I am relatively new to R and stats and am getting a little confused about multicollinearity. I am planning on carrying out ordinal logistic regression, and the majority of my independent variables are binary. There are, however, a few categorical variables, most of which possess 4 levels. As far as I can understand, before the analysis I should either create dummy variables of these, or define them as factors (in R).
The question I have concerns collinearity and associations within the categories themselves. For example, one of my categorical variables is whether or not food or water is left out for animals in the respondent's garden ('food_water', 4 levels: just food, just water, neither, or both). Originally, this comprised two separate binary variables (food [yes/no], water [yes/no]) that I have since combined as they were strongly associated with one another, i.e. most people who don't leave out food also don't leave out water, and those who do leave out food tend to leave out water too. I combined them into one variable to avoid having multiple 'correlated' variables 'skew' my analysis (please correct me if this is illogical or wrong).
Now, if R processes this food_water variable as dummy variables, would splitting the category into these dummies cause a multicollinearity effect (since the 'neither' and 'both' levels are technically associated with one another)? Should I instead just input one of the original variables for analysis (e.g. just the food binary variable) and use it as a proxy for water?
Any advice would be much appreciated!