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I am a biologist with an interest in experiment design. I recently refreshed my memory about what kinds of response variables that are possible, and made this chart (see jpeg). I would like feedback whether it is correct or not. I think it would be helpful to have a chart like this to show to my fellow biologists, who don't get much formal training in DOE/stats. Thanks! Chris

Response Variable Types Chart

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=== Responses to Bjorn's Comments ===
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Hi Bjorn, Thanks for your comments, let me respond to your points one-by-one:

:: You miss some big categories: [0, Inf) and/or (0, Inf), time-to-event with censoring, multivariate outcomes (discrete or continuous) etc.

  • Is there already a list of all response variable categories that includes the types I missed? I do not know time-to-event or multivariate responses (these are likely more advanced than what i see in my field of cell biology)
  • Are [0, Inf) and (0,Inf) on the real number line, or are these integer responses? Also, do these distributions tend to appear in certain fields over others?

:: Where I start to have a real headache is the "convert data to"

  • In the chart, "convert data" refers to the internal "conversion" of count data, from a contingency table for example, into proportion or log-odds data by the model fitting algorithm. I do not know how the math works, but from the outside it appears to me that a kind of "conversion" has occurred after fitting these models. Alternatively, the phrase "convert data" could be switched to "count data treated as…", or something like that.

:: Response distribution (omitting lots and lots of obvious and useful distributions)

  • From my experience i only know about the following major response distributions that can be used for modeling: gaussian, poisson, multinomial, and binomial
  • Are there other distributions commonly used, and are they associated with certain fields over others?

:: Model (any "modern" models from the 1960s onwards like logistic regression?

  • I believe the logit model is equivalent to logistic regression, but please correct me if that's wrong

:: Hierachical models?

  • What are hierarchical models and what are they used for?

:: Covariate adjustment?

  • What is covariate adjustment? If covariate adjustment is the inclusion of a continuous predictor variable with a categorical predictor, then maybe I can treat it as a separate issue from response variables, as it deals exclusively with the predictors, but again please correct me if that is not correct

Thanks again for your comments, Cheers, Chris

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  • $\begingroup$ You miss some big categories: [0, Inf) and/or (0, Inf), time-to-event with censoring, multivariate outcomes (discrete or continuous) etc., but that's less of a problem. Where I start to have a real headache is the "convert data to" (erm, sometimes, but certainly not usually before modeling), response distribution (ommitting lots and lots of obvious and useful distributions) and model (any "modern" models from the 1960s onwards like logistic regression? hierachical models? covariate adjustment?) bits. Often just applying on eof these test is plain wrong (e.g. non-randomized experiments). $\endgroup$ – Björn Jul 20 '20 at 21:29
  • $\begingroup$ Hi Bjorn, I did not have enough space to post my response to your comments - so I added them to the post itself. You mention several topics I'm not familiar with, so I will have to read up on them to understand your response completely I think. Thanks! $\endgroup$ – Chris Science Jul 21 '20 at 2:37
  • $\begingroup$ [ or (0, Inf) occurs a lot e.g. cell counts, quantities that can only be positive (electricity used by a device). I don't think there's a list of all possible outcome domains, it is almost futile to create one (but as your propose, one might have a list of the most common ones). Conversion: Importantly, models only really in a sense convert, if the converted version is a sufficient statistic (e.g. a proportion for Y heads out of N coin tosses is not, because it looses the information on the denominator). I guess Bernoulli dist. + logit-link is more or less logistic regression. $\endgroup$ – Björn Jul 21 '20 at 8:49
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    $\begingroup$ Other common distributions: (stepwise) exponential, Weibull, non-parametric survival approaches (cf Cox regression/Kaplan-Meier), gamma, hypergeometric & distributions implied by hierachical models (e.g. Poisson + normally dist. random effect on log-rate, logistic reg. with r.e. on logit-probability...). It does vary a lot by field. Hierarchical models = models using random effects to reflect some structure (e.g. multiple students in same class in same school = their grades are not independent). Covariate adj. is why the tests in your last row should not be recommended as such default choices. $\endgroup$ – Björn Jul 21 '20 at 9:00
  • $\begingroup$ Okay, thanks Bjorn! $\endgroup$ – Chris Science Jul 21 '20 at 13:03

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