Extracts (standardized) path coefficients from a psem object.
coefs(
modelList,
standardize = "scale",
standardize.type = "latent.linear",
test.statistic = "F",
test.type = "II",
intercepts = FALSE
)Returns a data.frame of coefficients, their standard errors,
degrees of freedom, and significance tests.
A list of structural equations, or a model.
The type of standardization: none, scale, range.
Default is scale.
The type of standardized for non-Gaussian responses:
latent.linear, Menard.OE. Default is latent.linear for binomial;
otherwise it is Menard.OE.
the type of test statistic generated by Anova
the type of test for significance of categorical variables
from Anova. Default is type "II".
Whether intercepts should be included in the coefficients table. Default is FALSE.
Jon Lefcheck <LefcheckJ@si.edu>, Jim Grace
P-values for models constructed using lme4 are obtained
using the Kenward-Roger approximation of the denominator degrees of freedom
as implemented in the Anova function.
Different forms of standardization can be implemented using the standardize
argument:
none No standardized coefficients are reported.
scale Raw coefficients are scaled by the ratio of the standard deviation
of x divided by the standard deviation of y. See below for cases pertaining to GLM.
range Raw coefficients are scaled by a pre-selected range of x
divided by a preselected range of y. The default argument is range which takes the
two extremes of the data, otherwise the user must supply must a named list where
the names are the variables to be standardized, and each entry contains a vector of
length == 2 to the ranges to be used in standardization.
For non-Gaussian responses, standardized coefficients are obtained in one of two ways:
latent.linear Referred to in Grace et al. 2019 as the standard form of
the latent-theoretic (LT) approach. In this method, there is assumed to be a continuous
latent propensity, y*, that underlies the observed binary responses. The standard
deviation of y* is computed as the square-root of the variance of the predictions
(on the linear or 'link' scale) plus the distribution-specific theoretical variance in the
case of binomial responses (for logit links: pi^2/3, for probit links: 1).
Menard.OE Referred to in Grace et al. 2019 as the standard form of
the observed-empirical (OE) approach. In this method, error variance is based on the
differences between predicted scores and the observed binary data. The standard
deviation used for standardization is computed as the square-root of the variance of
the predictions (on the linear scale) plus the correlation between the observed and
predicted (on the original or 'response' scale) values of y.
For categorical predictors: significance is determined using ANOVA (or analysis of
deviance). Because n-1 coefficients are reported for n levels, the output instead
reports model-estimated means in the Estimate column. This is done so all
n paths in the corresponding path diagram have assignable values.
The means are generated using function emmeans in the emmeans package.
Pairwise contrasts are further conducted among all levels using the default
correction for multiple testing. The results of those comparisons are given in the
significance codes (e.g., "a", "b", "ab") as reported in the multcomp::cld function.
For non-linear variables (i.e., smoothing functions from mgcv::gam), there are
no linear estimates reported.
Grace, J.B., Johnson, D.A., Lefcheck, J.S., and Byrnes, J.E. "Standardized Coefficients in Regression and Structural Models with Binary Outcomes." Ecosphere 9(6): e02283.
Anova, emmeans, cld
mod <- psem(
lm(rich ~ cover, data = keeley),
lm(cover ~ firesev, data = keeley),
lm(firesev ~ age, data = keeley),
data = keeley
)
coefs(mod)
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