I have data regarding an experiment. The dependent variable is a count variable ranged 0-5 (n of consecutive days out of 5 in which a subjects experienced a certain condition). I also have two factors: a factor with two levels (group) and a repeated-measure factor with three levels (time). I'm interested to investigate whether the average number of days when the condition occurs is significantly reduced in the treatment group compared to the control group along the time.
Given the nature of the dependent variable and that the observed distribution is very skewed towards 5 in all levels, which distribution should I use in the model?
As far as i know, binomial with logit is suitable for binary outcomes while poisson is for count variable ranging 0-to-infinite.
Thank you!
You may want to consider a negative binomial distribution. Depending on the difference between the mean and variance in your outcome variable (Poisson distributions assume that mean = variance) a negative binomial distribution may be a better bet.
Incidentally, there are other modeling options available to you. Based on your description above, you could also consider a multilevel model approach, in which you model the probability of an event occurring on a given day. This could be with or without time as a predictor if you are interested in determining whether the probability of your event of interest occurring changes over the 5 day window.
Best of luck.
-Matt
https://en.wikipedia.org/wiki/Multilevel_model
Since the counts are limited to 5 on the right side, I'm not sure Poisson or negative binomial would be appropriate. The best guess I have is to use ordinal regression. At least in its most popular instantiation in R, it uses a multinomial distribution (discrete, set number of categories), but accounts for the fact that e.g. 2 > 1, 3 > 2, etc.
I like the ordinal regression suggestion, but it does have drawbacks in interpretation given that it is essentially an implementation of a multinomial regression. I still think that a Poisson or negative binomial could work. If the concern is over a severe left-tail skew, you could flip the distribution of the outcome variable and model the number of days the event didn't occur (so no occurrence = 1, and occurrence = 0 summed across the 5 days). In some ways this could also make some conceptual sense as the occurrence of the event seems to be the norm and it's non-occurrence seems to be the desired deviation from the norm. Ultimately, non-occurrence rates may be the real outcome of interest.
Thank you Matthew and Salvatore for your suggestions!
I found that It could also be modeled with a logistic regression, with the single case value not being 0 or one but the % (n occurrence/n trial).
In R with glm, you also have to weight each case with n of trials.
https://www.r-bloggers.com/generalized-linear-models-for-predicting-rates/
What do you think?
The logistic idea is interesting. I have a couple of examples in R below.
I would think if you did it that way that you need an observation for each participant, which would be their count out of 5. This might be okay.
It's not perfect, because the 5 trials are not independent; you are looking at consecutive successes only.
Examples:
"Alternate logistic regression" subsection of the "Beta regression example with discrete counts" example:
http://rcompanion.org/handbook/J_02.html
First example:
http://rcompanion.org/rcompanion/e_06.html
Yes, you are absolutely right. The non-independence of the trials is a clear violation of the assumption for the bionomial.
A further idea is to add a repeated measure factor for the 5 trials and model it as a repeated measure "logistic regression" (better called generalized linear model with binomial distribution and logit link function). This is may not be very "compact" but a better option.
This line of thinking circles back to my previous suggestion to use a multilevel logistic model. Such an approach would help you navigate the non-independence of your data. Check out the lme4 and lmerTest packages in R. The glmer() function would allow you to run a generalized linear multilevel model.
Help, please!!!
My dependent variable is count dependent like in percentage (10%, 25%, 35%, 75% and 85% ---5 categories strictly). So I used GLM specifying family (negative binomial) and link (log) to analyze the data. Would you please guide me on the correct way of interpretation of the effect of independent variables on dependent variables for example a significant coefficient of 0.65 of particular predictor variable X on the response variable Y. It would be great if you suggest any similar research article. Thank you!!!
Sudip Adhikari
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