PLS-SEM

Journal of Accounting Literature 37 (2016) 19–35

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The use of partial least squares structural equation modelling (PLS-SEM) in management accounting research: Directions for future theory development Dr. Christian Nitzl University of the German Federal Armed Forces Munich, Institute of Management Accounting, Finance and Risk Management, WernerHeisenberg-Weg 39, 85577 Neubiberg, Germany

A R T I C L E I N F O

Article history: Received 26 August 2014 Received in revised form 12 February 2016 Accepted 14 September 2016 Keywords: Partial least squares Structural equation modelling Management accounting Theory development

A B S T R A C T

In management accounting research, the capabilities of Partial Least Squares Structural Equation Modelling (PLS-SEM) have only partially been utilized. These yet unexploited capabilities of PLS-SEM are a useful tool in the often explorative state of research in management accounting. After reviewing eleven top-ranked management accounting journals through the end of 2013, 37 articles in which PLS-SEM is used are identified. These articles are analysed based on multiple relevant criteria to determine the progress in this research area, including the reasons for using PLS-SEM, the characteristics of the data and the models, and model evaluation and reporting. A special focus is placed on the degree of importance of these analysed criteria for the future development of management accounting research. To ensure continued theoretical development in management accounting, this article also offers recommendations to avoid common pitfalls and provides guidance for the advanced use of PLS-SEM in management accounting research. ã 2016 University of Florida, Fisher School of Accounting. Published by Elsevier Ltd. All rights reserved.

1. Introduction Empirical research in management accounting is often shaped by a complex set of different variables, e.g., context variables such as uncertainty; therefore, research models can become inflated very rapidly (cf. Chenhall & Moers, 2007; Chenhall, 2012; Hartmann & Moers, 1999; Hartmann & Moers, 2003; Luft & Shields, 2014). For instance, Speklé (2001) shows that management control research suffers from a plurality of possible explanations, which also means that an exhaustive understanding of the central factors often does not exist. Rich knowledge about a certain topic seems to be achieved only in some fields in management accounting, e.g., in the areas of budgets and budgeting (Covaleski, Evans III, Luft, & Shields, 2003). Smith and Langfield-Smith (2004) argue that for most research areas in management accounting, the theoretical basis is weak. Hence, models in management accounting have to regularly build on a basic theory that is often derived from another research field (e.g., Abernethy, Bouwens, & van Lent, 2013; Hall, 2011; Hartmann & Maas, 2011; Hartmann & Slapni9 car, 2009). Thus, management accounting researchers have to learn about their research models in a rather data-driven manner (cf. Chenhall, 2012). For instance, researchers use contingency theory (Chenhall, 2003, 2006) or the theory of reasoned action (Fishbein & Ajzen, 1975) to develop their underlying hypotheses. Testing a model that comprises general measurement

E-mail address: christian.nitzl@unibw.[268_TD$IF]de (C. Nitzl). http://dx.doi.org/10.1016/j.acclit.2016.09.003 0737-4607/ã 2016 University of Florida, Fisher School of Accounting. Published by Elsevier Ltd. All rights reserved.

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C. Nitzl / Journal of Accounting Literature 37 (2016) 19–35

