Uses supplied predictions and standard errors of pairwise differences,
or the variance matrix of predictions to form, in an
alldiffs.object, for those components not already present,
(i) a table of all pairwise differences of the predictions,
(ii) the p-value of each pairwise difference, and
(iii) the minimum, mean, maximum and accuracy of LSD values.
Predictions that are aliased (or inestimable) are removed from the
predictions component of the alldiffs.object and
standard errors of differences involving them are removed from the sed
component.
If necessary, the order of the columns of the variables in the predictions
component are changed to be the initial columns of the predictions.frame
and to match their order in the classify. Also, the rows of predictions
component are ordered so that they are in standard order for the variables in the
classify. That is, the values of the last variable change with every row,
those of the second-last variable only change after all the values of the last
variable have been traversed; in general, the values of a variable are the same for
all the combinations of the values to the variables to its right in the
classify. The sortFactor or sortOrder arguments can be used
to order of the values for the classify variables, which is achieved using
sort.alldiffs.
Each p-value is computed as the probability of a t-statistic as large as or larger
than the absolute value of the observed difference divided by its standard error. The
p-values are stored in the p.differences component. The degrees of freedom of
the t-distribution is the degrees of freedom stored in the tdf attribute of
the alldiffs.object. This t-distribution is also used in calculating
the LSD statistics stored in the LSD component of the alldiffs.object.
# S3 method for data.frame
allDifferences(predictions, classify, vcov = NULL,
differences = NULL, p.differences = NULL, sed = NULL,
LSD = NULL, LSDtype = "overall", LSDsupplied = NULL,
LSDby = NULL, LSDstatistic = "mean",
LSDaccuracy = "maxAbsDeviation",
retain.zeroLSDs = FALSE,
zero.tolerance = .Machine$double.eps ^ 0.5,
backtransforms = NULL,
response = NULL, response.title = NULL,
term = NULL, tdf = NULL,
x.num = NULL, x.fac = NULL,
level.length = NA,
pairwise = TRUE, alpha = 0.05,
transform.power = 1, offset = 0, scale = 1,
transform.function = "identity",
inestimable.rm = TRUE,
sortFactor = NULL, sortParallelToCombo = NULL,
sortNestingFactor = NULL, sortOrder = NULL,
decreasing = FALSE, ...)An alldiffs.object with components
predictions, vcov, differences, p.differences
sed, and LSD.
The name of the response, the response.title,
the term, the classify, tdf, alpha, sortFactor
and the sortOrder will be set as attributes to the object.
Note that the classify in an alldiffs.object is based on the
variables indexing the predictions, which may differ from the
classify used to obtain the original predictions (for example,
when the alldiffs.objects stores a linear transformation of predictions.
Also, see predictPlus.asreml for more information.
A predictions.frame, or a data.frame, beginning
with the variables classifying the predictions and also containing columns
named predicted.value, standard.error and est.status;
each row contains a single predicted value. It may also contain columns
for the lower and upper limits of error intervals for the predictions.
Note that the names standard.error and
est.status have been changed to std.error and status
in the pvals component produced by asreml-R4; if the new names
are in the data.frame supplied to predictions, they will be
returned to the previous names.
A character string giving the variables that define the margins
of the multiway table that has been predicted. Multiway tables are
specified by forming an interaction type term from the
classifying variables, that is, separating the variable names
with the : operator.
A matrix containing the variance matrix of the predictions; it is used in
computing the variance of linear transformations of the predictions.
A matrix containing all pairwise differences between
the predictions; it should have the same number of rows and columns as there are
rows in predictions.
A matrix containing p-values for all pairwise differences
between the predictions; each p-value is computed as the probability of a t-statistic
as large as or larger than the observed difference divided by its standard error.
The degrees of freedom of the t distribution for computing it are computed as
the denominator degrees of freedom of the F value for the fixed term, if available;
otherwise, the degrees of freedom stored in the attribute tdf are used;
the matrix should be of the same size as that for differences.
A matrix containing the standard errors of all pairwise differences
between the predictions; they are used in computing the p-values.
An LSD.frame containing the mean, minimum and maximum LSD for determining
the significance of pairwise differences, as well as an assigned LSD and a measure
of the accuracy of the LSD. If LSD is NULL then the LSD.frame
stored in the LSD component will be calculated and
the values of LSDtype, LSDby and LSDstatistic added as attributes
of the alldiffs.object. The LSD for a single prediction
assumes that any predictions to be compared are independent; this is not the case if
residual errors are correlated.
