*! version 0.0.1 31May2019

Title

plssem postestimation -- Postestimation tools for plssem

Postestimation commands

The following postestimation commands are of special interest after
plssem:

Command Description

estat indirect estimation and
inference for indirect effects

estat total decomposition of
total effects

estat mediate testing of
a mediation effect

* estat vif variance inflation
factors for the structural model equations sample

* estat unobshet unobserved
heterogeneity assessment

* estat vif and estat unobshet are not available for models fitted using bootstrap.

The following standard postestimation commands are also available:

Command Description

predict fitted values and residuals

Syntax for estat

Display the estimation results for up to 5 indirect effects

estat indirect,
effects(efflist) [boot(#) seed(#) level(#) digits(#)]

Display the decomposition of the total effects in the corresponding direct and indirect effects

estat total
[, digits(#) plot]

Display the mediation analysis using partial least squares structural equation modelling

estat mediate
indep(varname) med(varname)
dep(varname) [breps(#) seed(#) zlc
rit rid bca level(#) digits(#)]

Display the variance inflation factors for the structural model equations

estat vif
[, digits(#)]

Display the assessment for the presence of unobserved heterogeneity

estat unobshet,
method(methodname) [numclass(#) maxclass(#)
dendrogram maxiter(#) stop(#) test reps(#)
restart(#) groups(numlist) popsize(#) numgen(#)
pmut(#) ptransf(#) maxitgas(#) seed(#)
plot name(varname) digits(#)]

Description for estat

estat indirect
estimates the (standardized) indirect effects and the corresponding tests of significance
using the Sobel's z statistic (default) as well as the bootstrap
approach (Sobel 1982,
Baron and Kenny 1986,
VanderWeele 2015). The command can
estimate up to five different indirect effects at a time. Each of these should
specified by sequentially typing the dependent, mediator and independent variable
from any PLS-SEM model. By adding the sub-option boot(#), you can obtain
the results based on the bootstrap approach. To facilitate the reproducibility of
bootstrap results, the sub-option seed(#) can further be added. Confidence intervals
(0.95 is the default) for the estimated indirect effects are also provided. To change
the level of confidence interval, the sub-option level(#) can be added. To change the
number of decimals used to display the model estimates, you can change the default (3)
to any other value by adding the sub-option digits(#).

estat total
produces the decomposition of the total effects into standardized direct and indirect effects.
Adding the sub-option plot generates a bar plot of the effects. You can change
the number decimals digits reported by setting the sub-option digits(#).

estat mediate
conducts a mediation analysis based on a fitted PLS-SEM model estimated using the
plssem command. Two methods are implemented, the
Baron and Kenny (1986) approach adjusted by
Iacobucci et al. 2007,
and that by Zhao et al. 2010.

estat vif
computes the variance inflation factors (VIFs) for the independent variables
of the equations in the structural part of a PLS-SEM model. With the
digit(#) sub-option you change the number decimals digits displayed.

estat unobshet
assesses the presence of unobserved heterogeneity in the fitted PLS-SEM model
using the methodname approach. Currently, the REBUS-PLS
(Trinchera 2007), FIMIX-PLS
(Hahn et al. 2007) and PLS-GAS
(Ringle et al. 2014) approaches are implemented.

Options for estat

boot(#),
an option used with estat indirect, allows to estimate the indirect
effects using bootstrap; the number of replications is specified via {#}.

seed(#),
an option used with estat indirect and estat mediate, allows to set
the bootstrap seed number.

level(#),
an option used with estat indirect and estat mediate, allows to set
the confidence level to use for indirect effects confidence intervals; default
is 0.95.

digits(#),
specifies the number of decimal digits to display in the output; default is 3.

plot,
an option used with estat total, provides a graphical representation of
the total effects decomposition.

method(methodname),
an option used with estat unobshet, allows choosing the method to use for
assessing the presence of unobserved heterogeneity; available methods are rebus,
fimix and gas; default is rebus.

numclass(#),
an option used with estat unobshet, allows to manually set the number of
classes to use in the REBUS-PLS analysis; minimum is 2. If not specified, the
number of classes is automatically chosen based on the Calinski-Harabasz
pseudo-F index stopping rule as implemented in cluster stop. In
this case, a Ward hierarchical clustering algorithm is used.