constructs such as behavioural intentions, attitudes or subjective norms for a specific judgement and decision-making situation would generally have a high degree of goodness-of-fit (GFI) because the model would reflect some established psychological processes. However, it would not explain the specifics of management accounting in particular. Specific variables must be included to hypothesize causes and effects that are relevant to the management accounting context (cf. Luft & Shields, 2002, 2003). Structure equation models (SEMs) offer flexibility for testing such models, allowing one to use multiple predictors and criterion variables, construct latent (unobservable) variables, model errors in measurement for observed variables, and test mediation and moderation relationships in a single model (Blanthorne, Jones-Farmer, & Almer, 2006; Fornell, 1987; Hair, Black, Babin, & Anderson, 2010; Hair, Hult, Ringle, & Sarstedt, 2016). Acknowledged management accounting scholars have emphasized the need for more SEM research in management accounting to test research models in a holistic fashion (Chenhall, 2003; Fornell & Larcker, 1981b; Hughes & Kwon, 1990; Shields & Shields, 1998; Shields, 1997). However, researchers in this field usually prefer methods they are familiar with. In contrast to other research fields, the use of SEM is generally less prevalent in management accounting (Chenhall & Smith, 2011; Henri, 2007; Smith & Langfield-Smith, 2004), where regression analysis has been the dominant method thus far (Oler, Oler, & Skousen, 2010). Due to the focus on certain methods that have been very useful in the past and the limited understanding of novel methods, it is reasonable that management accounting researchers are in danger of utilizing only specific methods. The domination of OLS is somewhat surprising, however, as Wilcox (1998, p. 311) argues that the “OLS estimator is one of the poorest choices researchers could make. In some cases, its standard error is more than 100 times larger than certain modern methods”. Chenhall (2012) encourages management accounting researchers to update their statistical skills regularly to ensure the delivery of highquality research. Rigdon (2013) warns researchers against making inferior choices based on limited knowledge of methodical alternatives. One such methodological alternative that researchers have limited knowledge about is PLS-SEM. Smith (2011, p. 83) describes PLS-SEM as a “poor man’s” SEM and does not recognize the usefulness and importance of PLS-SEM in testing complex explorative models. This statement implicitly reflects the strong tradition in management accounting research to use only confirmatory approaches to model testing (Smith & Langfield-Smith, 2004). PLS-SEM, as an SEM and a sibling of the covariance-based structure equation model (CB-SEM), was originally developed by Wold (1982) for situations in which only a weak theory exists and therefore a set of different possible influences have to be tested (cf. Bisbe, Batista-Foguet, & Chenhall, 2007; Smith, 2011). In the case of a weak theory basis, it is also unlikely that the necessary psychometric assumptions of CB-SEM are fulfilled for observed indicators, which will produce unacceptable results for data sets that are not the outcome of a long-term measurement process (Bisbe et al., 2007; Franke, Preacher, & Rigdon, 2008; Hughes & Kwon, 1990; Jöreskog, 1979; Rigdon, 2013). For archival or secondary data, the possibility of revising and refining construct measurements often does not exist at all (Rigdon, 2013). Because PLS-SEM is not constrained by identification and other technical aspects, it is possible to test complex models with many different constructs and indicators (Rigdon, 2013, 2014). Additionally, when research focuses on theory development, there should be a greater focus on not overlooking true effects (Willaby, Costa, Burns, MacCann, & Roberts, 2015). In addition, PLS-SEM realizes the required level of statistical power with smaller sample sizes than CB-SEM (Reinartz, Haenlein, & Henseler, 2009). In a nutshell, through its specific characteristics, PLS-SEM provides a useful tool for management accounting research due to the high degree of flexibility it offers for the interplay between theory and data (Chin, 1998a), which seems urgently necessary given the current state of research in management accounting, especially with regard to developing a more holistic map of causes and effects (Luft & Shields, 2003, 2014). However, as with any statistical tool, PLS-SEM requires considerable knowledge about the method applied, as it requires several choices that, if not made correctly, can lead to incorrect conclusions that will jeopardize future theory development in management accounting. Many guidelines on how to properly conduct PLS-SEM studies have been published (e.g., Chin, 2010; Hair, Ringle, & Sarstedt, 2011, 2013; Hair, Sarstedt, Ringle, & Mena, 2012; Henseler, Ringle, & Sinkovics, 2009; Marcoulides & Chin, 2013; Peng & Lai, 2012; Sosik, Kahai, & Piovoso, 2009). For the accounting context, Lee, Petter, Fayard, and Robinson (2011) provide an introduction to the general functionality of PLS-SEM as well as guidelines for assessing its measurements and structural models, which are much in line with the previously cited guidelines. However, in sharp contrast to Lee et al. (2011), who conclude that the use of PLS-SEM in accounting complies with best practices, the results of this review point to important areas of improvement for PLS-SEM applications in the field of management accounting and theory development. Therefore, this paper provides important insights into the state of the art of PLS-SEM and advises on its proper usage. Finally, Lee et al. (2011) review only a fraction of the relevant management accounting research journals.1 Consequently, the contribution of this paper is twofold. First, this paper extensively discusses the characteristics of PLSSEM and illustrates how these characteristics can be a useful tool in future management accounting research. Second, the aim of this paper is to provide recommendations for applying PLS-SEM based on the results of the review of management

