I want to use logistic regression to estimate the probability of whether an organism is active or not. My independent variable is time of day and my dependent variable is binary (1 = active, 0 = not active)
While time is continuous, in this case it loops back into itself. After 24 hours (or 1440 minutes) the t-variable resets to zero. This would mean that the graph would have to travel upwards and then back down into itself. I also suspect that the curvature upwards may be different from the curvature downwards.
Is there a sub-classification of logistic regression that accomplishes this?
a first, very quick and rough approach would be, to treat the time as categorical variable with, say, 24 categories for the 24 hours. Depending on your number of measurements you may reduce or increase the number of categories. The estimated regression coefficients will contain information on the shape of the curve.
There are certainly more elegant options, but I think they'll need assumptions on the shape of the curve. Maybe, you should start first with an adequate description; f.e. % of active subjects over time. Depending on this you may use other methods later, f.e. cosinor analysis. Logistic regression assumes basically a monotone relationship and may be not the best choice for cyclical data.
a first, very quick and rough approach would be, to treat the time as categorical variable with, say, 24 categories for the 24 hours. Depending on your number of measurements you may reduce or increase the number of categories. The estimated regression coefficients will contain information on the shape of the curve.
There are certainly more elegant options, but I think they'll need assumptions on the shape of the curve. Maybe, you should start first with an adequate description; f.e. % of active subjects over time. Depending on this you may use other methods later, f.e. cosinor analysis. Logistic regression assumes basically a monotone relationship and may be not the best choice for cyclical data.
One approach is to fit a robust smooth with 1/0 as the outcome and time as the (non-linear) predictor - the specific model is a logistic generalized additive model
https://www.researchgate.net/publication/225303313_Moving_Out_of_the_Linear_Rut_The_Possibilities_of_Generalized_Additive_Models
https://www.researchgate.net/publication/225303308_Generalized_Additive_Models_Graphical_Diagnostics_and_Logistic_Regression
This will allow for asymmetry - differential curvature - in the underlying relation and is far more flexible than a polynomial of time.
Article “Moving Out of the Linear Rut: The Possibilities of Generali...
Article Generalized Additive Models, Graphical Diagnostics, and Logi...
You could consider regarding your design as repeated measures and fit these with mixed models: http://lme4.r-forge.r-project.org/book/Ch4.pdf If strong non-linear effects are expected, current implementations may, however, often not be sufficient.
Sine and cosine transformations (you may need to convert to radians first) should be what you are looking for. A quick google search yielded this: http://scholar.harvard.edu/files/malf/files/circularttime-maluque_0.pdf
Cheers!
Hi,
I like Horst´s answer. However, if seasonality is an issue you might want to create f.e. 4 variables: 1+2: (absolute) distance to sunset / sunrise, 3+2: (absolute) distance to midday / midnight and use these as explanatory variables.
good luck!
Irene
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