# Find LSD values that minimize the number of errors in pairwise comparisons of predictions. Given an `alldiffs.object` with an `sed` component, a search is made of a set of equally spaced values between the minimum and maximum values of the LSDs, calculated from the `sed` component of the `alldiffs.object`, to identify LSD values that minimize the number of errors made in deciding on the significance of pairs of predicted values stored in the `alldiffs.object`. If `LSDtype` is set to `overall`, a search is made over the range of LSD values for all pairwise comparisons for a single LSD value; if `LSDtype` is set to `factor.combinations`, a separate search is made over the LSD values for the set of pairwise comparisons for each `factor.combination` in order to identify a single value for each set. The number of values used in the search is controlled by the argument `nvalues`. For each value in the search, the numbers of false positives and false negatives resulting from employing it as the LSD for each set of pairwise comparisons is calculated. A criterion that combines the false positives and negative is calculated using the `false.pos.wt`, the criterion being the number of false postives times the `false.pos.wt` plus the number of false negatives. The value chosen for the LSD is the smallest value from amongst those with the minimum value of the criterion and the least number of false positives. A secondary search with 10 equally spaced values is made of the interval below the chosen value and the search value immediately below it to check whether the chosen grid value can be further reduced without changing the value of either its criterion or the number of false positives. The primary options for changing the numbers of errors associated with the values resulting from the searching is to manipulate the `LSDby` and/or `false.pos.wt` arguments. ```r ## S3 method for class 'alldiffs' findLSDminerrors(alldiffs.obj, LSDtype = "overall", LSDby = NULL, alpha = 0.05, false.pos.wt = 10, nvalues = 100, retain.zeroLSDs = FALSE, zero.tolerance = .Machine$double.eps ^ 0.5, trace = FALSE, ...) ``` ## Arguments - `alldiffs.obj`: An `alldiffs.object`. - `LSDtype`: A `character` string that can be `overall` or `factor.combinations`. It determines whether the minimum LSD values that are obtained are those for (i) all pairwise comparisons of the predicted values, or (ii) for each combination of the values of the `factors` and `numerics` named in `LSDby`, unless there is only one prediction for a combination, when notional LSDs are calculated. The `LSDtype` specified here does not have to match that used in the creating the `alldiffs.object`. - `LSDby`: A `character` (vector) of variables names, being the names of some of the `factors` or `numerics` in the `classify`; for each combination of the values of the `factors` and `numerics`, the LSD errors are to be computed when `LSDtype` is `factor.combinatons`. The `LSDby` specified here does not have to match that used in the creating the `alldiffs.object`. - `alpha`: A `numeric` specifying the significance level for an LSD to compare a pair of predictions. - `false.pos.wt`: A `numeric` that specifies the weight (e.g. 3 so that a false positive is considered to be equivalent to three false negatives) to apply to the number of false positives in calculating the weighted sums of the numbers of false positives and negatives that is used as the criterion to be minimized in selecting the LSD value that results in the minimum number of errors. If, for a particular LSD value, the number of false positives is **p**, the number of false negatives is **n** and **w** the value of `false.pos.wt`, then then criterion for that LSD value is $(w p) + n$. The default of 10 for `false.pos.wt` greatly favours false negatives; a value with one false positive and no false negative will only be chosen over a value with no false positive when the latter value has more than 10 false negatives. - `nvalues`: A `numeric` specifying the number of equally spaced LSD values, between the minimum and maximum LSD values for a set of paired comparisons, to be used in the search for the LSD value with the minimum number of errors. - `retain.zeroLSDs`: A `logical` indicating whether to retain or omit LSDs that are zero when calculating the numbers of errors. - `zero.tolerance`: A `numeric` specifying the value such that if an LSD is less than it, the LSD will be considered to be zero. - `trace`: A `logical` indicating whether details of the searching are to be output. - ``...``: Provision for passing arguments to functions called internally - not used at present. ## Returns A `data.frame` containing the chosen LSD(s), its(their) numbers of false positives and negatives and the value(s) of the false criterion. ## Author(s) Chris Brien ## See Also `asremlPlus-package`, `exploreLSDs.alldiffs` `plotLSDs.data.frame`, `plotLSDs.alldiffs`, `plotLSDerrors.alldiffs`, `plotLSDerrors.data.frame`, `recalcLSD.alldiffs`, `redoErrorIntervals.alldiffs` ## Examples ```r 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) TS.diffs <- predictPlus(classify = "Sources:Type", asreml.obj = current.asr, wald.tab = current.asrt$wald.tab, present = c("Sources", "Type", "Species")) ## End(Not run) ## Use lmeTest and emmmeans to get predictions and associated statistics if (requireNamespace("lmerTest", quietly = TRUE) & requireNamespace("emmeans", quietly = TRUE)) { m1.lmer <- lmerTest::lmer(pH ~ Benches + (Sources * (Type + Species)) + (1|Benches:MainPlots), data=na.omit(WaterRunoff.dat)) TS.emm <- emmeans::emmeans(m1.lmer, specs = ~ Sources:Type) TS.preds <- summary(TS.emm) den.df <- min(TS.preds$df, na.rm = TRUE) ## Modify TS.preds to be compatible with a predictions.frame TS.preds <- as.predictions.frame(TS.preds, predictions = "emmean", se = "SE", interval.type = "CI", interval.names = c("lower.CL", "upper.CL")) ## Form an all.diffs object and check its validity TS.vcov <- vcov(TS.emm) TS.diffs <- allDifferences(predictions = TS.preds, classify = "Sources:Type", vcov = TS.vcov, tdf = den.df) validAlldiffs(TS.diffs) } ## Choose LSD values with the minimum mumber of error for pairwise comparisons of ## the predictions obtained using asreml or lmerTest if (exists("TS.diffs")) { ##Pick the LSD values for predictions obtained using asreml or lmerTest minLSD <- findLSDminerrors(TS.diffs) TS.diffs <- redoErrorIntervals(TS.diffs, LSDtype = "supplied", LSDsupplied = minLSD["LSD"]) TS.diffs$LSD minLSDs <- findLSDminerrors(TS.diffs, LSDtype = "factor.combinations", LSDby = "Sources") TS.diffs <- redoErrorIntervals(TS.diffs, LSDtype = "supplied", LSDby = "Sources", LSDsupplied = minLSDs["LSD"]) TS.diffs$LSD } ```

findLSDminerrors.alldiffs function