I'm working on a project where we observe behaviour on a task (eg. response time) and model this behaviour as a function of several experimentally manipulated variables as well as several observed variable (participant sex, participant IQ, responses on a follow-up questionnaire). I don't have concerns about multicollinearity amongst the experimental variables because they were specifically manipulated to be independent, but I am concerned about the observed variables. However, I'm unsure how to assess independence amongst the observed variables, partially because I seem to get somewhat different results depending on how I set up the assessent, and also because I'm not very familiar with correlation in the context where one or both variables are dichotomous.
For example, here are two different approaches to determining if sex is independent of IQ. I'm not a fan of null hypothesis significance testing, so in both approaches I build two models, one with a relationship and one without, then compute and AIC-corrected log likelihood ratio:
m1 = lm(IQ ~ 1) m2 = lm(IQ ~ sex) LLR1 = AIC(m1)-AIC(m2) m3 = glm(sex~1,family='binomial') m4 = glm(sex~IQ,family='binomial') LLR2 = AIC(m3)-AIC(m4)
However, these approaches yield somewhat different answers; LLR1 is about 7, suggesting strong evidence in favor of a relationship, while LLR2 is about 0.3, suggesting very weak evidence in favor of a relationship.
Furthermore, if I attempt to assess the independence between sex and another dichotomous observed variable, "yn", the resultant LLR similarly depends on whether I set up the models to predict sex from yn, or to predict yn from sex.
Any suggestions on why these differences are arising and how to most reasonably proceed?