/* TO DO:
1. help for estat mediate after plssemc must still be added
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/* ISSUES:
1.
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*! version 0.0.1 27Apr2018

Title

plssemc postestimation -- Postestimation tools for plssemc

Postestimation commands

The following postestimation commands are of special interest after
plssemc:

Command Description

estat indirect estimation and
inference for indirect effects

estat total decomposition of
total effects

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

* 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 variance inflation factors for the structural model equations

estat vif
[, 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 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.

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, allows to set the bootstrap seed
number.

level(#),
an option used with estat indirect, 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.

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

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 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

. plssemc (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

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.

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.