Abstract
The goal of PLS path modeling is primarily to estimate the variance of endogenous constructs and in turn their respective manifest variables (if reflective). Models with significant jackknife or bootstrap parameter estimates may still be considered invalid in a predictive sense. In this chapter, the objective is to shift from that of assessing the significance of parameter estimates (e.g., loadings and structural paths) to that of predictive validity. Specifically, this chapter examines how predictive indicator weights estimated for a particular PLS structural model are when applied on new data from the same population. Bootstrap resampling is used to create new data sets where new R-square measures are obtained for each endogenous construct in a model. The weighted summed (WSD) R-square represents how well the original sample weights predict when given new data (i.e., a new bootstrap sample). In contrast, the simple summed (SSD) R-square examines the predictiveness using the simpler approach of unit weights. Such an approach is equivalent to performing a traditional path analysis using simple summed scale scores. A relative performance index (RPI) based on the WSD and SSD estimates is created to represent the degree to which the PLS weights yield better predictiveness for endogenous constructs than the simpler procedure of performing regression after simple summing of indicators. In addition, a Performance from Optimized Summed Index (PFO) is obtained by contrasting the WSD R-squares to the R-squares obtained when the PLS algorithm is used on each new bootstrap data set. Results from two studies are presented. In the first study, 14 data sets of sample size 1,000 were created to represent two different structural models (i.e., medium versus high R-square) consisting of one endogenous and three exogenous constructs across seven different measurement scenarios (e.g., parallel versus heterogenous loadings). Five-hundred bootstrap cross validation data sets were generated for each of 14 data sets. In study 2, simulated data based on the population model conforming to the same scenarios in study 1 were used instead of the bootstrap samples in part to examine the accuracy of the bootstrapping approach. Overall, in contrast to Q-square which examines predictive relevance at the indicator level, the RPI and PFO indices are shown to provide additional information to assess predictive relevance of PLS estimates at the construct level. Moreover, it is argued that this approach can be applied to other same set data indices such as AVE (Fornell C, Larcker D, J Mark Res 18:39–50, 1981) and GoF (Tenenhaus M, Amato S, Esposito Vinzi V, Proceedings of the XLII SIS (Italian Statistical Society) Scientific Meeting, vol. Contributed Papers, 739–742, CLEUP, Padova, Italy, 2004) to yield RPI-AVE, PFO-AVE. RPI-GoF, and PFO-GoF indices.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chin, W. W. (1995). Partial least squares is to LISREL as principal components analysis is to common factor analysis. Technology Studies, 2, 315–319.
Chin, W. W. (1998). The partial least squares approach for structural equation modeling. In G. A. Marcoulides (Ed.), Modern methods for business research (pp. 295–336). New Jersy: Lawrence Erlbaum.
Chin, W. W., Marcolin, B. L., & Newsted, P. R. (2003). A partial least squares latent variable modeling approach for measuring interaction effects: Results from a monte carlo simulation study and electronic mail emotion/adoption study. Information Systems Research, 14(2), 189–217.
Du, Y.-P, Kasemsumran, S., Maruo, K., Nakagawa, T., & Ozaki, Y. (2006). Ascertainment of the number of samples in the validation set in Monte Carlo cross validation and the selection of model dimension with Monte Carlo cross validation. Chemometrics and Intelligent Laboratory Systems, 82, 83–89.
Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap (monographs on statistics and applied probability #57). New York: Chapman & Hall.
Fornell, C., & Larcker, D. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18, 39–50.
Geisser, S. (1974). A predictive approach to the random effect model. Biometrika, 61(1), 101–107.
Geisser, S. (1975). The predictive sample reuse method with applications. Journal of the American Statistical Association, 70, 320–328.
Picard, R. R., & Cook, R. D. (1984). Cross-validation of regression models. Journal of the American Statistical Association, 79(387), 573–585.
Stone, M. (1975). Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, Series B, 36(2), 111–133.
Tenenhaus, M., Amato, S., & Esposito Vinzi, V. (2004). A global Goodness-of-Fit index for PLS structural equation modelling. In Proceedings of the XLII SIS (Italian Statistical Society) Scientific Meeting, vol. Contributed Papers (pp. 739–742). Padova, Italy: CLEUP.
Tenenhaus, M., Esposito Vinzi, V., Chatelin, Y. M., & Lauro, C. (2005). PLS path modelling, computational statistics and data analysis (Vol. 48, No. 1, pp. 159–205). The Netherlands: North-Holland.
Xu, Q.-S., & Liang, Y.-Z. (2001). Monte Carlo cross valiation. Chemometrics and Intelligent Laboratory Systems, 56, 1–11.
Xu, Q.-S, Liang, Y.-Z, & Du, Y.-P. (2004). Monte Carlo cross-validation for selecting a model and estimating the prediction error in multivariate calibration. Journal of Chemometrics, 18, 112–120.
Werts, C. E., Linn, R. L., & Jöreskog, K. G. (1974). Intraclass reliability estimates: Testing structural assumptions. Educational and Psychological Measurement, 34(1), 25–33.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Chin, W.W. (2010). Bootstrap Cross-Validation Indices for PLS Path Model Assessment. In: Esposito Vinzi, V., Chin, W., Henseler, J., Wang, H. (eds) Handbook of Partial Least Squares. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32827-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-32827-8_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32825-4
Online ISBN: 978-3-540-32827-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)