Automatically calculate direct, indirect, total, and mediator effects for endogenous (response) variables in a 'piecewise' structural equation model (SEM).
semEff(
sem,
predictors = NULL,
mediators = NULL,
responses = NULL,
use.raw = FALSE,
ci.conf = 0.95,
ci.type = "bca",
digits = 3,
bci.arg = NULL,
...
)A piecewise SEM, comprising a list of fitted model objects, or,
alternatively, of boot objects (class "boot"), containing
bootstrapped model effects.
Names of variables for/through which to
calculate effects. If NULL (default), all predictors, endogenous
predictors (mediators), and endogenous variables (responses) will be used.
Logical, whether to use raw (unstandardised) effects for all calculations (if present).
A numeric value specifying the confidence level for confidence intervals on 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 numeric values.
A named list of any additional arguments to boot.ci,
excepting argument index.
Arguments to bootEff.
A list object of class "semEff", comprising:
all bootstrapped effects
summary tables of effects and confidence intervals
The eponymous function of this package calculates all direct,
indirect, total, and mediator effects for endogenous variables in a
'piecewise' structural equation model (SEM), that is, one where parameter
estimation is local rather than global (Shipley 2000, 2009; Lefcheck 2016).
The SEM simply takes the form of a list of fitted models, or bootstrapped
estimates from such models, describing hypothesised causal pathways from
predictors to response ('endogenous') variables. These are either direct,
or operate indirectly via other response variables ('mediators'). This list
should represent a directed ('acyclic') causal model, which should be named
(exactly) for each response variable and ordered from 'upstream' or
'causal' variables through to 'downstream' (i.e. those at the end of the
pathway). If sem is a list of fitted models, effects will first be
bootstrapped using bootEff (this may take a while!).
Direct effects are calculated as fully standardised model coefficients for each response variable, while indirect effects are the product of these direct effects operating along causal pathways in the SEM. The total effects of any given predictor on a response are then the sum of its direct and (all) its indirect effects. 'Mediator' effects are also calculated, as the sum of all indirect paths which operate through each individual mediator - useful to assess the relative importance of different mediators in affecting the response. All of these effect types are calculated automatically for all (default) or a subset of predictors, mediators, or response variables in the SEM.
Confidence intervals for effects are returned for each response, with
BCa intervals calculated by default using bootstrapped estimates for
each effect type (MacKinnon et al. 2004, Cheung 2009, Hayes &
Scharkow 2013). As indirect, total, and mediator effects are not directly
bootstrapped using the fitted models for response variables (i.e. via
bootEff), their equivalent 'bootstrapped' estimates are calculated
instead using each bootstrapped direct effect.
Correlated errors (and confidence intervals) are also returned if their
bootstrapped values are present in sem, or, if sem is a list
of fitted models, if specified to argument cor.err (see
bootEff). These represent residual relationships
among response variables, unaccounted for by the SEM.
All effects and bootstrapped effects are returned in lists for each response variable, with all except mediator effects also including the model intercept(s) - required for prediction (this will be zero for ordinary linear models with fully standardised effects).
Cheung, M. W. L. (2009). Comparison of methods for constructing confidence intervals of standardized indirect effects. Behavior Research Methods, 41(2), 425-438. https://doi.org/fnx7xk
Hayes, A. F., & Scharkow, M. (2013). The Relative Trustworthiness of Inferential Tests of the Indirect Effect in Statistical Mediation Analysis: Does Method Really Matter? Psychological Science, 24(10), 1918-1927. https://doi.org/bbhr
Lefcheck, J. S. (2016). piecewiseSEM: Piecewise structural equation
modelling in R for ecology, evolution, and systematics.
Methods in Ecology and Evolution, 7(5), 573-579.
https://doi.org/f8s8rb
MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence Limits for the Indirect Effect: Distribution of the Product and Resampling Methods. Multivariate Behavioral Research, 39(1), 99. https://doi.org/chqcnx
Shipley, B. (2000). A New Inferential Test for Path Models Based on Directed Acyclic Graphs. Structural Equation Modeling: A Multidisciplinary Journal, 7(2), 206-218. https://doi.org/cqm32d
Shipley, B. (2009). Confirmatory path analysis in a generalized multilevel context. Ecology, 90(2), 363-368. https://doi.org/bqd43d
# NOT RUN {
## SEM effects
(Shipley.SEM.Eff <- semEff(Shipley.SEM.Boot))
## Effects for selected variables
# semEff(Shipley.SEM.Boot, predictors = "lat")
# semEff(Shipley.SEM.Boot, mediators = "DD")
# semEff(Shipley.SEM.Boot, responses = "Live")
## Effects calculated using original SEM (models)
## (not typically recommended - better to use saved boot objects)
# system.time(
# Shipley.SEM.Eff <- semEff(Shipley.SEM, ran.eff = "site", seed = 53908)
# )
# }
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