# Can I run a logistic regression if my dependent variable has one category?

I have asked people to tell me as many words as they can in one minute (fluency task) and I want to analyze the properties of the words they are saying. My dataset has a column for correct words (dependent variable) and three columns with continuous data corresponding to different properties of the correct words only (frequency, familiarity, imageability).

I would like to know if running a logistic regression is OK, provided that my dependent variable is only 1s. This is the code I used in R:

q <- glm (Words ~ Frequency + Familiarity + Imageability, data=df)

Perhaps one way around it is to make it so my dependent variable has 1s for correct responses and 0s for incorrect responses. However, the incorrect responses do not have any values for frequency, familiarity, etc.

I would like to know if participants said words that were higher in frequency, as opposed to familiarity or imageability. Should I then run a glmer?

• I answered your question, but maybe you should elaborate what you are trying to do. There doesn't seem to be anything resembling a hypothesis here. There is also a huge question of the validity of some of your scales. Even if you measured familiarity and imageability it is not clear they are real things outside of your imagination. Familiarity is subjective so you would need a very good operational definition and imageability is very cognitively dependent on the preferences of the speaker. Some people have high natural imaging ability and some have very low. – Dave Harris Dec 13 '17 at 20:45

No, you cannot. It does beg the question of why you wanted to it that way anyway. If $q$ does not vary, then it cannot be analyzed. Indeed, from what you are describing there isn't really an inferential statement you could make. Nothing is random.