We consider the mathematical transformations used for assets of different valuation complexity in audit fee models. These mathematical transformations (such as logs and square roots) relate to the non-linear relationship between client size and audit fees. We use closed-end mutual fund audits to examine this question because virtually all fund assets are reported at fair value. We find that more complexly valued assets are less likely to follow the traditional log transformation because the presence of these assets has a stronger relationship with audit fees that is not fully captured by the coefficient on the logged variable alone. The significance of non-size variables was also found to differ in audit fee models of both closed-end funds and a broad-based sample of public companies when the mathematical transformation of size variables was permitted to vary. These results suggest that the non-linear relationship between client size and audit fees may not always be sufficiently captured by a log transformation and that future audit fee studies should consider different size transformations to test size measures and to more robustly assess the significance of other variables in audit fee models that may be of interest.

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