maxclass(#),
an option used with estat unobshet, allows to set the maximum number of
classes for which the automatic stopping rule is to be computed when
numclass(#) is not specified; default is 20.

dendrogram,
an option used with estat unobshet, allows to visualize the dendrogram
for a Ward hierarchical clustering algorithm on the base of the residuals of
the global model. The dendrogram allows to assess the quality of choice for the
number of classes. This option is available only when method(rebus) is
chosen.

maxiter(#),
an option used with estat unobshet, allows to set the maximum number
of iterations the REBUS-PLS algorithm runs; default is 50.

stop(#),
an option used with estat unobshet, allows to set the stopping rule for
the chosen algorithm; for REBUS-PLS this refers to the stability in class
composition from one iteration to the other (i.e. percentage of units changing
class at each iteration); for FIMIX-PLS it refers to the (absolute) change in the
complete loglikelihood value in the EM alogrithm. Default is 0.005
(i.e. 0.5%) when REBUS-PLS is chosen and 1e-5 when FIMIX-PLS is used.

test,
an option used with estat unobshet, allows to specify whether a
permutation test for the Global Quality Index (GQI) of a REBUS-PLS solution must
be performed. This option is available only when method(rebus) is
chosen.

reps(#),
an option used with estat unobshet, allows to set the number of replications
of the permutation test on the GQI; default is 50. This option is available
only when method(rebus) is chosen.

restart(#),
an option used with estat unobshet when the FIMIX-PLS method is chosen,
allows to set the number of EM algortihm runs in the estimation of the
mixture model's parameters; default is 10.

groups(numlist),
an option used with estat unobshet when the FIMIX-PLS method is chosen,
allows to compute the solution for a range of selected group number values and
compare them using a set of fit indices, namely Akaike's information criterion
(AIC), modified AIC with factor 3 (AIC3), modified AIC with factor 4 (AIC4),
Bayesian information criterion (BIC), consistent AIC (CAIC),
Hannan-Quinn criterion (HQ), minimum description length with factor 5 (MDL5),
log-likelihood (LnL), entropy statistic (EN), non-fuzzy index (NFI),
normalized entropy criterion (NEC).

popsize(#),
an option used with estat unobshet when the PLS-GAS method is chosen,
allows to set the size of each generation in the genetic algorithm; deafult
is 100.

numgen(#),
an option used with estat unobshet when the PLS-GAS method is chosen,
allows to set the number of generations to create during the genetic algorithm;
deafult is 1000.

pmut(#),
an option used with estat unobshet when the PLS-GAS method is chosen,
allows to set the probability to mutate for a chromosome (i.e. an individual in a
a generation) in the genetic algorithm; deafult is 0.3.

ptransf(#),
an option used with estat unobshet when the PLS-GAS method is chosen,
allows to set the probability to mutate for a single gene in a chromosome during
the genetic algorithm calculation; deafult is 0.1.

maxitgas(#),
an option used with estat unobshet, allows to set the maximum number
of iterations the PLS-GAS algorithm; default is 30.

seed(#),
allows to set the seed for reproducing results.

plot,
an option used with estat unobshet when the REBUS-PLS method is chosen,
allows to visualize the empirical distribution (i.e. the histogram)
corresponding to the replications of the permutation test on the GQI.

name(varname),
an option used with estat unobshet, allows to set the name of the variable
that will contain the final classification obtained.

dep(varname),
an option used with estat mediate, specifies the name of the dependent
variable to use in the mediation analysis.

med(varname),
an option used with estat mediate, specifies the name of the mediator
variable to use in the mediation analysis.

indep(varname),
an option used with estat mediate, specifies the name of the independent
variable to use in the mediation analysis.

breps(#),
an option used with estat mediate, specifies the number of bootstrap
replications to be performed. The default is 50.

zlc,
an option used with estat mediate providing the approach by
Zhao et al. 2010 together with
the Baron and Kenny (1986) approach
adjusted by Iacobucci et al. 2007
(default).

rit,
an option used with estat mediate providing the ratio of the indirect
effect to the total effect.

rid,
an option used with estat mediate providing the ratio of the indirect
effect to the direct effect.

bca,
an option used with estat mediate providing the bias-corrected accelerated
(BCa) bootstrap confidence intervals instead of the percentile confidence
intervals (default).

