Repeated measures ANOVA on proportion success or logistic multiple regression on total binary data?

Question

I have 24 subjects. I have measured distance displaced between image frames at a framerate of 1Hz, so how far did the subject move in a 1sec interval? The continuous movement variable contains many zeroes. I have assigned a second response variable as a binary outcome for movement/no-movment. I wish to test for a correlation between a given treatment and movement.

There are 3 treatment groups, with 8 subjects per treatment. No-treatment, vehicle, and experiment compound. Distance is recorded over ten trials (10 cycles). Each cycle contains 2 phases: 240sec of spontaneous movement, followed by 240sec of stimulus movement.

• Can one take the proportion of movement=1 / total frames per phase (i.e. precent time spent moving) and perform ANOVA on those percent values? One would use treatment between groups, while using phase and cycle within groups.

• Can one use logistic regression on binary movement response? The model would be something in the realm of movement ~ treatment + cycle + phase + (1|subject), and likely with interactions.

Each method naturally has its own concerns, however if one is the most obvious to you, then kindly state why the other should be avoided. Of important note, I wish to also model continuous distance displaced response, after modeling the binary movement/no-movement response. I wish to use the same independent variables if it is within reason.

Lastly, as one considers more interactions between independent variables within a model, does one also adjust alpha accordingly or do models written with R take this into account when reporting statistics?

Thank you for your input- understanding the why/why-not of either model is paramount to a proper analysis, but I cannot yet properly articulate why I think one or the other method is a better choice.

Answer 1

ANOVA on proportion data isn't appropriate, as the underlying assumptions aren't met. That's discussed frequently here, for example in this answer. With outcome values restricted to 0 and 1, the errors around the model predictions can be far from the assumed normal distribution. In some modeling scenarios you can even get model predictions outside that range.

You can use a generalized linear model for binomial regression, such as logistic regression, for a binary outcome. In your situation you should consider a hurdle model that combines the modeling of binary movement/no-movement with a model of the continuous distance moved if there is movement. See this answer, for example. The glmmTMB package referred to in that answer provides an implementation.

The coefficient estimates themselves aren't usually corrected for multiple comparisons. You shouldn't worry too much about coefficient p-values themselves, anyway. In many situations what's important is the reliability of model predictions, evaluated by point estimates and confidence intervals. Correction for multiple comparisons becomes important when evaluating multiple predictions from the model.