1 Lee et al. (2011) focus on accounting in general and do not survey the journals Accounting, Auditing and Accountability Journal (AAAJ),Accounting and Business Research (ABR), or The British Accounting Review (BAR). However, these journals can be found on Smith and Langfield-Smith’s (2004) list as important journals in empirical management accounting research. Moreover, Lee et al.’s (2011) list is incomplete. The authors argue that the Journal of Accounting Research (JAR) and the Journal of Management Accounting Research (JMAR) do not contain any articles that use PLS-SEM. However, for the period reviewed for their contribution, there is at least one article in each of these journals.


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accounting research. Therefore, this paper provides an overview of important technical aspects and improvements in PLSSEM. For example, I discuss a new criterion for the assessment of the reliability of reflective measurements and a new method for the control of common measure variance. Such critical recommendations are vital for ensuring the rigor of research and publications in future management accounting research and theory development using PLS-SEM. 2. Survey of the use of PLS-SEM in management accounting research The focus of the journal selection was to analyse a selected set of journals that publish highly regarded management accounting research to review the use and the current state of PLS-SEM. The selection is therefore mainly based on the journal selection of Smith and Langfield-Smith (2004), who aim to provide an overview of SEM in management accounting research. In addition to the journal selection of Smith and Langfield-Smith (2004), the analysis also includes the journal Management Accounting Research (MAR), which has grown in importance in recent years as an internationally recognized journal that specializes in management accounting (cf. Chenhall & Smith, 2011; Van der Stede, Young, & Chen, 2005). The journals were reviewed for the period from 1980 to 2013. Two different people independently conducted a full text search in Google Scholar, EBSCO Business and JSTOR Source Complete as well as in the online versions of the journals using the keywords “partial least squares” and “PLS”. Because the search was conducted by two individuals independently; a continuous process of scrutinizing the lists by an additional person ensured that all of the PLS-SEM articles in the target journals were identified. Table 1 shows the list of the surveyed journals with the relevant articles. Accounting; Organizations and Society has published the most articles using PLS-SEM (ten articles; 27.0%); followed by Management Accounting Research (seven articles; 18.9%). Whereas Smith and Langfield-Smith (2004) wonder why PLS-SEM was used in only one paper over the time period from 1980 to 2001, today one can find several articles in practically every top management accounting journal. The only reviewed journal that has not yet published any research using PLS-SEM is the Journal of Accounting and Economics (JAE). Fig. 1 shows the number of articles over the last 20 years; the line indicates the cumulative number of articles, and the bars illustrate the absolute number of articles per year (in accordance with Hair et al., 2016). Overall, this figure indicates that the management accounting community has adopted PLS-SEM very quickly and on a broad scale, particularly over the last decade. 3. Critical issues in the use of PLS-SEM in management accounting research In accordance with Hair, Sarstedt, Ringle et al. (2012), each of the 37 articles was analysed with regard to the following key criteria: (1) the reasons for using PLS-SEM, (2) data characteristics, (3) model characteristics, (4) model evaluation, and (5) Table 1 PLS-SEM Studies in Top Management Accounting Journals. Accounting, Auditing and Accountability Journal (AAAJ)

