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I have data from a study based on survey responses (n=379). Some of the questions of said survey are related to suicidal thoughts and others are related to psychopathy. Each question has a related score (from 0 to 4), so every individual has a suicidal thoughts score (ST) and a psychopathy score (Psy). Both of this variables are numerical, discrete, positive between 0 and a maximum score. I am interested in examining the relationship (if there is one) between the two scores, and my first idea was to model ST by using Psy as predictor.

The main problem is that ST is not normally distributed. In fact, it is inflated with 0s very heavily: enter image description here

I am very new to statistical modelling so I didn't knew where to start looking. From my searches, the better suited forms of regression are based on:

  • Zero-inflated Poisson distribution. ST is numerical and discrete. However, it is not an event that occurs repeatedly, but a score representing sum of the score of individual answers in a survey. Also, the Poisson does not have an upper limit, while ST does have one (although there is no occurrences in the dataset).
  • Zero-inflated Beta distribution after transforming ST from absolute score to fraction of the total possible score. I also discarded this option because the beta is a continuous distribution.

Also, I have many other variables that may be worth to incorporate in the model, like sex, age, education level, among others. Should I introduce them to my model? I have read about mixed effects models but I am not sure if this kind of model is appropiate or if I would be complicating things more than necessary.

Is there a kind of regression that better suits my data? Are my thoughts on the presented two options erroneous? Am I missing something? Please let me know.

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The main problem is that ST is not normally distributed

Please note that there is no requirement for any of the variables in a regression model to be normally distributed. Sometimes we may like the residuals to be normally distributed.

In this case it is clear that you have a zero-inflated response and from the description you also have count data. A beta model might be indicated when the response is continuous and bounded, but I don't see a lot of point in transforming it. The data would appear to be naturally modelled with a zero-inflated poisson, or maybe negative binomial.

As regards mixed models, if you have repeated measures within participants, or some other clustering (eg geographic), then a mixed model would be the way to go. So this would be a generalised linear mixed model, and in particular a zero-inflated poisson or negative binomial. A number of packages in R can fit such models such as GLMMAdaptive and glmmTMB

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