Hi Philip,

Thanks for your response, it was very enlightening. I studied a little

about periodic regression and tried to do the test in R. At first I have no

fixed or random effects to add, since these data are simple, just an index

over time, measured every half hour, for a day. I am posting part of the

script to know if it is correct and if the result makes sense. As I

understand it, only one time-related variable are significant. I am trying

to read about possible interpretations of this result without much success.

>

tad.lm<-glm(tad$index~(cos(2*pi*(tad$hora/24)))+(sin(2*pi*(tad$hora/24))),

family=quasipoisson)

> summary(tad.lm)

Call:

glm(formula = tad$index ~ (cos(2 * pi * (tad$hora/24))) + (sin(2 *

pi * (tad$hora/24))), family = quasipoisson)

Deviance Residuals:

Min 1Q Median 3Q Max

-2.1060 -0.7502 -0.3460 0.3112 2.3771

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 0.3172 0.1503 2.111 0.0404 *

cos(2 * pi * (tad$hora/24)) -1.1927 0.1979 -6.027 2.85e-07 ***

sin(2 * pi * (tad$hora/24)) -0.1641 0.1697 -0.967 0.3386

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for quasipoisson family taken to be 1.121044)

Null deviance: 97.400 on 47 degrees of freedom

Residual deviance: 44.898 on 45 degrees of freedom

AIC: NA

As for the part of your answer about the aggregation test, I do not think I

understood, do you have some suggestion of literature for me to try to

understand? In that case, I have to test if some samples of the index are

significantly higher than others. I have already thought of non-parametric

tests, since this index does not have normal distribution, but I still have

not found any suitable for this case.

Thank you!!

Cheers,

Thiago

Thiago A. Leão Pires

Ph.D. student in Ecology - UNICAMP

Collaborator Researcher - UNIFESP

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