LSD.frame: Description of an LSD frame

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

Description of an LSD frame

Description

A data.frame that stores Least Significant differences (LSDs) for predictions for a fitted model.

Value

A data.frame that can be a component of an alldiffs.object and that contains LSD values and statistics to be used in determining the significance of the pairwise differences. In particular, they are used in calculating halfLeastSignificant limits to be included in a predictions.frame.

Exactly what an LSD.frame contains is determined by the following arguments to functions that return an alldiffs.object: LSDtype, LSDby, LSDstatistic, LSDaccuracy and LSDsupplied. The rownames of the LSD.frame indicate, for each of its rows, for what group of predictions the entries in the row were calculated, this being controlled by the LSDtype and LSDby arguments. The values for all of the LSD arguments are stored as attributes to the alldiffs.object and the predictions and, if present backtransforms, components of the alldiffs.object.

An LSD.frame always has the eight columns c, minimumLSD, meanLSD, maximumLSD, assignedLSD, accuracyLSD, falsePos and falseNeg.

1. c: This gives the number of pairwise comparison of predictions for the combinations of the factor levels given by the row name. If the row name is overall then it is for all predictions.

2. minimumLSD, meanLSD, maximumLSD: These are computed for either overall, factor.combinations, per.prediction or supplied LSD values, as specified by the LSDtype argument. The meanLSD is calculated using the square root of the mean of the variances of set of pairwise differences appropriate to the specific LSDtype argument.

   For overall, the mean, minimum and maximum of the LSDs for all pairwise comparisons are computed.

   If factor.combinations was specified for LSDtype when the LSDs were being calculated, then the LSD.frame contains a row for each combination of the values of the factors and numerics specified by LSDby. The values in a row are calculated from the LSD values for the pairwise differences for each combination of the factors and numerics values, unless there is only one prediction for a combination, when notional LSDs are calculated that are based on the standard error of the prediction multiplied by the square root of two.

   For per.prediction, the minimum, mean and maximum LSD, based, for each prediction, on the LSD values for all pairwise differences involving that prediction are computed.

   For supplied, the LSD.frame is set up based on the setting of LSDby: a single row with name overall if LSDby is NULL or, if LSDby is a vector of factor and numeric names, rows for each observed combinations of the values of the named factors and numerics. The LSDsupplied argument is used to provide the values to be stored in the column assignedLSD.

3. assignedLSD: The assignedLSD column contains the values that are assigned for use in calculating halfLeastSignificant error.intervals. Its contents are determined by LSDstatistic and LSDsupplied arguments. The LSDsupplied argument allows the direct specification of values to be placed in the assignedLSD column of the LSD.frame. The default is to use the values in the meanLSD column.

4. LSDaccuracy: The LSDaccuracy gives an indication of the proportion that the correct LSD for a single predicted.value might deviate from its assignedLSD value. The contents of the accuracyLSD column is controlled by the LSDaccuracy argument.

5. falsePos and falseNeg: These columns contain the number of false positives and negatives if the assignedLSD value(s) is(are) used to determine the significance of the pairwise predictions differences. Each LSD value in the assignedLSD column is used to determine the significance of pairwise differences that involve predictions for the combination of values given by the row name for the LSD value.

See recalcLSD.alldiffs for more information.

Author(s)

Chris Brien

See Also

recalcLSD.alldiffs, redoErrorIntervals.alldiffs, predictPresent.asreml,
predictPlus.asreml

Examples

  data(Oats.dat)
  
  ## Use asreml to get predictions and associated statistics

  ## Not run: 
  m1.asr <- asreml(Yield ~ Nitrogen*Variety, 
                   random=~Blocks/Wplots,
                   data=Oats.dat)
  current.asrt <- as.asrtests(m1.asr)
  Var.diffs <- predictPlus(m1.asr, classify="Nitrogen:Variety", 
                          wald.tab = current.asrt$wald.tab, 
                          tables = "none")
  
## End(Not run)
  
  ## 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)
    #Get predictions
    Var.emm <- emmeans::emmeans(m1.lmer, specs = ~ Nitrogen:Variety)
    Var.preds <- summary(Var.emm)
    ## 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

    #Set up an alldiffs object, which includes overall LSDs
    Var.diffs <- allDifferences(predictions = Var.preds, classify = "Variety:Nitrogen", 
                                     sed = Var.sed, vcov = Var.vcov, tdf = 45)
  }

  if (exists("Var.diffs"))
  {
    ## Use recalcLSD to get LSDs for within Variety differences
    Var.LSD.diffs <- recalcLSD(Var.diffs, 
                               LSDtype = "factor.combinations", LSDby = "Variety")
    print(Var.LSD.diffs$LSD)
  }

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