# 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

## 2 Answers

A logistic regression finds some kind of (linear) relation between your independent and dependent variables. If your dependent variables always has the same value this seems superfluous, since all the variation is explained by a fixed value. Therefore, no variation is explained by your independent variables.

This can hardly be the thing you are looking for. You should think about what you want to research, how this can be analysed and consequently how to assess your findings statistically.

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.

• Thank you for your answer, Dave. 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? – B4ltimore Dec 13 '17 at 20:55
• Well, if Frequency is a population parameter, and the sample is random, then regardless of anything else, they should not do so. They should adopt the group norm if the sample is large enough and representative. Any variability should be due to chance and would be irrelevant. – Dave Harris Dec 13 '17 at 21:40
• How do you define familiarity and how do you define imageability? Is your concept that frequency is a function of familiarity and imageability? – Dave Harris Dec 13 '17 at 21:41
• Well, in fact the data comes from 3 different groups. Should I use "group" instead of "words" as my dependent variable? – B4ltimore Dec 13 '17 at 21:50
• What do familiarity and imageability mean? – Dave Harris Dec 13 '17 at 21:51