Say, I have a dataset that looks at how many times my 5 babies chases a cat around the house . I'm trying to estimate 'y' which is the number of times the cat runs one complete round around the house as a function of the color of the dress the babies wear and the speed at which the babies are walking. But, I also have information about the type of food the babies ate and if the weather is cloudy or sunny on that specific day. What food the baby chooses to eat can be dependent on the weather.
I want to estimate y as fn of color and speed:
Now, my model is
But, I'm wondering if I can also add information about the food and weather, which are not part of my fixed effects into my model( without including interactions)