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.
See LSD.frame for further information on the values in a row of this
data.frame and how they are calculated.
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.
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.
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.
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.
A logical indicating whether to retain or omit LSDs that are zero when
calculating the summaries of LSDs.
A numeric specifying the value such that if an LSD is less than it, the LSD will be
considered to be zero.
A data.frame containing the backtransformed values of the predicted
values that is consistent with the predictions component, except
that the column named predicted.value is replaced by one called
backtransformed.predictions. Any error.interval values will also
be the backtransformed values. Each row contains a single predicted value.
A character specifying the response variable for the
predictions. It is stored as an attribute to the alldiffs.object.
A character specifying the title for the response variable
for the predictions. It is stored as an attribute to the alldiffs.object.
A character string giving the variables that define the term
that was fitted using asreml and that corresponds to classify.
It only needs to be specified when it is different to classify; it
is stored as an attribute of the alldiffs.object.
It is likely to be needed when the fitted model includes terms that involve
both a numeric covariate and a factor that
parallel each other; the classify would include the covariate and
the term would include the factor.
an integer specifying the degrees of freedom of the standard error. It is used as
the degrees of freedom for the t-distribution on which p-values and confidence
intervals are based.
It is stored as an attribute to the alldiffs.object.
A character string giving the name of the numeric covariate that
(i) is potentially included in terms in the fitted model and (ii) is the
x-axis variable for plots. Its values will not be converted to a factor.
A character string giving the name of the factor that
(i) corresponds to x.num and (ii) is potentially included in
terms in the fitted model. It should have the same number of levels as the
number of unique values in x.num. The levels of
x.fac must be in the order in which they are to be plotted
- if they are dates, then they should be in the form
yyyymmdd, which can be achieved using as.Date. However, the levels
can be non-numeric in nature, provided that x.num is also set.
The maximum number of characters from the levels of factors to use in the row and column labels of the tables of pairwise differences and their p-values and standard errors.
A logical indicating whether all pairwise differences of the
predictions and their standard errors and p-values are to be
computed and stored. If FALSE, the components differences
and p.differences will be NULL in the returned
alldiffs.object.
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.
A numeric specifying the power of a transformation, if
one has been applied to the response variable. Unless it is equal
to 1, the default, back-transforms of the predictions will be
obtained and presented in tables or graphs as appropriate.
The back-transformation raises the predictions to the power equal
to the reciprocal of transform.power, unless it equals 0 in
which case the exponential of the predictions is taken.
A numeric that has been added to each value of the
response after any scaling and before applying any power transformation.
A numeric by which each value of the response has been multiplied
before adding any offset and applying any power transformation.
A character giving the name of a function that
specifies the scale on which the predicted values are defined. This may be the
result of a transformation of the data using the function or the use of the
function as a link function in the fitting of a generalized linear (mixed)
model (GL(M)M). The possible transform.functions are
identity, log, inverse, sqrt, logit,
probit, and cloglog. The predicted.values and
error.intervals, if not StandardError intervals, will be
back-transformed using the inverse function of the transform.function.
The standard.error column will be set to NA, unless (i)
asreml returns columns named transformed.value and
approx.se, as well as those called predicted.values and
standard.error (such as when a GLM is fitted) and
(ii) the values in transformed.value are equal to those obtained by
backtransforming the predicted.values using the inverse function
of the transform.function. Then, the approx.se values will be
saved in the standard.error column of the backtransforms
component of the returned alldiffs.obj. Also, the
transformed.value and approx.se columns are removed from both
the predictions and backtransforms components of the
alldiffs.obj. Note that the values that end up in the standard errors
column are approximate for the backtransformed values and are not used in
calculating error.intervals.
A logical indicating whether rows for predictions that
are not estimable are to be removed from the components of the
alldiffs.object.
A character containing the name of the
factor that indexes the set of predicted values that determines
the sorting of the components. If there is only one variable in the
classify term then sortFactor can be NULL and
the order is defined by the complete set of predicted values.
