redoErrorIntervals.alldiffs: Adds or replaces the error intervals stored in a prediction component of an `alldiffs.object`.

Description

Given an alldiffs.object, adds or replaces error.intervals for its prediction component. If the backtransforms component is present, the transform.power, offset and scale will be retrieved from the backtransforms attributes, ignoring the values for the function's arguments, and the backtransformed error.intervals will also be calculated.

Usage

# S3 method for alldiffs
redoErrorIntervals(alldiffs.obj, error.intervals = "Confidence", 
                   alpha = 0.05, 
                   avsed.tolerance = 0.25, accuracy.threshold = NA,
                   LSDtype = NULL, LSDsupplied = NULL, 
                   LSDby = NULL, LSDstatistic = "mean", 
                   LSDaccuracy = "maxAbsDeviation", 
                   retain.zeroLSDs = FALSE, 
                   zero.tolerance = .Machine$double.eps ^ 0.5, ...)

Value

An alldiffs.object with components

predictions, vcov, differences, p.differences

sed, LSD and, if present in alldiffs.obj, backtransforms.

If error.intervals is not "none", then the

predictions component and, if present, the

backtransforms component will contain columns for the lower and upper values of the limits for the interval. The names of these columns will consist of three parts separated by full stops: 1) the first part will be lower or upper; 2) the second part will be one of Confidence,

StandardError or halfLeastSignificant; 3) the third component will be limits.

The name of the response, the term, the classify and

tdf, as well as the degrees of freedom of the standard error, will be set as attributes to the object. Also, if error.intervals is "halfLeastSignificant", then those of

LSDtype, LSDby and LSDstatistic that are not NULL

will be added as attributes of the object and of the predictions frame; additionally, LSDvalues will be added as attribute of the

predictions frame, LSDvalues being the LSD values used in calculating the error.intervals.

Arguments

alldiffs.obj

An alldiffs.object.

error.intervals

A character string indicating the type of error interval, if any, to calculate in order to indicate uncertainty in the predicted values. Possible values are "none", "StandardError", "Confidence" and "halfLeastSignificant". The default is for confidence limits to be used. The "halfLeastSignificant" option results in half the Least Significant Difference (LSD) being added and subtracted to the predictions, the LSD being calculated using the square root of the mean of the variances of all or a subset of pairwise differences between the predictions. If the LSD is zero, as can happen when predictions are constrained to be equal, then the limits of the error intervals are set to NA. If LSDtype is set to overall, the avsed.tolerance is not NA and the range of the SEDs divided by the average of the SEDs exceeds avsed.tolerance then the error.intervals calculations and the plotting will revert to confidence intervals.

alpha

A numeric giving the significance level for LSDs or one minus the confidence level for confidence intervals. It is stored as an attribute to the alldiffs.object.

avsed.tolerance

A numeric giving the value of the SED range, the range of the SEDs divided by the square root of the mean of the variances of all or a subset of the pairwise differences, that is considered reasonable in calculating error.intervals. To have it ignored, set it to NA. It should be a value between 0 and 1. The following rules apply:

If avsed.tolerance is NA then mean LSDs of the type specified by LSDtype are calculated and used in error.intervals and plots.
Irrespective of the setting of LSDtype, if avsed.tolerance is not exceeded then the mean LSDs are used in error.intervals and plots.
If LSDtype is set to overall, avsed.tolerance is not NA, and avsed.tolerance is exceeded then error.intervals and plotting revert to confidence intervals.
If LSDtype is set to factor.combinations and avsed.tolerance is not exceeded for any factor combination then the half LSDs are used in error.intervals and plots; otherwise, error.intervals and plotting revert to confidence intervals.
If LSDtype is set to per.prediction and avsed.tolerance is not exceeded for any prediction then the half LSDs are used in error.intervals and plots; otherwise, error.intervals and plotting revert to confidence intervals.

accuracy.threshold

A numeric specifying the value of the LSD accuracy measure, which measure is specified by LSDaccuracy, as a threshold value in determining whether the hallfLeastSignificant error.interval for a predicted value is a reasonable approximation; this will be the case if the LSDs across all pairwise comparisons for which the interval's LSD was computed, as specified by LSDtype and LSDby, are similar enough to the interval's LSD, as measured by LSDaccuracy. If it is NA, it will be ignored. If it is not NA, a column of logicals named LSDwarning will be added to the predictions component of the alldiffs.object. The value of LSDwarning for a predicted.value will be TRUE if the value of the LSDaccuracy measure computed from the LSDs for differences between this predicted.value and the other predicted.values as compared to its assignedLSD exceeds the value of accuracy.threshold. Otherwise, the value of LSDwarning for a predicted.value will be FALSE.

LSDtype

A character string that can be overall, factor.combinations, per.prediction or supplied. It determines whether the values stored in a row of a LSD.frame are the values calculated (i) overall from the LSD values for all pairwise comparison2, (ii) the values calculated from the pairwise LSDs for the levels of each factor.combination, unless there is only one prediction for a level of the factor.combination, when a notional LSD is calculated, (iii) per.prediction, being based, for each prediction, on all pairwise differences involving that prediction, or (iv) as supplied values of the LSD, specified with the LSDsupplied argument; these supplied values are to be placed in the assignedLSD column of the LSD.frame stored in an alldiffs.object so that they can be used in LSD calculations.

