Size Variables in Audit Fee Models: An Examination of the Effects of Alternative Mathematical Transformations
研究了审计费用模型中客户资产规模的不同数学变换（如对数、平方根）对模型结果的影响，发现复杂估值资产更不符合传统对数变换，建议未来研究考虑多种规模变换以更稳健地评估其他变量。
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 nonsize 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.