alldiffs.object.Effects the linear transformation of the predictions in the
supplied alldiffs.object, the transformation being specified
by a matrix or a formula. The values of
the transformed values are stored in an alldiffs.object.
A matrix might be a contrast matrix or
a matrix of weights for the levels of a
factor used to obtain the weighted average over
the levels of that factor. A formula gives
rise to a projection matrix that linearly transforms
the predictions so that they conform to the model specified by the
formula, this model being a submodel of that inherent
in the classify.
If pairwise = TRUE, all pairwise differences between the
linear transforms of the predictions, their standard errors,
p-values and LSD statistics are computed as using
allDifferences.data.frame.
This adds them to the alldiffs.object as additional
list components named differences, sed,
p.differences and LSD.
If a transformation has been applied (any one of
transform.power is not one, scale is not one and
offset is nonzero), the backtransforms of the transformed
values and of the lower and upper limits of their error.intervals
are added to a data.frame that is consistent with a
predictions.frame. If transform.power is other than
one, the standard.error column of the data.frame
is set to NA. This data.frame is added to the
alldiffs.object as a list component called
backtransforms.
The printing of the components produced is controlled by the
tables argument. The order of plotting the levels of
one of the factors indexing the predictions can be modified
and is achieved using sort.alldiffs.
# S3 method for alldiffs
linTransform(alldiffs.obj, classify = NULL, term = NULL,
linear.transformation = NULL, EGLS.linTransform = TRUE,
Vmatrix = FALSE, error.intervals = "Confidence",
avsed.tolerance = 0.25, accuracy.threshold = NA,
LSDtype = "overall", LSDsupplied = NULL,
LSDby = NULL, LSDstatistic = "mean",
LSDaccuracy = "maxAbsDeviation",
zero.tolerance = .Machine$double.eps ^ 0.5,
response = NULL, response.title = NULL,
x.num = NULL, x.fac = NULL,
tables = "all", level.length = NA,
pairwise = TRUE, alpha = 0.05,
inestimable.rm = TRUE, ...)A alldiffs.object with the linear transformation of the predictions
and their standard errors and all pairwise differences between the linear
transforms of their predictions, their standard errors and p-values
and LSD statistics.
If the supplied alldiffs.object contained a backtransforms
component, then the returned alldiffs.object will contain
a backtransforms component with the backtransformed linear transformation
of the predictions. The backtransformation will, after backtransforming for any
power transformation, subtract the offset and then divide by the scale.
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 response.title,
the term, the classify, tdf, alpha, sortFactor
and the sortOrder 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.
An alldiffs.object.
A character string giving the variables that
define the margins of the multiway table corresponding to the
predictions in alldiffs.obj.
Multiway tables are specified by forming an interaction type
term from the classifying variables, that is, separating the
variable names with the : operator.
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.
A formula or a matrix.
If a formula is given then it is taken to be a submodel of
a model term corresponding to the classify. The projection matrix
that transforms the predictions so that they conform to the submodel
is obtained; the submodel does not have to involve variables in the
classify, but the variables must be columns in the predictions
component of alldiffs.obj and the space for the submodel must be a
subspace of the space for the term specified by the classify.
For example, for classify set to "A:B", the submodel
~ A + B will result in the predictions for the combinations of
A and B being made additive for the factors
A and B. The submodel space corresponding to A + B is
a subspace of the space A:B. In this case both the submodel and the
classify involve only the factors A and B. To fit an intercept-only
submodel, specify linear.transformation to be the formula ~1.
If a matrix is provided then it will be
used to apply the linear transformation to the predictions.
The number of rows in the matrix should equal the
number of linear combinations of the predictions desired and
the number of columns should equal the number of predictions.
In either case, as well as the values of the linear combinations, their standard errors, pairwise differences and associated statistics are returned.
A logical indicating whether or not the
linear.transformation of the predictions stored in an
alldiffs.object by fitting a submodel supplied in a
formula is to take into account the variance of the
predictions using a Estimated Generalized Least Squares (EGLS) approach.
This is likely to be appropriate when the variance matrix of the predictions
is not compound symmetric i.e. when not all the variances are equal or not
all the covariances are equal. If the variance matrix is compund symmetric,
then the setting of EGLS.linTransform will not affect the transformed
predictions.
A logical indicating whether the variance matrix of the
predictions will be stored as a component of the alldiffs.object
that is returned. If linear.transformation is set, it will
be stored irrespective of the value of Vmatrix.
A character string indicating the type of error interval, if any,
to calculate in order to indicate uncertainty in the results.
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.
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.
