I dont know how to correctly present a logistic regression model in expressions or formula in a manuscript or a report, especially with a multiple-level categorical variable. For instance, I have a 3-level treatments (treatment) as the explanatory variable: control, low, and high. The outcome (Y) is alive or dead. Can someone suggest how to write down the formula? Is there a standard formula or an easy understandable formula, especially for non-statistical readers (biology or medicine)? I am bit afraid that if I present the model using matrix format, the readers would not get the idea that there are two values of coefficient beta. But for me, it would be nice to see more forms of presentations.
This is what I can think of:
Y_i ~ Binomial(1,p_i)
logit(p_i) = intercept + beta_k*treatment_i
where i indicates the ith sample. For beta_k, k=low when the ith sample has treatment low; and k=high when the ith sample has treatment high.
Thanks very much