If LSDtype is NULL (the default), the LSDtype attribute of the alldiffs.obj will be used; it is also NULL, then the LSDtype will be set to overall.

See LSD.frame for further information on the values in a row of this data.frame and how they are calculated.

LSDsupplied

A data.frame or a named numeric containing a set of LSD values that correspond to the observed combinations of the values of the LSDby variables in the predictions.frame or a single LSD value that is an overall LSD. If a data.frame, it may have (i) a column for the LSDby variable and a column of LSD values or (ii) a single column of LSD values with rownames being the combinations of the observed values of the LSDby variables. Any name can be used for the column of LSD values; assignedLSD is sensible, but not obligatory. Otherwise, a numeric containing the LSD values, each of which is named for the observed combination of the values of the LSDby variables to which it corresponds. (Applying the function dae::fac.combine to the predictions component is one way of forming the required combinations for the (row) names.) The values supplied will be incorporated into assignedLSD column of the LSD.frame stored as the LSD component of the alldiffs.object.

LSDby

A character (vector) of variables names, being the names of the factors or numerics in the classify; for each combination of their levels and values, there will be or is a row in the LSD.frame stored in the LSD component of the alldiffs.object when LSDtype is factor.combinatons.

LSDstatistic

A character nominating one or more of minimum, q10, q25, mean, median, q75, q90 or maximum as the value(s) to be stored in the assignedLSD column in an LSD.frame; the values in the assignedLSD column are used in computing halfLeastSignificant error.intervals. Here q10, q25, q75 and q90 indicate the sample quantiles corresponding to probabilities of 0.1, 0.25, 0.75 and 0.9 for the group of LSDs from which a single LSD value is calculated. The function quantile is used to obtain them. The mean LSD is calculated as the square root of the mean of the squares of the LSDs for the group. The median is calculated using the median function. Multiple values are only produced for LSDtype set to factor.combination, in which case LSDby must not be NULL and the number of values must equal the number of observed combinations of the values of the variables specified by LSDby. If LSDstatistic is NULL, it is reset to mean.

LSDaccuracy

A character nominating one of maxAbsDeviation, maxDeviation, q90Deviation or RootMeanSqDeviation as the statistic to be calculated as a measure of the accuracy of assignedLSD. The option q90Deviation produces the sample quantile corresponding to a probability of 0.90. The deviations are the differences between the LSDs used in calculating the LSD statistics and each assigned LSD and the accuracy is expressed as a proportion of the assigned LSD value. The calculated values are stored in the column named accuracyLSD in an LSD.frame.

retain.zeroLSDs

A logical indicating whether to retain or omit LSDs that are zero when calculating the summaries of LSDs.

zero.tolerance

A numeric specifying the value such that if an LSD is less than it, the LSD will be considered to be zero.

...

further arguments passed to recalcLSD.alldiffs.

Author

Chris Brien

Examples

Run this code

data(WaterRunoff.dat)

##Use asreml to get predictions and associated statistics

if (FALSE) {
asreml.options(keep.order = TRUE) #required for asreml-R4 only
current.asr <- asreml(fixed = pH ~ Benches + (Sources * (Type + Species)), 
                      random = ~ Benches:MainPlots,
                      keep.order=TRUE, data= WaterRunoff.dat)
current.asrt <- as.asrtests(current.asr, NULL, NULL)
TS.diffs <- predictPlus(classify = "Sources:Type", 
                        asreml.obj = current.asr, 
                        wald.tab = current.asrt$wald.tab, 
                        present = c("Sources", "Type", "Species"))
}

## Use lmeTest and emmmeans to get predictions and associated statistics

if (requireNamespace("lmerTest", quietly = TRUE) & 
    requireNamespace("emmeans", quietly = TRUE))
{
  m1.lmer <- lmerTest::lmer(pH ~ Benches + (Sources * (Type + Species)) + 
                              (1|Benches:MainPlots),
                            data=na.omit(WaterRunoff.dat))
  TS.emm <- emmeans::emmeans(m1.lmer, specs = ~ Sources:Species)
  TS.preds <- summary(TS.emm)
  den.df <- min(TS.preds$df, na.rm = TRUE)
  ## Modify TS.preds to be compatible with a predictions.frame
  TS.preds <- as.predictions.frame(TS.preds, predictions = "emmean", 
                                   se = "SE", interval.type = "CI", 
                                   interval.names = c("lower.CL", "upper.CL"))
  
  ## Form an all.diffs object and check its validity
  TS.vcov <- vcov(TS.emm)
  TS.diffs <- allDifferences(predictions = TS.preds, 
                             classify = "Sources:Species", 
                             vcov = TS.vcov, tdf = den.df)
  validAlldiffs(TS.diffs)
}  

## Plot p-values for predictions obtained using asreml or lmerTest
if (exists("TS.diffs"))
{
  ##Recalculate the LSD values for predictions obtained using asreml or lmerTest  
  TS.diffs <- redoErrorIntervals.alldiffs(TS.diffs, 
                                          error.intervals = "halfLeastSignificant")

}