J. of Accounting and Economics (JAE)

Ferreira, Moulang, and Hendro (2010) Verbeeten (2008)

No article

Accounting and Business Research (ABR) Hartmann and Maas (2011) Sholihin and Pike (2009) Van Rinsum and Verbeeten (2012) Accounting, Organizations and Society (AOS) Anderson et al. (2002) Chang, Cheng, and Trotman (2013) Chapman and Kihn (2009) Chenhall (2005) Fayard, Lee, Leitch, and Kettinger (2012) Hall (2008) Hall and Smith (2009) Hartmann and Slapni9 car (2009) Naranjo-Gil and Hartmann (2007) Vandenbosch (1999) Behavioral Research in Accounting (BRIA) Chenhall (2004) Lin and Fan (2011) Mahama and Cheng (2013) Miller, Denison, and Matuszewski (2013) Contemporary Accounting Research (CAR) Abernethy et al. (2013) Nicolaou, Sedatole, and Lankton (2011)

J. of Accounting Research (JAR) Bouwens and van Lent (2007) J. of Management Accounting Research (JMAR) Bouwens and van Lent (2006) Chenhall, Kallunki, and Silvola (2011) Naranjo-Gil and Hartmann (2006) Management Accounting Research (MAR) Abernethy, Bouwens, and van Lent (2010) Burkert and Lueg (2013) Hall (2011) Hartmann and Slapni9 car (2012) Homburg and Stebel (2009) Mahama (2006) Pondeville, Swaen, and De Rongé (2013) The Accounting Review (TAR) Dowling (2009) Elbashir et al. (2011) Ittner et al. (1997) The British Accounting Review (BAR) Lau and Martin-Sardesai (2012) Sholihin, Pike, Mangena, and Li (2011)

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[(Fig._1)TD$IG]


Fig. 1. Development of PLS-SEM Studies in Management Accounting Research.

reporting. Each one of these criteria plays an important role in furthering theory development in management accounting. Additionally, these five criteria facilitate the identification of critical issues and common misapplications of PLS-SEM. The first criterion in particular shows how special characteristics can play a useful role in future theory development in management accounting. Furthermore, the selection of these key criteria allows a comparison with the findings from the review study conducted by Hair, Sarstedt, Ringle et al. (2012). With their focus on over 300 articles in top-ranked marketing journals, their study can be seen as a benchmark for a business discipline where the use of PLS-SEM is already wellestablished. 3.1. Reasons for using PLS-SEM in management accounting research Several rationales for the use of PLS-SEM have been extensively discussed in the methodological literature (Hair et al., 2016). Because the use of PLS-SEM is relatively new in management accounting, it often requires a detailed explanation and valid justification for why it is preferred over other methods (cf. Chin, 2010). In the first contribution using PLS-SEM in management accounting by Ittner, Larcker, and Rajan (1997), the authors had to explain the exact functionality of the algorithm of PLS-SEM. From the total of 37 studies, 33 (89.2%) addressed the issue of why they used PLS-SEM. The two most frequently mentioned reasons for using PLS-SEM in management accounting research were related to a small sample size (29 studies, 78.4%) and a non-normal distribution of data (25 studies, 67.6%). Another reason discussed was the simultaneous estimation of multiple and interrelated dependent relationships between variables and the use of latent construct measurement (nine studies, 24.3%). Additional reasons for using PLS-SEM pertained to exploratory objectives (eight studies, 21.6%) and formative measures (six studies, 16.2%). Other substantive reasons for choosing PLS-SEM, such as the ability to leverage model complexity (five studies, 13.5%) and prediction orientation (one study, 2.7%), were rarely mentioned. Apparently, so far, the main reasons for using PLS-SEM are technical aspects such as sample sizes or the distribution of data. However, there are important new technical developments in the last several years that should not be overlooked by management accounting scholars. For example, researchers have questioned whether the use of PLS-SEM should be based on distribution considerations because of the existence of robust CB-SEM estimator options (cf. Gefen, Rigdon, & Straub, 2011; Goodhue, Lewis, & Thompson, 2012; Henseler et al., 2009). In addition, there is a recent trend to counteract the problem of inconsistency in PLS estimates. PLS-SEM yields loadings that are too large and path coefficient estimates that are too small in a population with finite moments of appropriate order (Dijkstra, 2010). Thus, Dijkstra and Henseler (2015) introduce a consistent PLS-SEM (PLSc-SEM) that provides a bias correction in the case of reflective measurements. However, a pure concentration on certain technical arguments bears the risk that PLS-SEM will be applied similarly to a recipe in a cookbook without sufficient reflection. An often neglected reason for using PLS-SEM in management accounting is that it is also useful when “prediction” is an important part of answering the research question (Lohmöller, 1989; Reinartz et al., 2009), whereas factor-based methods such as CB-SEM are unsuitable for prediction because of the indeterminacy problem (Rigdon, 2012, 2014; Sarstedt, Ringle, Henseler, & Hair, 2014). Malmi and Granlund (2009) perceive the main focus of management accounting theories to be at least implicitly always on prediction due to the search for economic efficiency or shareholder value maximization. In line with that argument, Merchant (2012) contends that the current management accounting research focuses too much on