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.
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 numeric specifying the value such that if a predicted.value,
its variance-covariance, or an LSD is less than it, the LSD will be
considered to be zero.
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 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.
A character vector containing a combination of
none,
predictions, vcov, backtransforms, differences,
p.differences, sed, LSD and all.
These nominate which components of the alldiffs.object to print.
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 tables is equal to
"differences" or "all" or error.intervals is
equal to "halfLeastSignificant", they will be stored
irrespective of the value of pairwise.
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 logical indicating whether rows for predictions
that are not estimable are to be removed from the components of
the alldiffs.object.
further arguments passed to redoErrorIntervals.alldiffs.
Chris Brien
For a matrix \(\mathbf{L}\), vector of predictions \(\mathbf{p}\) and variance matrix of the predictions \(\mathbf{V}_p\), the linear transformed predictions are given by \(\mathbf{Lp}\) with variance matrix \(\mathbf{LV}_p\mathbf{L}^\mathrm{T}\). The last matrix is used to compute the variance of pairwise differences between the transformed values.
If linear.transformation is a matrix, \(\mathbf{M}\) say, then the
linear-transformation matrix, \(\mathbf{L}\), is just the supplied
matrix \(\mathbf{M}\).
If linear.transformation is a formula and EGLS.linTransform
is TRUE, then a matrix \(\mathbf{M}\) is obtained that is the design matrix
for all of the terms in the formula. Using \(\mathbf{M}\), the
linear-transformation matrix, \(\mathbf{L}\), is formed as
\(\mathbf{M} (\mathbf{M}^\top \widehat{\mathbf{V}}^- \mathbf{M})^- (\mathbf{M}^\top \widehat{\mathbf{V}}^-)\).
On the other hand, for linear.transformation a formula
and EGLS.linTransform set to FALSE, \(\mathbf{L}\) is
formed as the sum of the orthogonal projection matrices obtained using
pstructure.formula from the package dae; grandMean
is set to TRUE and orthogonalize to "eigenmethods".
linTransform, predictPlus.asreml, as.alldiffs,
print.alldiffs, sort.alldiffs,
subset.alldiffs, allDifferences.data.frame,
redoErrorIntervals.alldiffs,
recalcLSD.alldiffs, pickLSDstatistics.alldiffs,
predictPresent.asreml,
plotPredictions.data.frame,
as.Date, predict.asreml
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)
#Get additive predictions directly using predictPlus
diffs.sub <- predictPlus.asreml(classify = "Sources:Species", Vmatrix = TRUE,
linear.transformation = ~ Sources + Species,
asreml.obj = current.asr, tables = "none",
wald.tab = current.asrt$wald.tab,
present = c("Type","Species","Sources"))
}
## Use lmeTest and emmmeans to get predictions and associated statistics
if (requireNamespace("lmerTest", quietly = TRUE) &
requireNamespace("emmeans", quietly = TRUE))
{
m1.lmer <- lmerTest::lmer(pH ~ Benches + (Sources * Species) +
(1|Benches:MainPlots),
data=na.omit(WaterRunoff.dat))
SS.emm <- emmeans::emmeans(m1.lmer, specs = ~ Sources:Species)
SS.preds <- summary(SS.emm)
den.df <- min(SS.preds$df, na.rm = TRUE)
## Modify SS.preds to be compatible with a predictions.frame
SS.preds <- as.predictions.frame(SS.preds, predictions = "emmean",
se = "SE", interval.type = "CI",
interval.names = c("lower.CL", "upper.CL"))
## Form an all.diffs object and check its validity
SS.vcov <- vcov(SS.emm)
SS.diffs <- allDifferences(predictions = SS.preds, classify = "Sources:Species",
vcov = SS.vcov, tdf = den.df)
validAlldiffs(SS.diffs)
#Get additive predictions
diffs.sub <- linTransform(SS.diffs, classify = "Sources:Species",
linear.transformation = ~ Sources + Species,
Vmatrix = TRUE, tables = "none")
}
##Calculate contrasts from prediction obtained using asreml or lmerTest
if (exists("diffs.sub"))
{
#Contrast matrix for differences between each species and non-planted for the last source
L <- cbind(matrix(rep(0,7*32), nrow = 7, ncol = 32),
diag(1, nrow = 7),
matrix(rep(-1, 7), ncol = 1))
rownames(L) <- as.character(diffs.sub$predictions$Species[33:39])
diffs.L <- linTransform(diffs.sub,
classify = "Sources:Species",
linear.transformation = L,
tables = "predictions")
}
Run the code above in your browser using DataLab