I have data consisting of the distance cats travelled each hour, collected over four or five days per cat. The cats were measured in different seasons and I want to know whether the activity of the cat varied with hour, dependent on the season. For example, were cats more nocturnal in summer? I am not sure whether the output is showing that there is a difference in the mean activity, or a difference in the pattern of activity over time?
My data is structured with the headings: Cat_ID, season, day, hour, distance.
Using the mgvc package, my GAMM model is then constructed like this:
mod1 <- gamm(distance ~ s(hour) + s(hour,by=season,bs="cc",fx=TRUE,k=6) + season, random = list(id = ~1), data = dn, na.action=na.exclude)
The output is:
> summary(mod1$gam) Family: gaussian Link function: identity Formula: dn$distance ~ s(hour) + s(hour, by = season, bs = "cc", fx = TRUE, k = 6) + season Parametric coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 160.77 13.68 11.756 <2e-16 *** seasonSummer -15.33 18.33 -0.836 0.403 seasonWinter -25.49 17.74 -1.437 0.151 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Approximate significance of smooth terms: edf Ref.df F p-value s(hour) 1 1 5.526 0.018769 * s(hour):seasonSpring 4 4 5.009 0.000499 *** s(hour):seasonSummer 4 4 1.529 0.190775 s(hour):seasonWinter 4 4 2.856 0.022273 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 R-sq.(adj) = NA Scale est. = 21730 n = 5226 Warning messages: 1: In as.numeric(object$y) - object$fitted.values : longer object length is not a multiple of shorter object length 2: In w * (as.numeric(object$y) - object$fitted.values) : longer object length is not a multiple of shorter object length
I want to know if the 'parametric coefficients' are telling me that there is no difference between the mean distance travelled in spring and summer (p=0.403) nor between spring and winter (p=0.151), or if there is no difference between the activity over the day, i.e. the pattern of activity.
Thank you so much for any help you can provide