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generalizability and statistical significance rather than on deriving useful implications for practitioners. He shows that an empirical study might display that, in a broad sample, a correlation between x and y of 0.09 is significantly different from 0 but that the size of the R2 is small. A path coefficient of 0.10 can explain, at best, only 1% of the variance in the focal variable. A researcher should be aware that even with a high global-fit-index (GFI) in an SEM, other critical values such as the coefficient of determination can be low. Even if an effect with a path connection of 0.10 is significant, the question remains whether it is really theoretically interesting for a practical-orientated discipline such as management accounting. PLS-SEM maximizes the explained variance in the dependent variables based on a specific set of hypothesized relationships in a model. The higher the R2 score of a dependent variable, the better is its prediction (Hair et al., 2016). These elements of PLSSEM make it particularly useful for success driver studies, especially in combination with formative measurements (Albers, 2010; Hair et al., 2011). Moreover, latent variable scores of PLS-SEM can be interesting for further practical interpretation, such as importance-performance matrix analysis (Hair et al., 2016). A further often neglected reason for using PLS-SEM is that PLS-SEM allows for an easier integration of formative construct measurements into an SEM. Formative measurements have high practical relevance for management accounting research (Bisbe et al., 2007). Every formative indicator captures a specific aspect of a latent construct. In this way, the calculated weight for a formative indicator can be interpreted in the same way as the beta coefficient in a regression analysis (Hulland, 1999). These estimated weights for formatively measured constructs offer researchers the possibility of identifying specific success drivers and their relative importance (Albers, 2010). Rodgers and Guiral (2011) show that formative measurements are necessary for analysing financial and managerial data, such as assets, expenses, and revenues, in a structural equation model (cf. Goh, Ali, & Rasli, 2014). Such archival data plays a very important role for performance measurements in management accounting. For example, the measurement of company performance may comprise different components, such as ROI, market share, or earnings per share, as separate aspects of a formative construct measurement (Gefen et al., 2011). In contrast to PLS-SEM, the constraints for accommodating formative indicators in CB-SEM often contradict the theoretical assumptions (Diamantopoulos, 2011) and lead to identification problems (Jarvis, MacKenzie, & Podsakoff, 2003). McIntosh, Edwards, and Antonakis (2014), who are strong proponents of CB-SEM, emphasize that the decision to use PLSSEM should be made on the basis of whether there is a formative measurement part of the measurement model (which the authors seem to claim as the only legitimate reason for a study to use PLS-SEM). However, there are only a few contributions that use archival data or secondary data in PLS-SEM in management accounting so far. Interestingly, the first published article in a top-tier management accounting journal using PLS-SEM by Ittner et al. (1997) uses a combination of archival data and other latent measured variables. Unfortunately, the authors pay to little attention to the differentiation of formative and reflective measurements and