Large language models (LLMs) are increasingly used to support automated writing evaluation (AWE), both for purposes of scoring and feedback. However, LLMs present challenges to interpretability, making it hard to evaluate the construct validity of scoring and feedback models. BIOT (best interpretable orthogonal transformations) is a new method of analysis that makes dimensions of an embedding interpretable by aligning them with external predictors. It was originally developed to improve the interpretability of multidimensional scaling models. However, This paper shows that BIOT can be used to align LLM embeddings with an interpretable writing trait model developed using multidimensional analysis of classical NLP features to measure latent dimensions of writing style and writing quality. This makes it possible to determine whether an AWE model built using an LLM is aligned with known (and construct-relevant) dimensions of textual variation, supporting construct validity. Specifically, we examine the alignment between the hidden layers of deBERTA, a small LLM that has been shown to be useful for a variety of natural language processing applications, and a writing trait model developed through factor analysis of classical features used in existing AWE models. Specific dimensions of transformed deBERTA layers are strongly correlated with these classical factors. When the transformation matrix derived using BIOT is applied to token vectors, it is also possible to visualize which tokens in the original text contributed to high or low scores on a specific dimension. • Large language models (LLMs) are increasingly used to support automated writing evaluate (AWE). • LLMs present challenges to interpretability, making it hard to evaluate construct validity of scoring and feedback models. • BIOT is a new interpretation method that aligns embedding dimensions with external predictors. • Specifically, BIOT can be used to align LLM embeddings with classical NLP measures of aspects of style and writing quality. • This demonstrates a general method to determine whether an LLM latently represents construct-relevant dimensions.