DHARMa (version 0.3.3.0)

testTemporalAutocorrelation: Test for temporal autocorrelation

Description

This function performs a standard test for temporal autocorrelation on the simulated residuals

Usage

testTemporalAutocorrelation(simulationOutput, time = NULL,
  alternative = c("two.sided", "greater", "less"), plot = T)

Arguments

simulationOutput

an object with simulated residuals created by simulateResiduals

time

the time, in the same order as the data points. If not provided, random values will be created

alternative

a character string specifying whether the test should test if observations are "greater", "less" or "two.sided" compared to the simulated null hypothesis

plot

whether to plot output

Details

The function performs a Durbin-Watson test on the uniformly scaled residuals, and plots the residuals against time. The DB test was originally be designed for normal residuals. In simulations, I didn't see a problem with this setting though. The alternative is to transform the uniform residuals to normal residuals and perform the DB test on those.

If no time values are provided, random values will be created. The sense of being able to run the test with time = NULL (random values) is to test the rate of false positives under the current residual structure (random time corresponds to H0: no spatial autocorrelation), e.g. to check if the test has noninal error rates for particular residual structures (note that Durbin-Watson originally assumes normal residuals, error rates seem correct for uniform residuals, but may not be correct if there are still other residual problems).

Testing for temporal autocorrelation requires unique time values - if you have several observations per time value, either use the recalculateResiduals function to aggregate residuals per time step, or extract the residuals from the fitted object, and plot / test each of them independently for temporally repeated subgroups (typical choices would be location / subject etc.). Note that the latter must be done by hand, outside testSpatialAutocorrelation.

See Also

testResiduals, testUniformity, testOutliers, testDispersion, testZeroInflation, testGeneric, testSpatialAutocorrelation, testQuantiles

Examples

# NOT RUN {
testData = createData(sampleSize = 40, family = gaussian())
fittedModel <- lm(observedResponse ~ Environment1, data = testData)
res = simulateResiduals(fittedModel)

# Standard use
testTemporalAutocorrelation(res, time =  testData$time)

# If no time is provided, random values will be created
testTemporalAutocorrelation(res)

# If you have several observations per time step

timeSeries1 = createData(sampleSize = 40, family = gaussian())
timeSeries1$location = 1
timeSeries2 = createData(sampleSize = 40, family = gaussian())
timeSeries2$location = 2
testData = rbind(timeSeries1, timeSeries2)

fittedModel <- lm(observedResponse ~ Environment1, data = testData)
res = simulateResiduals(fittedModel)

# for this, you cannot do testTemporalAutocorrelation(res, time = testData$time)
# because here we would have observations with the same time, i.e. 
# zero difference in time. We have two options a) aggregate observations
# b) calculate / test per subset. Testing per subset might also be useful
# if you have several locations, regardless of whether the times are 
# identical, because you would expect the autocorrelation structure to be 
# independent per location

# testing grouped residuals 

res = recalculateResiduals(res, group = testData$time)
testTemporalAutocorrelation(res, time = unique(testData$time))

# plotting and testing per subgroup

# extract subgroup
testData$Residuals = res$scaledResiduals
temp = testData[testData$location == 1,]

# plots and tests
plot(Residuals ~ time, data = temp)
lmtest::dwtest(temp$Residuals ~ 1, order.by = temp$time)

# }