If there is more than one variable in the classify term
then sortFactor must be set. In this case the sortFactor
is sorted in the same order within each combination of the values of
the sortParallelToCombo variables: the classify variables, excluding the
sortFactor. There should be only one predicted value for
each unique value of sortFactor within each set defined by a
combination of the values of the classify variables, excluding the
sortFactor factor.
The order to use is determined by either sortParallelToCombo or
sortOrder.
A list that specifies a combination of the values
of the factors and numerics, excluding sortFactor, that
are in classify. Each of the components of the supplied list
is named for a classify variable and specifies a single value for it. The
combination of this set of values will be used to define a subset of the predicted
values whose order will define the order of sortFactor. Each of the other
combinations of the values of the factors and numerics will be sorted
in parallel. If sortParallelToCombo is NULL then the first value of
each classify variable, except for the sortFactor factor,
in the predictions component is used to define sortParallelToCombo.
If there is only one variable in the classify then
sortParallelToCombo is ignored.
A character containing the name of the
factor that defines groups of the sortFactor within which the predicted
values are to be ordered.
If there is only one variable in the classify then
sortNestingFactor is ignored.
A character vector whose length is the same as the number
of levels for sortFactor in the predictions component of the
alldiffs.object. It specifies the desired order of the
levels in the reordered components of the alldiffs.object.
The argument sortParallelToCombo is ignored.
The following creates a sortOrder vector levs for factor
f based on the values in x:
levs <- levels(f)[order(x)].
A logical passed to order that detemines whether
the order for sorting the components of the alldiffs.object
is for increasing or decreasing magnitude of the predicted values.
provision for passsing arguments to functions called internally - not used at present.
Chris Brien
asremlPlus-package, as.alldiffs, as.predictions.frame,
sort.alldiffs, subset.alldiffs,
print.alldiffs, renewClassify.alldiffs,
redoErrorIntervals.alldiffs,
recalcLSD.alldiffs, pickLSDstatistics.alldiffs,
plotPredictions.data.frame,
predictPlus.asreml, predictPresent.asreml
data(Oats.dat)
## Use asreml to get predictions and associated statistics
if (FALSE) {
m1.asr <- asreml(Yield ~ Nitrogen*Variety,
random=~Blocks/Wplots,
data=Oats.dat)
current.asrt <- as.asrtests(m1.asr)
Var.pred <- asreml::predict.asreml(m1.asr, classify="Nitrogen:Variety",
sed=TRUE)
if (getASRemlVersionLoaded(nchar = 1) == "3")
Var.pred <- Var.pred$predictions
Var.preds <- Var.pred$pvals
Var.sed <- Var.pred$sed
Var.vcov <- NULL
wald.tab <- current.asrt$wald.tab
den.df <- wald.tab[match("Variety", rownames(wald.tab)), "denDF"]
}
## Use lmerTest and emmmeans to get predictions and associated statistics
if (requireNamespace("lmerTest", quietly = TRUE) &
requireNamespace("emmeans", quietly = TRUE))
{
m1.lmer <- lmerTest::lmer(Yield ~ Nitrogen*Variety + (1|Blocks/Wplots),
data=Oats.dat)
Var.emm <- emmeans::emmeans(m1.lmer, specs = ~ Nitrogen:Variety)
Var.preds <- summary(Var.emm)
den.df <- min(Var.preds$df)
## Modify Var.preds to be compatible with a predictions.frame
Var.preds <- as.predictions.frame(Var.preds, predictions = "emmean",
se = "SE", interval.type = "CI",
interval.names = c("lower.CL", "upper.CL"))
Var.vcov <- vcov(Var.emm)
Var.sed <- NULL
}
## Use the predictions obtained with either asreml or lmerTest
if (exists("Var.preds"))
{
## Order the Varieties in decreasing order for the predictions values in the
## first N level
Var.diffs <- allDifferences(predictions = Var.preds,
classify = "Nitrogen:Variety",
sed = Var.sed, vcov = Var.vcov, tdf = den.df,
sortFactor = "Variety", decreasing = TRUE)
print.alldiffs(Var.diffs, which="differences")
## Change the order of the factors in the alldiffs object and reorder components
Var.reord.diffs <- allDifferences(predictions = Var.preds,
classify = "Variety:Nitrogen",
sed = Var.sed, vcov = Var.vcov, tdf = den.df)
print.alldiffs(Var.reord.diffs, which="predictions")
}
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