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Here's the approach I used to calculate the onset (10th percentile) and end (90th percentile) of migration. I created a new column with the cumulative number of birds each day from the predicted daily values, and found the day of year where each percentile was reached: newdf <- newdf %>% mutate( cumulative_birds = cumsum(fitted), # cumulative ...

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You could do the following: Measure how far your spline is from the straight horizontal line. Then generate a bunch of sets of random data. Fit a spline to each set and see how many have bigger differences between a straight line and the spline than yours does. The exact nature of the random data could be a few different things - one choice is to use data ...

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In a GAM, you model the condition mean (and derive or possibly estimate any other parameters required, depending on how strict your definition of a GAM is) given the stated/assumed distribution of the response. Your comment With GAM - I'm not sure how to interpret the "smoothed" predictors. Both [GAM and QR] seem to not assume any underlying conditional ...

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You could take this to extreme and ask why wouldn't we use non-parametric model like $k$-NN regression? Actually, the opposite question Why would anyone use KNN for regression? was asked, and you can check it for more detailed discussion. You can also make the question more broad and ask why wouldn't we use more complicated models instead of simpler ones? ...

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In the wikipedia-definition of the $\chi^2$-distribution (https://en.wikipedia.org/wiki/Chi-squared_distribution), $k$ (the "degrees of freedom") is an integer. However, the distribution itself can be evaluated for non-integer values, too. In your case, your change in deviance is tiny (the value is not actually shown, except that it is less than 0.001), ...

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