in large language models (LLMs)? This question has attracted considerable attention, with most studies analyzing the extent to which the language skills of LLMs resemble rules. As of yet, it is not known whether linguistic generalization in LLMs could equally well be explained as the result of analogical processes, which can be formalized as similarity operations on stored exemplars. A key shortcoming of prior research is its focus on linguistic phenomena with a high degree of regularity, for which rule-based and analogical approaches make the same predictions. Here, we instead examine derivational morphology, specifically English adjective nominalization, which displays notable variability. We introduce a new method for investigating linguistic generalization in LLMs: focusing on GPT-J, we fit cognitive models that instantiate rule-based and analogical learning to the LLM training data and compare their predictions on a set of nonce adjectives with those of the LLM, allowing us to draw direct conclusions regarding underlying mechanisms. As expected, rule-based and analogical models explain the predictions of GPT-J equally well for adjectives with regular nominalization patterns. However, for adjectives with variable nominalization patterns, the analogical model provides a much better match. Furthermore, GPT-J's behavior is sensitive to the individual word frequencies, even for regular forms, a behavior that is consistent with an analogical account of regular forms but not a rule-based one. These findings refute the hypothesis that GPT-J's linguistic generalization on adjective nominalization involves rules, suggesting similarity operations on stored exemplars as the underlying mechanism. Overall, our study suggests that analogical processes play a bigger role in the linguistic generalization of LLMs than previously thought.