Interpretation of ANODEV table

questions concerning analysis/theory using program MARK

Interpretation of ANODEV table

Postby B.K. Sandercock » Fri Dec 07, 2018 8:15 am

Analysis of Deviance (ANODEV) is a tool in Program Mark for that can be used for estimating how much of the annual variation in a parameter can be explained by an annual covariate. It's been awhile since I last used the tool so I had to review the calculations. Apologies if I overlooked the information but I don't think the details are in the Mark help menu or the Mark manual yet. I'm adding a short note to the phidot forum on interpretation of the statistics in the ANODEV table in case anybody else needs a quick reminder.

Taking the dipper example, how much of the annual variation in apparent survival is explained by the flood covariate? You might fit three nested models: a global model with time-dependence Phi(t), a covariate model for flood Phi(flood), and a constant model Phi(.). The dipper model has 7 occcasions and 6 transitions. The flood model has flood years in the second and third transitions (see page 6-19 of the manual). Detection rates are set as p(t) for all models, but just as an example. That gives the following model selection table:
Code: Select all
-----------------------------------------------------------------------------
                               Delta    AICc     Model                     
Model                   AICc    AICc   Weight  Likelihood   #Par    Deviance
-----------------------------------------------------------------------------
{Phi(flood) p(t)}    674.034    0.00  0.86436      1.0000  8.0000     75.211
{Phi(.) p(t)}        678.748    4.71  0.08185      0.0947  7.0000     82.003
{Phi(t) p(t)}        679.588    5.55  0.05378      0.0622  11.000     74.473
-----------------------------------------------------------------------------

Selecting the menu options for Tests | ANODEV | Select All | OK produces the following summary table:
Code: Select all
   
Source              df       Dev    Mean Dev     F      P     
=============================================================
Uncorrected Total   11     82.003
Grand Mean           7     74.473
Corrected Total      4      7.530
Total Covariate      1      6.792      6.792  27.5959  0.0134
Error                3      0.738      0.246
=============================================================

The calculations in the ANODEV table follow the basics of the Likelihood ratio test for nested models where differences in deviance are a chi-square statistic, and differences in K are the df (see page 3-14 of the manual). The Uncorrected Total is the deviance of Phi(.), the Grand Mean is the deviance of Phi(t), and the Corrected Total is the difference between the two deviances: 82.003-74.473 = 7.530. The Total Covariate is the difference between the deviances of Phi(.) and Phi(flood): 82.003-75.211 = 6.792. The percentage of annual variation in apparent survival explained by flooding can be calculated as: 6.792/7.530 = 90.2%. The Error is the leftover unexplained variation or 0.738/7.530 = 9.8%. The Mean Dev values are calculated as Dev/df, and the F-Statistic is then the ratio of the two Mean Dev values: 6.792/0.246 = 27.5959. Flooding explains a significant amount of the annual variation in apparent survival (F1,3 = 27.6, P = 0.013). The above models are based on fixed effects, but Appendix D of the Mark manual addresses random effects. Corrections welcome if I've made any errors.

Regards,

Brett K. Sandercock
Norwegian Institute for Nature Research
B.K. Sandercock
 
Posts: 48
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