use negative loadings for the measurement of the power of a CEO. A researcher should bear in mind that a wrongly defined measurement can heavily bias the inner model estimations of an SEM and therefore jeopardize theory development in management accounting research (Bisbe et al., 2007; Rodgers & Guiral, 2011). Nevertheless, the study by Ittner et al. (1997) provides a good orientation into the use of archival data in management accounting research using PLSSEM. An important neglected reason for using PLS-SEM in management accounting is that it is useful for theory development when models are complex and in an explorative stage. Smith and Langfield-Smith (2004) describe three different model strategies based on Jöreskog (1993) that can be applied for theory development in management accounting. The first is the strictly confirmatory strategy in which a single theoretical model is tested and is either accepted or rejected. A second possible approach is the alternative models strategy, in which a finite number of competing models are considered. Based upon certain criteria, these proposed models are evaluated, and the best-fitting model is selected. The final possible strategy is the model-generating strategy, in which an initially proposed theoretical model is repeatedly modified until some critical values are fulfilled. An example of an explorative strategy can be found in Smith, Everly, and Johns (1993). The authors improve their research model in a CB-SEM based on GFI by adding and dropping path connections. CB-SEM uses common factors to represent theoretical constructs and a simultaneous approach for the estimation of the parameters. Hence, this full information estimation of complex models with CB-SEM is often connected with problems obtaining a solution (Henseler et al., 2014; Reinartz et al., 2009). Therefore, CB-SEM forces a researcher regularly to modify a model in a certain way to fulfil the specific CB-SEM statistical requirements. However, deciding based on GFIs and other criteria whether a model is true does not automatically mean that a researcher actually found the true theoretical model. There are often alternative models that have the same GFI but with substantially different explanations for the data (Chin, 1998a). Based on the present state of theory/knowledge in a research area, one of the above strategies should be used to further theory development. As described previously, the present situation in management accounting is largely on an explorative stage and requires further theory development (Luft & Shields, 2014; Shields, 2015; Smith & Langfield-Smith, 2004). Identifying different plausible explanations and testing them in one single model can be very challenging due to the extensive range of possible theories in management accounting (Chapman, Hopwood, & Shields, 2007). Luft and Shields (2014, p. 554) conclude that “[m]ore plausible explanations provided by more diverse theories often mean that more different independent variables are potentially relevant. Using a larger number of variables is likely to require more data collection, more complex research designs to take into account the relations among these variables, and/or more knowledge on the part of researchers to deal with the resulting theoretical and methodological issues.” Smith and Langfield-Smith (2004) critically mention that the focus of management accounting research has mainly been on confirmation strategies so far and often does not reflect the true complex theoretical situations. Apparently, more model discovery strategies are

