Visualising our data
With the climatewin code above, we have compared all possible climate windows for our Mass dataset. However, one danger of the exploratory approach that we employ is that there is a risk of detecting seemingly suitable climate windows simply by statistical chance. In other words, if we fit enough climate windows one of them will eventually look good.
To overcome this concern, we have designed a number of plotting options that allow users to visualise their climate window data and determine if the ‘best’ window detected represents a real period of climate sensitivity or simply a statistical fluke.
We have designed 6 different plotting functions to help users visualise and interpret their climatewin results. Below we will discuss each plot in detail.
Plot delta AICc values
As a first step, we can look at the distribution of delta AICc values across all tested climate windows. In the below plot, blue regions represent climate windows with limited strength (AICc values similar to the null model) while red regions show strong models.
In our Mass example, we can see an obvious region of strong windows around the left of the graph. This seems to suggest that there is a clear area of sensitivity.
plotdelta(dataset = MassOutput)
Plot model weights
Another way to visualise the delta AICc data is through the use of model weights (Burnham, Anderson & Huyvaert 2011 source). In short, the higher a model weight value the greater confidence we have that this model is the true ‘best’ model. While our top climate window is the most likely single window to best explain the data, our confidence that this top window represents the true ‘best’ model may still be low.
If we sum the weights of multiple models, we can now be more confident that we encompass the true best model, but we are less sure of its exact location. In our model weights plot we shade all models that make up the top 95% of model weights. Therefore, we can be 95% confident that the true ‘best’ model falls within the shaded region. In our example using the Mass dataset, we can see that the top 95% of model weights falls within a small region roughly corresponding to the peak in delta AICc seen above. In fact, we can be 95% sure that the best climate window falls within only 7% of the total fitted models. This result suggests that our results are not produed by chance.
plotweights(dataset = MassOutput)
Plot model coefficients
While we are often interested in estimating the location of the best climate window, we may also be interested in understanding the relationship between climate and our biological response. The plotbeta function generates a similar colour plot to that used to model delta AICc, which shows the spread of model coefficients across all fitted climate windows. In the below plot, we can see that windows around our best model show a negative relationship between temperature and mass, while other models show little correlation.
plotbetas(dataset = MassOutput)
Delta AICc histograms
So far both our plots of delta AICc and model weights seem to suggest that there is a true period of climate sensitivity within our data. To better understand how likely it is that we would achieve such a result by chance we can also compare the outcomes of our climate window analysis with a similar analysis on randomised data (i.e. data with no climate signal). To generate this random data we can use the function randwin, which uses a similar syntax to that of climatewin. The additional parameter repeats determines the number of times that biological data should be randomised and analysed. We recommend using a minimum of 5 repeats for best results.
MassRand <- randwin(repeats = 5,
xvar = list(Temp = MassClimate$Temp),
cdate = MassClimate$Date,
bdate = Mass$Date,
baseline = lm(Mass ~ 1, data = Mass),
cinterval = "day",
furthest = 100, closest = 0,
type = "fixed", cutoff.day = 20, cutoff.month = 05,
stat = "mean",
func = "lin")Now we can compare the distribution of delta AICc values for our original climate window analysis and the same analysis on randomised data. If our climate window results are due to statistical chance we would expect to see a similar distribution of delta AICc values between both random and real data.
As we can see below, the distribution of delta AICc values in the real data (top histogram) has a much longer tail than that of the randomised data (bottom histogram). The dashed line on the plot represents the 99th quantile of the randomised data, therefore we can be confident that the large negative values of delta AICc we find in our real data are unlikely to occur by random chance.
plothist(dataset = MassOutput, datasetrand = MassRand)
Median window
To represent the model weight plot in a different way, plotwin shows boxplots of the start and end point of all climate windows that make up the top 95% of model weights. The values above each boxplot represent the median start and end time for these models.
In the below example, the median start and end values of the top models corresponds almost exactly with our best window determined using delta AICc. In situations where model weights are more dispersed such a match would be less likely.
plotwin(dataset = MassOutput)
Best model plot
Although the above plots give us strong confidence that our results represent a real period of climate sensitivity, we have not considered how well climate within this period actually explains variation in the biological data. Although temperature in March and April explains variation in mass better than at other points in time, temperature over this period may still not explain variation in the biological data that well.
Using the plotbest function, we can plot our best model over the biological data. Examining this plot can help us determine whether it may be more appropriate to test alternative relationships of climate (e.g. quadratic or cubic) by adjusting the parameter func.
While it is easy to save the Dataset output from the climatewin function, the BestModel object can often be lost when we start a new R session. To overcome this issue, the singlewin function allows you to generate BestModel and BestModelData for a single climate window.
MassSingle <- singlewin(xvar = list(Temp = MassClimate$Temp),
cdate = MassClimate$Date,
bdate = Mass$Date,
baseline = lm(Mass ~ 1, data = Mass),
cinterval = "day",
furthest = 72, closest = 15,
type = "fixed", cutoff.day = 20, cutoff.month = 05,
stat = "mean",
func = "lin")NOTE: In the singlewin function the values of furthest and closest now equate to the start and end time of the single window, rather than the range over which multiple windows will be tested.
We can use the output from the singlewin function to plot the best data.
plotbest(dataset = MassOutput,
bestmodel = MassSingle$BestModel,
bestmodeldata = MassSingle$BestModelData)
The plotall function
While each of these plots provides useful information for the user, they are best viewed in conjunction. The plotall function allows users to create an array of all 6 graphics to contrast and compare the different information they provide.
plotall(dataset = MassOutput,
datasetrand = MassRand,
bestmodel = MassSingle$BestModel,
bestmodeldata = MassSingle$BestModelData)