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Computational models of verbal analogy and relational similarity judgments can employ different types of vector representations of word meanings (embeddings) generated by machine-learning algorithms. An important question is whether human-like relational processing depends on explicit representations of relations (i.e., representations separable from those of the concepts being related), or whether implicit relation representations suffice. Earlier machine-learning models produced static embeddings for individual words, identical across all contexts. However, more recent Large Language Models (LLMs), which use transformer architectures applied to much larger training corpora, are able to produce contextualized embeddings that have the potential to capture implicit knowledge of semantic relations. Here we compare multiple models based on different types of embeddings to human data concerning judgments of relational similarity and solutions of verbal analogy problems. For two datasets, a model that learns explicit representations of relations, Bayesian Analogy with Relational Transformations (BART), captured human performance more successfully than either a model using static embeddings (Word2vec) or models using contextualized embeddings created by LLMs (BERT, RoBERTa, and GPT-2). These findings support the proposal that human thinking depends on representations that separate relations from the concepts they relate.