حسابداری برای سنگینی نمونه برداری در مدل سازی مسیر PLS: شبیه سازی و نمونه تجربی  Accounting for sampling weights in PLS path modeling: Simulations and empirical examples

. Introduction The partial least squares (PLS) path modeling method combines econometric prediction with the psychometric modeling of unobserved (latent) conceptual variables, which are indirectly observed by means of multiple manifest variables (Lohmoller, 1989; Wold, € 1982). The method can be applied to different observation forms, such as survey responses and transactional data, although most applications focus on survey responses to psychological variables like job attitude or satisfaction (Rigdon, 2012). PLS path modeling is increasingly applied across behavioral science disciplines, such as business, psychology, sociology, education, and economics (Lu, Kwan, Thomas, & Cedzynski, 2011), with a special focus on strategic management (Hair, Sarstedt, Pieper, & Ringle, 2012), information systems (Ringle, Sarstedt, & Straub, 2012), international business (Richter, Sinkovics, Ringle, & Schlagel, 2016 € ) and marketing (Hair et al., 2012). These researchers usually apply the method to the data as is, aiming to estimate population parameters from the sample they have collected. By doing so, they assume that the sample represents the population very well, but this presumption might not always be fulfilled. Researchers who work with survey data sometimes conduct complicated sampling designs to obtain a representative sample of the population of interest, or use a simple random sample (Magee, Robb, & Burbidge, 1998). Others might just use a convenience sample without a specific sampling strategy. Whatever the case, population members may not be equally likely to be included in the sample, which means the sampling units (observations) have different probabilities of selection compared with their occurrence in the population (Winship & Radbill, 1994). If the analysis does not incorporate the unequal probability of selection, a substantial bias may arise in the parameter estimates (Asparouhov, 2005; Pfeffermann, 1993). For instance, the relevance of this issue has been shown in regression analyses (e.g., Korn & Graubard, 1995) and in latent variable structural equation model (SEM) analyses (e.g., Kaplan & Ferguson, 1999). The use of sampling weights is a possible solution to correct the results with, for example, weighted means or weighted variances, when estimating population parameters (DuMouchel & Duncan, 1983). Not only can imperfectionsin the sample due to unequal probabilities of selection be corrected by applying appropriate weights, but also imperfections in terms of unit nonresponse and noncoverage (Groves, Dillman, Eltinge, & Little, 2002). In regression analysis, for example, weighted least squares (WLS) is used to account for sampling weights to obtain consistent population parameters (DuMouchel & Duncan, 1983). In the context of sampling weights, this regression estimator only differs from the usual application of WLS for heteroskedastic errors by its motivation for and choice of weights (Magee et al., 1998). In terms of covariance-based structural equation modeling (CB-SEM), Asparouhov (2005) shows how to incorporate sampling weights via the WLS estimator into SEMs with mixed outcomes (Muthen, 1984).1 In PLS path modeling, to the best of our knowledge no similar technique has been proposed to take sampling weights into account.