68 
Teil C - Annex 
For carrying out the modelling, comprehensive data exploration (described in Zuur et al. 2010) 
and model validation (Wood et al. 2006, Zuur et al. 2009, 2010,2012a,b) are required to check, 
whether the model assumptions regarding the basic distribution of data and correlations are 
supported by residual variance distribution. Model validation examines aberrations, homoge 
neity of variance, normal distribution of residuals, zero inflation, correlated predictor variables, 
interactions and the assumption of independence of data (Zuur et al. 2010). Model validation 
results in suitable models correctly describing the data. Predetermination to use GAMM or 
GLMM is not reasonable. Conversely, mixed models are absolutely necessary, since the ques 
tion as such is simple: how to harbour porpoises (response) react to pile driving of founda 
tions (predictor). However, this process is influenced by seasonal and geographic distribution 
of harbour porpoises and differences in the measuring equipment, which ideally are taken into 
account in the model as random effects. Model validation must take into account also spatial 
and temporal autocorrelation effects. Temporal autocorrelation can, for instance, be accom 
modated in “mgcv” by introduction of an autocorrelation structure; spatial autocorrelation 
should be checked by variograms (Zuur et al. 2010). 
To achieve the highest possible temporal resolution of harbour porpoise activity in relation to 
the pile driving events (hours with pile driving events = hour “0”), evaluation takes into account 
either the harbour porpoise-positive minutes per hour (DPM hr 1 ) or, alternatively, the harbour 
porpoise-positive 10-minute periods per hour (DP10M hr 1 ). Using the influence of predictor 
variables, the impact of pile driving activities can be described both spatially (e. g. distance to 
the pile driving site) and temporally (e. g. hour relative to the pile driving event). The correlation 
of spatial and temporal effects is complex and may be characterised, for example, by intro 
ducing an interaction term (predictor space x predictor time or as a tensor product). Moreover, 
the model may include also temporal parameters (time of day, month, year) and, depending 
on the data set, other parameters, for instance, those describing the pile driving event more 
closely (e. g. duration, average energy used kJ hr 1 , measured noise immission at site of 
C-POD measurement). The p-values obtained by modelling are not to be equalled with tradi 
tional statistics, which is why p-values that are close to the alpha level of 5% must be critically 
examined. As a rule, evaluation is carried out by an ANOVA or log-likelihood test. 
If the calibration data are available in evaluable form, they preferably should be included in the 
model. The inclusion of the POD-ID as a random factor can, under certain circumstances (fast 
change of measurement equipment and homogeneous utilisation of a preferably small equip 
ment pool across the project stations), lead to improvement of the model results. However, 
this is not an equipment-specific characteristic and can therefore be subject to strong influ 
ences from seasonal and geographical distribution of harbour porpoises: accordingly, it is a 
collective factor. The error distribution is dependent on data inspection and model validation. 
Potentially suitable distributions may be Poisson, Binominial and negative Binominial distribu 
tions, their derivatives for compensation of overdispersion (quasi-) as well as zero-inflated 
distributions (Zero Inflated or Altered Binomial (ZIB, ZAB), Zero Inflated or Altered Poisson 
(ZIP, ZAP) and Zero Inflated or Altered Negative Binomial (ZINB, ZANB)). 
Recovery times (waiting time) 
As an alternative to a GAM with “harbour porpoise activity” (DPM h-1) as dependent variable, 
the influence of pile driving activities on harbour porpoise recovery times may be analysed. In 
this approach, the waiting times between individual harbour porpoise events (“encounters”) 
are taken as measure for re-utilisation of the area in reference to the pile driving activities. The 
waiting times after end of a pile driving event are numbered (categorial variable) and com 
pared to uninfluenced waiting times. Since it is highly probable that the end of pile driving ac 
tivities coincides with a longer rather than with a shorter waiting time (“Bus Paradox”: Ito et.