predictPlus.asreml: Forms the predictions for a term, their pairwise differences...

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

Forms the predictions for a term, their pairwise differences and associated statistics. A factor having parallel values may occur in the model and a linear transformation of the predictions can be specified. It results in an object of class alldifffs.

Description

This function forms the predictions for term using classify and the supplied asreml object and stores them in an alldiffs.object. If x.num is supplied, the predictions will be obtained for the values supplied in x.pred.values and, if supplied, x.plot.values will replace them in the alldiffs.object that is returned. If x.fac, but not x.num, is specified, predictions will involve it and, if supplied, x.plot.values will replace the levels of x.fac in the alldiffs.object that is returned. In order to get the correct predictions you may need to supply additional arguments to predict.asreml through ... e.g. present, parallel, levels. Any aliased predictions will be removed, as will any standard error of pairwise differences involving them.

Also calculated are the approximate degrees of freedom of the standard errors of the predictions. If the denominator degrees of freedom for term are available in wald.tab, they are used. Otherwise the residual degrees of freedom or the maximum of the denominator degrees in wald.tab, excluding the Intercept, are used. Which is used depends on the setting of dDF.na. These degrees of freedom are used for the t-distribution on which p-values and confidence intervals are based. It is stored as an attribute to the alldiffs.object. The degrees of freedom are also used in calculating the minimum, mean and maximum LSD for comparing pairs of predictions, which are also stored in the alldiffs.object.

If pairwise = TRUE, all pairwise differences between the predictions, their standard errors, p-values and LSD statistics are computed using allDifferences.data.frame. This adds them to the alldiffs.object as additional list components named differences, sed, p.differences and LSD.

If a linear transformation of the predictions is specified then the values of this linear transformation are returned, instead of the original predictions, along with their standard errors and the pairwise differences and associated statistics.

If a transformation has been applied in the analysis (any one of transform.power is not one, scale is not one and offset is nonzero), the backtransforms of the transformed values and their lower and upper error intervals are added to a data.frame that is consistent with the predictions data.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 'asreml'
predictPlus(asreml.obj, classify, term = NULL, 
            inestimable.rm = TRUE, 
            linear.transformation = NULL, EGLS.linTransform = TRUE, 
            error.intervals = "Confidence", alpha = 0.05, 
            wald.tab = NULL, dDF.na = "residual",  dDF.values = NULL, 
            pairwise = TRUE, Vmatrix = FALSE, 
            avsed.tolerance = 0.25, accuracy.threshold = NA, 
            LSDtype = "overall", LSDsupplied = NULL, LSDby = NULL, 
            LSDstatistic = "mean", LSDaccuracy = "maxAbsDeviation", 
            x.num = NULL, x.fac = NULL,  
            x.pred.values = NULL, x.plot.values = NULL, 
            titles = NULL,  tables = "all" , level.length = NA, 
            transform.power = 1, offset = 0, scale = 1, 
            transform.function = "identity", 
            sortFactor = NULL, sortParallelToCombo = NULL, 
            sortNestingFactor = NULL, sortOrder = NULL, 
            decreasing = FALSE, trace = FALSE, ...)

Arguments

asreml.obj	asreml object for a fitted model.
classify	A character string giving the variables that define the margins of the multiway table to be predicted. Multiway tables are specified by forming an interaction type term from the classifying variables, that is, separating the variable names with the : operator. To predict the overall mean, set the classify to "(Intercept)".
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.
inestimable.rm	A logical indicating whether rows for predictions that are not estimable are to be removed from the components of the alldiffs.object.
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. It might be a contrast matrix or a matrix of weights for a factor used to obtain the weighted average over that factor. 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.
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.
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.
wald.tab	A data.frame containing the pseudo-anova table for the fixed terms produced by a call to wald.asreml. The main use of it here is in determining the degrees of freedom for calculating confidence or half-LSD error.intervals and p-values, the latter to be stored in the p.differences component of the alldiffs.object that is created.
dDF.na	A character specifying the method to use to obtain approximate denominator degrees of freedom. when the numeric or algebraic methods produce an NA. Consistent with when no denDF are available, the default is "residual" and so the residual degrees of freedom from asreml.obj$nedf are used. If dDF.na = "none", no substitute denominator degrees of freedom are employed; if dDF.na = "maximum", the maximum of those denDF that are available, excluding that for the Intercept, is used; if all denDF are NA, asreml.obj$nedf is used. If dDF.na = "supplied", a vector of values for the denominator degrees of freedom is to be supplied in dDF.values. Any other setting is ignored and a warning message produced. Generally, substituting these degrees of freedom is anticonservative in that it is likely that the degrees of freedom used will be too large.
dDF.values	A vector of values to be used when dDF.na = "supplied". Its values will be used when denDF in a test for a fixed effect is NA. This vector must be the same length as the number of fixed terms, including (Intercept) whose value could be NA.
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.
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.
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. 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.
titles	A list, each component of which is named for a column in the data.frame for asreml.obj and contains a character string giving a title to use in output (e.g. tables and graphs). Here they will be used for table headings.
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.
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.
x.pred.values	The values of x.num for which predicted values are required. If levels is set for passing to predict.asreml, x.pred.values is ignored. Note that while levels is an alternative to x.pred.values, x.pred.values allows more general setting of the levels to be predicted.
x.plot.values	The actual values to be plotted on the x axis. They are needed when values different to those in x.num are to be plotted or x.fac is to be plotted because there is no x.num term corresponding to the same term with x.fac.
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.
transform.power	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 stored in the backtransforms component of the alldiffs.object. 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.
offset	A numeric that has been added to each value of the response after any scaling and before applying any power transformation.
scale	A numeric by which each value of the response has been multiplied before adding any offset and applying any power transformation.
transform.function	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.
sortFactor	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.
sortParallelToCombo	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.
sortNestingFactor	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.
sortOrder	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)].
decreasing	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.
trace	A logical that control output from ASReml-R. If TRUE then partial iteration details are displayed when ASReml-R functions are invoked; if FALSE then no output is displayed.
...	further arguments passed to predict.asreml.

Value

For linear.transformations set to NULL, an S3-class alldiffs.object with predictions and their standard errors and, depending on the settings of the arguments, all pairwise differences between predictions, their standard errors and p-values and LSD statistics. Also, unless the sortFactor or sortOrder arguments are invoked, 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. In addition, if necessary, the order of the columns of the variables in the predictions component are changed to match their order in the classify.

If transform.power or scale is not one or offset is not zero, it will contain a data.frame 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 name of the response, the response.title, the term, the classify, tdf, 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. 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.

For linear.transformations set to other than NULL, an alldiffs.object with the linear.transformation applied to the predictions and their standard errors and, depending on the settings of the arguments, all pairwise differences between the linearly transformed predictions, their standard errors and p-values and LSD statistics. (See also linTransform.alldiffs.)

Author(s)

Chris Brien

See Also

alldiffs.object, as.alldiffs, print.alldiffs, linTransform.alldiffs, sort.alldiffs,
subset.alldiffs, allDifferences.data.frame, redoErrorIntervals.alldiffs,
recalcLSD.alldiffs, exploreLSDs.alldiffs, pickLSDstatistics.alldiffs,
predictPresent.asreml, plotPredictions.data.frame, as.Date, predict.asreml

Examples

## Not run: 
data(WaterRunoff.dat)
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)
diffs <- predictPlus(classify = "Sources:Type", 
                     asreml.obj = current.asr, 
                     wald.tab = current.asrt$wald.tab, 
                     present = c("Sources", "Type", "Species"))

## End(Not run)

asremlPlus documentation built on Oct. 27, 2024, 5:06 p.m.