Gamma regression is probably the most appropriate of common glm's. You should probably dig into what these warnings are and what they mean. Often there are problems fitting the model, which aren't theoretical, but are related to the software being able to confidently fit the model. Usually there are settings in the algorithm that can be changed. And sometimes warnings can be ignored.

You commented that negative Binomial regression is for analysis of counts. "Frequency of behaviours" sounds like count data to me. If it is not count data, what is it? Please clarify.

Re your other outcome variable (duration of behaviour), have you considered quantile regression?

The gamma distribution model in Generalized Linear Models (GLM) is often best suited for continuous, non-normally distributed data.

Bruce Weaver I tried using negative binomial regression for focal data, which is not count data. It produces output, but I'm unsure if the output is valid or not. I haven't tried quantile regression yet. Will try to look into it. Thanks for the suggestion. =)

Nurfarah Ain Limin can you please provide more information about your dependent variables and maybe show some examples? I really dont get what you are measuring. What are "focal data"??? We cannot say if your output is valid with insufficient information. Equivalently, what are "scan" data and how does this fit into a binomial regression? Are there only two possible states 0 vs. 1, i.e. attribute, symptom, condition is present or not?

Rainer Duesing Pardon for the lack of information. I observed behaviours using two methods: focal and scan samplings. The data for focal sampling is the duration of a behaviour performed (in seconds). If the target individual performs a behaviour, say walking, for 60s, so the data is 60. If it does not perform the behaviour, it is 0. Meanwhile, the data for scan sampling is the frequency of a behaviour performed. For example, if the individual performs a behaviour, it's marked as 1, if it doesn't perform the behaviour, it's marked as 0. There are 6 trials of scan sampling with 10 minutes of intervals. The factors I'd like to analyse are sex, age category and time. Both focal & scan data are not normally distributed. For scan data, I think Poisson or negative binomial regression are more appropriate since frequency of behaviours is considered as count data. My concern is the analysis of focal data - duration of behaviours, it's continuous, but not normally distributed. I'm unsure of which model is most appropriate to be used to analyse focal sampling data.

Thanks for clarification Nurfarah Ain Limin but some points are still not clear to me.

1) Are both information, i.e. focal and scan data, assessed from the same trials? You write "there are 6 trials of scan sampling..." does it mean, that you also have 6 trials for the focal sampling?

2) If you have 6 trials of focal sampling, how did you "merge" the trials?

3) For the focal sampling, is it only possible to have integer values, i.e. 59, 60 and so on?

And just some comments:

a) it is not the data that has to be normally distributed, but the errors, which can be estimated with the residuals. If these are sufficiently normal, an OLS regression might work

b) if you have count data, I would agree that nonetheless an negative binomial model might be more appropriate. You explicitly mentioned that participants may show no behavior at all, which was coded as 0. Therefore, it might be reasonable to use a zero inflated negative binomial model, where the zeros are explicitly modeled.

c) If I understood it correcly for the scan data, you have 6 trials of each participant, where each trial can be coded as 0 or 1. If this is true, you shoudl think about a multilevel logistic regression, to account for the dependency that the 6 trials are assessed within each person.

d) This concerns my question 1) and 2), if you also have 6 trials for the focal data, it might reasonable not to merge all trials together, but to use a multilevel model as well.

For analyses, I would suggest R and the glmmTMB package or if you want it Bayesian the brms package. Both should be able to handle this.

Sal Mangiafico Thank you for your suggestion. I used Gamma, and multiple warnings appeared as the data is zero inflated, continuous data. The warnings mention that zero data is not used in analysis and that maximum number of step-halvings was reached but the log-likelihood value cannot be improved. I tried transformed +1 for data that has 0 value and run gamma but it can't execute it.

Rainer Duesing Thank you for your suggestions. I have successfully analysed the scan sampling data. For your information, the 6 trials are only for scan sampling. Since focal sampling records the duration of a behaviour performed by an individual, it has an integer value. For example, if the individual is lying for 2 minutes straight, the value would be 120 seconds. Currently, I'm using SPSS to analyse the data. I haven't tried R yet. But I'll look into your suggestion. Thanks again.

note that the Gamma disribution is only valid for positive values > 0.

Nurfarah Ain Limin, if you want to use SPSS, take a look at the GENLINMIXED command, and at this book if you can get your hands on it:

• https://www.routledge.com/Multilevel-Modeling-of-Categorical-Outcomes-Using-IBM-SPSS/Heck-Thomas-Tabata/p/book/9781848729568
• https://www.ibm.com/docs/en/spss-statistics/28.0.0?topic=reference-genlinmixed

Bruce Weaver Thank you very much for your suggestion. Since my focal sampling data is zero-inflated, continuous data, is it possible to use Tweedie with log link function?

Marie Frances Smith Thank you. I realized it's only valid for data with values > 0 through the warnings. Is there any solution for this? I tried transforming it (+1) and running the test again, but it couldn't be executed. Another alternative I have is Tweedie with log link. Do you think it is appropriate to use it for my focal sampling data that is zero-inflated and continuous?

Nurfarah Ain Limin , the error distribution and link function settings for GENLINMIXED can be found here:

• https://www.ibm.com/docs/en/spss-statistics/28.0.0?topic=genlinmixed-target-options-subcommand-command

Hi Nurfarah Ain Limin,

I see two different questions regarding the choice of statistical model:

1: Family of distribution to model residuals: Understanding the processes that generated your response variable usually helps (e.g. counts -> Poisson, negative Binomial, zero-inflated Poisson, etc.) Gamma would be for continuous measures with a lower boundary (e.g. concentrations cannot be negative). Each family of distribution has an associated link functions/transformations (e.g. log) and variance function.

If you use R, there are many distributions, including many zero-inflated distributions available through the packages glmmTMB, mgcv, gamlss, or brms (bayesian) for example.

2. Linearity: Given the family of distribution (and link function) chosen, is the relationship linear? Based on your domain knowledge, you could know whether the relationship should be linear or not (or even the shape). Plotting the data on using the transformed response variable will also show you the shape of the relationship. Finally, plotting the residuals of a linear model vs fitted value would show whether the relationship is linear (no trend in residuals) or not.

For nonlinear relationships, there are many approaches (e.g. transforming the independent variable, polynomials, smoothing splines, etc.)

In any case, definitely inspect the residuals of your model to validate it.

Alain Zuur gives a good overview of the workflow to choose (and present) a regression model.

Article A protocol for conducting and presenting results of regressi...

Hope that helps