*! version 0.5.3 22Feb2024

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 htmt heterotrait-monotrait
ratio of correlations for assessing discriminant validity

estat ci confidence intervals
for all model's coefficients

estat f2 Cohen's f^2 effect
sizes

estat ic Model's information and
selection criteria

estat dist model's distance
measures

estat blindfolding blindfolding
procedure

* estat vif is 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(#)]

Display the assessment of discriminant validity using heterotrait-monotrait
ratios of correlations

estat htmt,
[cutoff(#) digits(#)]

Display the confidence intervals for all model's coefficients

estat ci,
type(citype) [level(#) digits(#)]

Display the Cohen's f^2 effect sizes

estat f2,
[digits(#)]

Display the model's information and selection criteria

estat ic,
[digits(#)]

Display the model's distance measures

estat dist,
[digits(#)]

Blindfolding procedure

estat blindfolding,
distance(#) [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.

estat htmt
assesses discriminant validity using heterotrait-monotrait ratios of correlations; both
the HTMT (arithmetic average of correlations) and HTMT2 (geometric average of correlations)
approaches are available.

estat ci
computes the confidence intervals for both the measurement and structural models'
coefficients; different types of confidence intervals are available.

estat f2
computes the Cohen's f^2 effect sizes (Cohen 1988).

estat ic
computes some information and selection criteria for the fitted model for each
structural equation of the model separately, as suggested by
Sharma et al. 2019. More specifically,
the command provides the following indexes: Akaike information criterion (AIC),
Corrected AIC (AICc), Unbiased AIC (AICu), Bayesian information criterion (BIC),
final prediction error (FPE), Hannan-Quinn criterion (HQ) and Corrected HQ criterion
(HQc). The definitions used by the commend for these indexes can be found in table B1
of Sharma et al. 2019.

estat dist
computes some measures of the distance between the empirical and the model-implied
indicator correlation matrices. Currently, the geodesic distance, the squared Euclidean
distance and the the maximum likelihood-based distance function are implemented.

estat blindfolding
computes the Q2 and q2 values (Geisser 1974;
Stone 1974) to assess the out-of-sample
predictive relevance. These measures are obtained by using the blindfolding procedure
for a specified omission distance.

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 and estat ci, 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.

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.

cutoff(#),
an option used with estat htmt, specifies the cutoff value to use for
showing the heterotrait-monotrait ratios.

type(citype),
an option used with estat ci, allows to choose the type of confidence
intervals to compute; available methods are standard_z (assumes
a standard normal distribution), standard_t (assumes
a t distribution with n - 1 degrees of freedom), percentile (utilizes
the quantiles of the distribution of the bootstrap resample estimates), and
bc (bias-corrected confidence interval).

distance(#),
an option used with estat blindfolding, allows to set the omission distance
to use in the blindfolding procedure; it must be an integer larger than 1
and it has to be chosen so that the number of observations used in model
estimation divided by the omission distance is not an integer.

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 ci

estat ci stores the following in r():

Scalars

e(level) confidence level

Macros

e(ci_type) type of confidence intervals

Matrices

r(path_ci) matrix of path coefficients confidence intervals

r(load_ci) matrix of loadings confidence intervals

Stored results for estat htmt

estat htmt stores the following in r():

Matrices

r(htmt) matrix of heterotrait-monotrait ratios (HTMT)

r(htmt2) matrix of advanced heterotrait-monotrait ratios (HTMT2)

Stored results for estat f2

estat f2 stores the following in r():

Matrices

r(f2) matrix of the Cohen's f^2 effect sizes

Stored results for estat ic

estat ic stores the following in r():

Matrices

r(ic) matrix of the model's information and selection criteria

Stored results for estat dist

estat dist stores the following in r():

Matrices

r(dist) matrix of the model's distance measures

Stored results for estat blindfolding

estat blindfolding stores the following in r():

Matrices

r(Q2) matrix with the Q2 measures

r(q2) matrix with the q2 measures

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)

Discriminant validity assessment (HTMT)

. estat htmt

Structural model assessment

. estat vif

. estat f2

. estat ic

Indirect effects

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

Confidence intervals

. estat ci, type(bc) digits(5)

Predictions

. predict, xb residuals

. describe *_hat *_res

Authors

Sergio Venturini

Department of Economics and Social Sciences

Università Cattolica del Sacro Cuore, Italy

sergio.venturini@unicatt.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.

Cohen, J. 1988. Statistical Power Analysis for the Behavioral Sciences. Mahwah, NJ: Erlbaum.

Geisser, S. 1974. A predictive approach to the random effects model. Biometrika, 61, 101–107.

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. 2022. A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM). Third 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.

Mehmetoglu, M., and Venturini, S. 2021. Structural Equation Modelling with Partial Least Squares Using Stata and R. CRC Press.

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

Sharma, P., Sarstedt, M., Shmueli, G., Kim, K. H., Thiele, K. O. 2019. PLS-Based Model Selection: The Role of Alternative Explanations in Information Systems Research. Journal of the Association for Information Systems, 20(4), 346-397.

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.

Stone, S. 1974. Cross-validatory choice and assessment of statistical pre- dictions.
Journal of the Royal Statistical Society, 36, 111–147.

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.