It seems like you are exploring different options for summarizing and interpreting data in the context of field ecology and management practices. Your options involve transforming the variables, expressing them as differences in means or log-odds ratios, and considering latent constructs. Here are some thoughts on each option:

Option 1: Log-transformed differences in means Using a log transformation on both the dependent variable (DV) and independent variable (IV) can be a valid approach in certain situations, particularly when the relationship between the variables is expected to be multiplicative rather than additive. By treating the coefficients (bi) as elasticity coefficients, you can interpret them as the percentage change in the DV associated with a one-unit change in the IV on a logarithmic scale. This approach can be useful for examining how changes in the IV relate to proportional changes in the DV.

Option 2: Log-odds ratios Expressing the differences in means as log-odds ratios (log(bi/bi+1)) can be appropriate when you are interested in studying the relationship between two categorical variables and examining changes in odds. This approach is commonly used in logistic regression, where the log-odds ratio represents the change in the log-odds of the outcome for a one-unit change in the IV.

Option 3: Exploring alternative approaches It's difficult to provide a specific option without more context about your research question and the nature of your data. However, you could consider other techniques such as regression analysis, generalized linear models (GLMs) with appropriate link functions, or non-linear models depending on the specific assumptions and characteristics of your data. These techniques can provide insights into the relationships between variables and allow you to interpret the effects in terms of practical implications for management purposes.

It's important to carefully consider the assumptions underlying each approach and assess whether they are appropriate for your specific research context. Additionally, consulting with experts or statisticians with knowledge in your field can provide valuable insights and help you select the most suitable approach for analyzing and interpreting your data.

Lastly, conducting sensitivity analyses or simulation studies can help evaluate the robustness and limitations of your chosen approach under different conditions, further strengthening the validity of your findings.

Remember to thoroughly document your methods, assumptions, and reasoning to ensure transparency and reproducibility in your research.