# logistic regression factor/categorical predictor without reference/contrast

I did an experiment and there are 3 treatments. My hypothesis is that treatment A & C will lead to response 1 and treatment B will lead to response 0. I'm not trying to get a comparison result like "compared with B, A is more likely to cause 1". So I don't want a reference category.

My initial fomula: logit(y) = b0 + b1 * treatment + b2 * quantitative_predictor_1 + ...

This seems not working as I wish in SPSS or R.

I searched and read the question here (Can multiple logistic regression be performed without a reference/baseline?) but I'm not sure if OP was asking the same question as mine. I read the no constant/intercept approach but I don't know if it fits my situation.

Besides that, I don't know how to do this outside Stata like the answer suggested, and I'm not sure how to apply this in multilevel analysis (my subjects were measured several times within a period of time, I've tried lme4).

Update:

I realized that what I need to test the hypothesis is a null model like 'A, B, C, cause outcome 1 or 0 randomly (odds-ratio=1)'. This is the reference group I need, not A, B, or C. If I only have the variable treatment (A, B, C) and the outcome (1, 0), a Chisq-test or Fisher-test can show there are group differences (and I guess the reference is '3 groups have similar percentages of 0s and 1s'). With all the other variables, I want to push for logistic regression, although my thinking might be wrong.

What about trying a decision tree with response as the outcome variable? In r you can use the rpart package and function. This doesn't allow you to establish an argument for causality and you don't get coefficients for the other variables but you didn't say you needed that. Your expected result will be to see a branch where A,C go one direction and B goes to the other, and that ultimately the final leaves are higher probability 0 under the B branch and higher probability 1 under the A/C branch.

• Thank you for your suggestion! However, causality is my main argument... Sorry that I didn't mention it and it misled you. – leoce Aug 24 '18 at 5:57

The question you link to Can multiple logistic regression be performed without a reference/baseline? has answers which clarify that this was about not having a reference category on the left hand side in multinomial logistic regression whereas you want to do it on the right hand side. Standard software will have converted your categorical variable into two indicator variables since you already have an intercept. If you try removing the intercept (in R -1 in your formula) this may give you the result you want. This will depend to some extent on exactly what you mean by leading to response 1 or 0 in your scientific question.

• Thank you for the help! The 2nd paragraph of the answer by @MaartenBuis discussed no reference on the right side, which seems similar to my question. I'm not sure if it can be done in multilevel analysis though. – leoce Aug 24 '18 at 6:03