Analysis of sapflow measurements of Larch trees within the inner alpine dry Inn- valley PhD student: Marco Leo Advanced Statistics WS 2010/11
Overview Background Principle of sapflow measurements Collection of environmental data Statistical analysis of time series data Descriptive statistics Multiple linear regression Autocorrelation
Principle of sapflow measurements Two sensors installed into the sapwood The top sensor is heated Temperature difference between the sensors Calculation of the sapflow density [ml cm 2 min] Relative sapflow for data interpretation ! Dependent variable
Dependence of environmental parameters Collected environmental data: (independent variables)
Typical sesonal course of sapflow density
Box plots I
Box plots II
Scatter plots
Multiple linear regression (model VPD 2 )
y vs. fitted and residuals vs. time
What is Autocorrelation ? Autocorrelation is the correlation of a signal with itself (Parr 1999). part of the data:
Testing Autocorrelation Durbin Watson Test durbinWatsonTest(model_LA_2) lag Autocorrelation D-W Statistic p-value Alternative hypothesis: rho != 0 H 0 : α = 0 → No Autocorrelation H 1 : α ≠ 0 → Autocorrelation
Determine the strength of the Autocorrelation Autocorrelation Function (ACF) Partial Autocorrelation Function (PACF) Y t = α Y t-1 + ε t
Time series model - ARIMA Elimination of the Autocorrelation Results: Summary Table with coefficients and standard errors
Residual plots
ACF and Partial ACF
Multicollinearity Variance Inflation Factors (vif) tolerance = 1/vif
Differential effect of the independent variables b j …regression coefficient S xj …standard deviation of x j S y …standard deviation of y
Optimal VPD for sapflow
Helpful R commands/features for using time series data: Arima model: the output differs from a lm model Residual diagnostic – plot(model_LA_2$resid,xlab="day of year",main="VPD2 model“) Create lines to get an overview of diagnostic plots – abline(h=0,col="red") – abline(0,1,col="red")
Thank you for your attention !