linTransform.alldiffs: Calculates a linear transformation of the predictions stored...

In asremlPlus: Augments 'ASReml-R' in Fitting Mixed Models and Packages Generally in Exploring Prediction Differences

Calculates a linear transformation of the predictions stored in an alldiffs.object.

Description

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.

Usage

## S3 method for class '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, ...)

Arguments

alldiffs.obj	An alldiffs.object.
classify	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.
term	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.
linear.transformation	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.
EGLS.linTransform	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.
Vmatrix	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.
error.intervals	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.
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 comparisons, unless there is only one, possibly repeated, prediction, when a notional LSD is calculated, (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.
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.
zero.tolerance	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.
response	A character specifying the response variable for the predictions. It is stored as an attribute to the alldiffs.object .
response.title	A character specifying the title for the response variable for the predictions. It is stored as an attribute to the alldiffs.object.
x.num	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.
x.fac	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.
tables	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.
level.length	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.
pairwise	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.
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.
inestimable.rm	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.

Details

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".

Value

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.

Author(s)

Chris Brien

See Also

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

Examples

data(WaterRunoff.dat)

##Use asreml to get predictions and associated statistics

## Not run: 
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"))

## End(Not run)

## 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")
}

asremlPlus documentation built on Nov. 7, 2025, 5:07 p.m.