Generate predicted values for SEM direct, indirect, or total effects.
predEff( mod, newdata = NULL, effects = NULL, eff.boot = NULL, re.form = NA, type = c("link", "response"), interaction = NULL, use.raw = FALSE, ci.conf = 0.95, ci.type = "bca", digits = 3, bci.arg = NULL, parallel = "no", ncpus = NULL, cl = NULL, ... )
A fitted model object, or a list or nested list of such objects.
An optional data frame of new values to predict, which should
contain all the variables named in
A numeric vector of effects to predict, or a list or nested
list of such vectors. These will typically have been calculated using
For mixed models of class
The type of prediction to return (for GLMs). Can be either
An optional name of an interactive effect, for which to return standardised effects for a 'main' continuous variable across different values or levels of interacting variables (see Details).
Logical, whether to use raw (unstandardised) effects for all calculations (if present).
A numeric value specifying the confidence level for confidence intervals on predictions (and any interactive effects).
The type of confidence interval to return (defaults to
The number of significant digits to return for interactive effects.
A named list of any additional arguments to
The type of parallel processing to use for calculating
confidence intervals on predictions. Can be one of
Number of system cores to use for parallel processing. If
Optional cluster to use if
A numeric vector of the predictions, or, if bootstrapped effects are
supplied, a list containing the predictions and the upper and lower
confidence intervals. Optional interactive effects may also be appended.
Predictions may also be returned in a list or nested list, depending on the
mod (and other arguments).
Generate predicted values for SEM direct, indirect, or total effects
on a response variable, which should be supplied to
effects. These are
used in place of model coefficients in the standard prediction formula,
with values for predictors drawn either from the data used to fit the
original model(s) (
mod) or from
newdata. It is assumed that effects are
fully standardised; however, if this is not the case, then the same
centring and scaling options originally specified to
stdEff() should be
re-specified – which will then be used to standardise the data. If no
effects are supplied, standardised (direct) effects will be calculated from
the model and used to generate predictions. These predictions will equal
the model(s) fitted values if
newdata = NULL,
unique.eff = FALSE, and
re.form = NULL (where applicable).
Model-averaged predictions can be generated if averaged
supplied to the model in
mod, or, alternatively, if
specified (passed to
mod is a list of candidate models
effects can also be passed using this latter method). For mixed model
predictions where random effects are included (e.g.
re.form = NULL), the
latter approach should be used, otherwise the contribution of random
effects will be taken from the single model instead of (correctly) being
averaged over a candidate set.
If bootstrapped effects are supplied to
eff.boot (or to
part of a boot object), bootstrapped predictions are calculated by
predicting from each effect. Confidence intervals can then be returned via
bootCI(), for which the
type should be appropriate for the original
form of bootstrap sampling (defaults to
"bca"). If the number of
observations to predict is very large, parallel processing (via
pSapply()) may speed up the calculation of intervals.
Predictions are always returned in the original (typically unstandardised)
units of the (link-transformed) response variable. For GLMs, they can be
returned in the response scale if
type = "response".
Additionally, if the name of an interactive effect is supplied to
interaction, standardised effects (and confidence intervals) can be
returned for effects of a continuous 'main' variable across different
values or levels of interacting variable(s). The name should be of the form
"x1:x2...", containing all the variables involved and matching the name
of an interactive effect in the model(s) terms or in
effects. The values
for all variables should be supplied in
newdata, with the main continuous
variable being automatically identified as that having the most unique
# Predict effects (direct, total) m <- shipley.sem e <- shipley.sem.eff dir <- getDirEff(e) tot <- getTotEff(e) f.dir <- predEff(m, effects = dir, type = "response") f.tot <- predEff(m, effects = tot, type = "response") f.dir$Live[1:10]#> 1 2 3 4 5 6 7 8 #> 0.9998907 0.9525798 0.9657500 0.9894445 0.9943723 0.9993621 0.9911463 0.9582557 #> 9 10 #> 0.9982749 0.9989735f.tot$Live[1:10]#> 1 2 3 4 5 6 7 8 #> 0.9975858 0.5742006 0.5783691 0.7196629 0.9436709 0.9840953 0.8998478 0.5468860 #> 9 10 #> 0.9462890 0.9887104# Using new data for predictors d <- na.omit(shipley) xn <- c("lat", "DD", "Date", "Growth") seq100 <- function(x) seq(min(x), max(x), length = 100) nd <- data.frame(sapply(d[xn], seq100)) f.dir <- predEff(m, nd, dir, type = "response") f.tot <- predEff(m, nd, tot, type = "response") f.dir$Live[1:10]#> 1 2 3 4 5 6 7 8 #> 0.3000301 0.3279412 0.3571239 0.3874066 0.4185852 0.4504280 0.4826822 0.5150813 #> 9 10 #> 0.5473542 0.5792338f.tot$Live[1:10]#> 1 2 3 4 5 6 7 #> 0.05467217 0.06338280 0.07337353 0.08479648 0.09781007 0.11257517 0.12924985 #> 8 9 10 #> 0.14798252 0.16890356 0.19211539# Add CIs # dir.b <- getDirEff(e, "boot") # tot.b <- getTotEff(e, "boot") # f.dir <- predEff(m, nd, dir, dir.b, type = "response") # f.tot <- predEff(m, nd, tot, tot.b, type = "response") # Predict an interactive effect (e.g. Live ~ Growth * DD) xn <- c("Growth", "DD") d[xn] <- scale(d[xn]) # scale predictors (improves fit) m <- lme4::glmer(Live ~ Growth * DD + (1 | site) + (1 | tree), family = binomial, data = d) nd <- with(d, expand.grid( Growth = seq100(Growth), DD = mean(DD) + c(-sd(DD), sd(DD)) # two levels for DD )) f <- predEff(m, nd, type = "response", interaction = "Growth:DD") f$fit[1:10]#> 1 2 3 4 5 6 7 8 #> 0.2935548 0.3230365 0.3539953 0.3862284 0.4194906 0.4535009 0.4879507 0.5225155 #> 9 10 #> 0.5568659 0.5906810f$interaction#> Growth:DD_1 Growth:DD_2 #> 0.393 0.286# Add CIs (need to bootstrap model...) # system.time(B <- bootEff(m, R = 1000, ran.eff = "site")) # f <- predEff(m, nd, B, type = "response", interaction = "Growth:DD") # Model-averaged predictions (several approaches) m <- shipley.growth # candidate models (list) w <- runif(length(m), 0, 1) # weights e <- stdEff(m, w) # averaged effects f1 <- predEff(m[], effects = e) # pass avg. effects f2 <- predEff(m, weights = w) # pass weights argument f3 <- avgEst(predEff(m), w) # use avgEst function stopifnot(all.equal(f1, f2)) stopifnot(all.equal(f2, f3)) # Compare model fitted values: predEff() vs. fitted() m <- shipley.sem$Live f1 <- predEff(m, unique.eff = FALSE, re.form = NULL, type = "response") f2 <- fitted(m) stopifnot(all.equal(f1, f2)) # Compare predictions using standardised vs. raw effects (same) f1 <- predEff(m) f2 <- predEff(m, use.raw = TRUE) stopifnot(all.equal(f1, f2))