Prediction for double-constrained correspondence analysis (dc-CA)

Prediction of traits from environment, environment from traits and response from trait and environment data.

Usage

# S3 method for class 'dcca'
predict(
  object,
  ...,
  type = c("envFromTraits", "traitsFromEnv", "response", "SNC", "CWM", "lc", "lc_traits"),
  rank = "full",
  newdata = NULL,
  weights = NULL,
  scaling = "symmetric"
)

Arguments

object: return value of dc_CA.
...: Other arguments passed to the function (currently ignored).
type: type of prediction, c("envFromTraits", "traitsFromEnv", "response", "lc", "lc_traits") for environmental values, values of traits, response (expected abundance) and constrained scores for sites and species. "SNC" is equivalent with "envFromTraits". "CWM" is equivalent with "traitsFromEnv".
rank: rank (number of axes to use). Default "full" for all axes (no rank-reduction).
newdata: Data in which to look for variables with which to predict. For type = "envFromTraits" or "traitsFromEnv" or type = "lc_traits" or "lc", newdata is a data frame of trait and environmental values, respectively, which are used for the prediction or the calculation of scores. If omitted, fitted values are generated (use fitted.dcca instead). For type = "response", newdata is a list of two data frames with trait and environmental values in this order, e.g. list(traits = dataTraits, env = dataEnv).
weights: list of weights of species and of sites in newdata when type = "response", else ignored (default NULL yielding equal species and site weights, both summing to 1). Example: weights = list(species = c(100, 1, 1), sites = c(1, 1, 1, 1)), in that order, with traits of three new species in newdata[[1]] and environmental values (and levels of factors) of four new sites in newdata[[2]]. Species weights are scaled to a sum of one.
scaling: numeric (1,2 or 3) or character "sites", "species" or "symmetric". Default: "symmetric". Either site- (1) or species- (2) related scores are scaled by eigenvalues, and the other set of scores have unit weighted mean square or with 3 both are scaled symmetrically to weighted mean squares equal to the square root of eigenvalues. Negative values are treated as the corresponding positive ones by abs(scaling).

Value

a matrix with the predictions. The exact content of the matrix depends on the type of predictions that are being made.

Details

Variables that are in the model but not in newdata are set to their weighted means in the training data. Predictions are thus at the (weighted) mean of the quantitative variables not included. Predictions with not-included factors are at the reference level (the first level of the factor).

For type = "response", many of the predicted values may be negative, indicating expected absences (0) or small expected response values.

With type = "traitsFromEnv" and newdata = NULL, predict gives the fitted mean traits, i.e. the fitted community weighted means. With type = "envFromTraits" and newdata = NULL, predict gives the fitted mean environment, i.e. the fitted species niche centroids (see fitted.dcca). See fitted.dcca.

Examples

data("dune_trait_env")

# rownames are carried forward in results
rownames(dune_trait_env$comm) <- dune_trait_env$comm$Sites

mod <- dc_CA(formulaEnv = ~ A1 + Moist + Mag + Use + Condition(Manure),
             formulaTraits = ~ SLA + Height + LDMC + Condition(Seedmass) + Lifespan,
             response = dune_trait_env$comm[, -1],  # must delete "Sites"
             dataEnv = dune_trait_env$envir,
             dataTraits = dune_trait_env$traits,
             verbose = FALSE)

# Ten 'new' sites with a subset of the variables in mod 
# X_lot will be ignored as it is not part of the model
newEnv <- dune_trait_env$envir[1:10, c("A1", "Mag", "Manure", "X_lot")]
newEnv[2,"A1"] <- 3.0
rownames(newEnv) <- paste0("NewSite", 1:10)

pred.traits <- predict(mod, type = "traitsFromEnv", newdata = newEnv)
#> Warning: newdata does not contain the predictor variables
#>  Moist,Use
#> These are set at their mean values and,
#> for factors, at the reference level
#> The current formula is
#>  ~ Manure + A1 + Moist + Mag + Use
head(pred.traits)
#>               SLA   Height     LDMC Lifespanannual Lifespanperennial
#> NewSite1 23.49280 26.38356 266.8780   0.0420223885         0.9579776
#> NewSite2 25.31359 25.43822 255.1297  -0.0008408709         1.0008409
#> NewSite3 23.72696 27.51990 262.5873   0.0250113500         0.9749886
#> NewSite4 23.71135 27.44414 262.8733   0.0261454193         0.9738546
#> NewSite5 25.23184 27.30383 229.8117   0.0211790573         0.9788209
#> NewSite6 24.91963 25.78871 235.5326   0.0438604419         0.9561396


# Eight 'new' species with a subset of traits that are included in the model 
# Variable "L" will be ignored as it is not in the model 
newTraits <- dune_trait_env$traits[1:8, c("Species", "SLA", "LDMC", "L")]
newTraits[3,"SLA"]<- 18 
rownames(newTraits) <- paste("Species",LETTERS[1:8] )# or another meaningful name.

pred.env <- predict(mod, type = "envFromTraits", newdata = newTraits)
#> Warning: newdata does not contain the predictor variables
#>  Height,Lifespan,Seedmass
#> These are set at their mean values and,
#> for factors, at the reference level
#> The current formula is
#>  ~ Seedmass + SLA + Height + LDMC + Lifespan
head(pred.env)
#>                 A1    Moist     MagSF     MagBF     MagHF     MagNM      Use
#> Species A 4.418925 3.099357 0.4193545 0.1162310 0.2567447 0.2076698 1.792234
#> Species B 3.655381 2.386016 0.4099394 0.1990894 0.2308547 0.1601165 1.487752
#> Species C 3.932918 2.921976 0.4313648 0.1056551 0.2053991 0.2575811 1.618013
#> Species D 3.891226 2.356745 0.3966054 0.2306193 0.2703075 0.1024678 1.564131
#> Species E 3.133064 2.374767 0.4345196 0.1466711 0.1530670 0.2657424 1.313215
#> Species F 4.117969 2.529417 0.3968530 0.2149759 0.2829311 0.1052401 1.651777


pred.resp <- predict(mod, type = "response", newdata = list(newTraits, newEnv),
                     weights = list(species = rep(1:2, 4), sites = rep(1, 10)))
#> Warning: newdata does not contain the predictor variables
#>  Height,Lifespan,Seedmass
#> These are set at their mean values and,
#> for factors, at the reference level
#> The current formula is
#>  ~ Seedmass + SLA + Height + LDMC + Lifespan
#> Warning: newdata does not contain the predictor variables
#>  Moist,Use
#> These are set at their mean values and,
#> for factors, at the reference level
#> The current formula is
#>  ~ Manure + A1 + Moist + Mag + Use
colSums(pred.resp) # about alternating 0.8 and 1.6 (reflecting the new species weights)
#> Species A Species B Species C Species D Species E Species F Species G Species H 
#> 0.6754447 1.4335014 0.7063500 1.3996597 0.7529561 1.3738211 0.7113281 1.3499565 
rowSums(pred.resp) # about equal rowsums
#>   NewSite1   NewSite2   NewSite3   NewSite4   NewSite5   NewSite6   NewSite7 
#>  0.9528552  0.1295043  0.5920024  0.6160593  0.7202928  1.2014298  0.1325513 
#>   NewSite8   NewSite9  NewSite10 
#> -0.2042446  2.7755022  1.4870650