Syntax for predict

predict [, statistic noouter noinner]

statistic

Main
xb linear predictions

residuals residuals

Description for predict

predict creates new variables containing linear predictions and residuals. These
quantities are provided only for reflective blocks of manifest variables in the
measurement/outer model and for endogenous latent variables in the structural/inner model.

The newly computed predictions will replace those already present in the data set.

Options for predict

Main

xb calculates the linear predictions (fitted values).

residuals calculates the residuals.

Options

nooouter fitted values and residuals for the measurement/outer model
are not saved in the data set.

nooinner fitted values and residuals for the structural/inner model
are not saved in the data set.

Stored results for estat indirect

estat indirect stores the following in r():

Matrices

r(indirect) matrix of indirect effect testing results

Stored results for estat mediate

estat mediate stores the following in r():

Matrices

r(mediate) matrix of indirect effect testing results

Stored results for predict

predict stores the following in r():

Matrices

r(fitted) matrix of fitted values for the outer and inner models

r(residuals) matrix of residuals for the outer and inner models

Examples

Setup

. sysuse workout2, clear

Model estimation

. plssem (Attractive > face sexy) (Appearance > body appear attract) (Muscle > muscle strength endur) (Weight > lweight calories cweight), structural(Appearance Attractive, Muscle Appearance, Weight Appearance)

Multicollinearity assessment

. estat vif

Indirect effects

. estat indirect, effects(Muscle Appearance Attractive, Weight Appearance Attractive)

Predictions

. predict, xb residuals

. describe *_hat *_res

Assessment of unobserved heterogeneity using REBUS-PLS

. estat unobshet, test reps(200) plot

Assessment of unobserved heterogeneity using FIMIX-PLS

. estat unobshet, method(fimix) groups(1/5) stop(1e-5) restart(3)

Authors

Sergio Venturini

Department of Management

Università degli Studi di Torino, Italy

sergio.venturini@unito.it

Mehmet Mehmetoglu

Department of Psychology

Norwegian University of Science and Technology

mehmetm@svt.ntnu.no

References

Baron, R. M., and Kenny, D. A. 1986. The Moderator-Mediator Variable Distinction in Social Psychological
Research: Conceptual, Strategic, and Statistical Considerations. Journal of
Personality and Social Psychology, 51, 1173-1182.

Hahn, C., Johnson, M. D., Herrmann, A., and Huber, F. 2002. Capturing Customer Heterogeneity Using a
Finite Mixture PLS Approach. Schmalenbach Business Review, 54, 243-269.

Hair, J. F., Hult, G. T. M., Ringle, C. M., and Sarstedt, M. 2017. A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM). Second edition. Sage.

Hair, J. F., Sarstedt, M., Ringle, C. M., and Gudergan, S. P. 2018. Advanced Issues in Partial Least Squares Structural Equation Modeling. Sage.

Iacobucci, D., Saldanha, N., & Deng, X. 2007. A meditation on mediation: evidence
that structural equation models perform better than regressions. Journal of
Consumer Psychology, 17, 140-154.

Ringle, C. M., Sarstedt, M., and Schlittgen, R. 2014. Genetic algorithm segmentation
in partial least squares structural equation modeling. OR Spectrum, 36, 251–276.

Sobel, M. N. 1982. Asymptotic Confidence Intervals for Indirect Effects in Structural Equations
Models. In Leinhart, S. (ed.), Sociological Methodology, pp. 290-312. Jossey-Bass.

Trinchera, L. 2007. Unobserved Heterogeneity in Structural Equation Models: a new approach to latent class detection in PLS Path Modeling. Ph.D. Thesis.

VanderWeele, T. J. 2015. Explanation in Causal Inference. Oxford University Press.

Zhao, X., Lynch, J. G. Jr., & Chen, Q. 2010. Reconsidering Baron and Kenny: myths and
truths about mediation analysis. Journal of Consumer Research, 37, 197-206.