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 effects or all those used to fit
mod.
A numeric vector of effects to predict, or a list or nested
list of such vectors. These will typically have been calculated using
semEff(), bootEff(), or stdEff(). Alternatively, a boot object
produced by bootEff() can be supplied.
A matrix of bootstrapped effects used to calculate confidence
intervals for predictions, or a list or nested list of such matrices. These
will have been calculated using semEff() or bootEff().
For mixed models of class "merMod", the formula for random
effects to condition on when predicting effects. Defaults to NA, meaning
random effects are averaged over. See predict.merMod() for further
specification details.
The type of prediction to return (for GLMs). Can be either
"link" (default) or "response".
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 "bca"
– see Details). See boot.ci() for further specification details.
The number of significant digits to return for interactive effects.
A named list of any additional arguments to boot.ci(),
excepting argument index.
The type of parallel processing to use for calculating
confidence intervals on predictions. Can be one of "snow", "multicore",
or "no" (for none – the default).
Number of system cores to use for parallel processing. If NULL
(default), all available cores are used.
Optional cluster to use if parallel = "snow". If NULL
(default), a local cluster is created using the specified number of cores.
Arguments to stdEff().
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
structure of 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 effects are
supplied to the model in mod, or, alternatively, if weights are
specified (passed to stdEff()) and 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 effects, as
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
values.
# 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$Live[1:10]
#> 1 2 3 4 5 6 7 8
#> 0.9998907 0.9525798 0.9657500 0.9894445 0.9943723 0.9993621 0.9911463 0.9582557
#> 9 10
#> 0.9982749 0.9989735
f.tot$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$Live[1:10]
#> 1 2 3 4 5 6 7 8
#> 0.3000301 0.3279412 0.3571239 0.3874066 0.4185852 0.4504280 0.4826822 0.5150813
#> 9 10
#> 0.5473542 0.5792338
f.tot$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$fit[1:10]
#> 1 2 3 4 5 6 7 8
#> 0.2935549 0.3230365 0.3539954 0.3862285 0.4194907 0.4535010 0.4879508 0.5225156
#> 9 10
#> 0.5568660 0.5906810
f$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[[1]], 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")
#> Warning: longer object length is not a multiple of shorter object length
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))