[Basta-users] Calculating daily mortality rates for models with cont. covariates using estimates

[Dries Van de Loock]

Dear BaSTA community,



Thanks to your help and BaSTA, we could statistically confirm some of our
expectations on post-fledging survival in a afrotropical passerine
<http://lists.r-forge.r-project.org/pipermail/basta-users/2015-October/000131.html>.




While *plotfancybasta()* and *plot() *produce nice graphs for categorical
variables, we are looking for a way to visualise the impact of *continues
covariates* on survival of the fledglings.



More specifically, we fitted a weibull survival curve with makeham shape +
mass at fledging (SMI) as a covariate (base model + 1 covariate) and find a
negative relation with mortality (CI does not include zero).



Coefficients:

          Estimate  StdErr Lower95%CI Upper95%CI SerAutocor UpdateRate
PotScaleReduc

c          0.02704 0.01595   0.009527   0.066033    0.56051     0.2223
        1.017

b0         0.06541 0.06751   0.001576   0.252938    0.38508     0.2605
        1.002

b1         0.90422 0.63824   0.043231   2.358846    0.06547     0.2501
        1.001

gamma.SMI -0.03971 0.01978  -0.083632  -0.006801    0.55284     0.2526
        1.003

pi.1       0.14211 0.01089   0.121642   0.163994    0.03578     1.0000
        1.001



We see two ways to visualise this


1. Daily mortality rates over a two month period (y-axis) plotted against
time (x-axis) for a discrete number of SMI values. As such, you visualise
the mortality shape for a number of SMI values over a two month period.


2. The cumulative mortality probabilities (y-axis) after a two month period
plotted against SMI (x-axis). We then expect that cumulative mortality
probabilities will decrease with increasing SMI.



To do this, we could use the estimates to calculate (i) the daily mortality
rates over a two month period and use these to calculate (ii) the
cumulative mortality probabilities after a two month period for a discrete
number of SMI values within the measured range (for example : 20,
25,30,35).




While we successfully calculate daily mortality rates fitting the estimates
in the function (b0 * b1 * ((b1 * k)^(b0 - 1))) + c) when no covariates
were added to the model, we failed to find a method on how to include the
gamma estimate in the function.




Any help on how we can calculate daily mortality rates for a specific value
of the covariate and be able to produce these graphs is highly appreciated.



Best wishes,



Dries Van de Loock

PhD student

Terrestrial Ecology Unit

Department of Biology

Ghent University

KL Ledeganckstraat 35

B-9000 Ghent, Belgium

Phone: +32 (0)9 265 50 39

http://www.ecology.ugent.be/terec/
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