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necessary. Due to the lack of theories, a complete specification of relationships a priori is not possible, which therefore requires learning in a data-driven fashion. PLS-SEM can be an important tool for theory development in management accounting. Wold (1980, 1985) notes that the major advantage of PLS-SEM is that it is developed through the inclusion of a new variable, an indicator, or a new path relation or through the deletion of one of them. Thus, it reflects an evolutionary approach in which modifications and improvements are made based on the results, which gradually consolidates the design. PLS-SEM can handle complex exploratory situations better than other statistical methods because it is better at avoiding inadmissible solutions and factor indeterminacy (cf. Henseler et al., 2014), as PLS-SEM uses composites to represent theoretical constructs as proxies and applies a stepwise approach to parameter estimation (Rigdon, 2013). Furthermore, PLS-SEM as a limited information method is robust to misspecification (Gerbing & Hamilton, 1994). Therefore, PLS-SEM delivers a high degree of freedom in modelling complex situations with different data bases. However, it is also not conducive to start with a saturated PLS-SEM as a complete explorative approach with all possible connections between latent variables or indicators (Marcoulides & Chin, 2013). Such developed exploratory models can yield different considered variables or causal ordering (Ittner, 2014). Zimmerman (2001) states that, without theories, data collection and analysis are blind. Theories provide guidance with respect to the possible relationships that might exist and thereby define what types of data need to be collected. Models that are tested based on weak theories must begin with preliminary (“strawmen”) hypotheses. A promising approach also seems to be mixed method studies, in which case studies are used to identify possible influences as well as the types of relations (e.g., moderation), which can be tested in the next step in a PLS-SEM (Modell, 2005, 2010). How such theoretical development can be conducted using PLS-SEM in general can be illustrated using an example by Malmi and Granlund (2009). Malmi and Granlund (2009) suggest developing a theory of organizational incentive systems that can explain how to design and use such systems. Such a model could be based on theories such as agency theory, expectancy theory, and goal-setting theory. Through the inclusion of specific constructs (e.g., performance measures) and relationships, the new model can become a specific theory in management accounting. To test this incentive model, many different relationships and possible explanatory variables must be included, implying that SEM would be very exploratory at the beginning. The developed incentive system model can be tested using PLS-SEM across firms, industries, and countries to increase the reliability and validity of the theoretical concept. The last step is very important to further theory development because it is unlikely that a single tested model will provide conclusive evidence on a certain topic in management accounting (Shields, 2015). The aim of this process is to find management accounting theories of a “coherent set of propositions used as principles of explanation for a class of phenomena assumed to hold throughout a broad range of specific instances” (Malmi & Granlund, 2009, p. 605). Finally, Hartmann and Maas (2011) explore why the role of management accounts varies across business units by investigating how uncertainty influences the controller’s role. They do so by examining the effects through the role of budget systems. In the first step, the authors formulate three hypotheses regarding how uncertainty, the role of budgeting, and the role of the controller are causally connected based on the concept of uncertainty as a central factor in contingency theory (Fig. 2). This approach is in line with the above-mentioned statement that exploratory models also need a theoretical foundation, as they can yield different causal ordering. Based on the theoretical elaboration, the authors go into more detail in the next step by differentiating between the used constructs and connecting each following construct with each antecedent construct (Fig. 3). This process reflects the study’s explorative approach because for the subcategories, the lack of a guiding theory in management accounting prevents a complete theoretical derivation. Furthermore, such differentiation is also useful because the possibility of a practical interpretation grows with a more detailed approach. In the last step, the research model is tested for path coefficient significance and whether the influence is positive or negative. That approach reveals many interesting observations. For example, Hartmann and Maas (2011) find that only “enabling budget use” and “business partner role” are directly affected by the different constructs of uncertainty. However, the authors do not pay sufficient attention to mediation effects when they state that controllers’ corporate policeman role is not affected by any type of uncertainty. This statement is only true for direct effects and not for mediated effects via “enabling budget use” to the “corporate policeman role”. In particular, paying attention to mediation effects in the explorative phase is

[(Fig._2)TD$IG]

Fig. 2. Conceptual research model by Hartmann and Maas (2011, p. 444).


[(Fig._3)TD$IG]

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Fig. 3. Tested Path Model by Hartmann and Maas, 2011Hartmann and Maas (2011, p. 444).

important and can provide many interesting insights into how effects hinder or support each other. Hence, it is always advisable to test mediation/indirect effects in explorative models as a standard practice (Zhao, Lynch, & Chen, 2010). The explorative approach in the study by Hartmann and Maas (2011) is also supported by the fact that the authors use newly developed latent constructs for the measurement of the use of the budget system. Because this construct is not widely tested, it is advisable to use PLS-SEM because PLS-SEM is less affected by model misspecification. In the case of the study by Hartmann and Maas (2011), the measurements for “enabling budget use” and “coercive budget use” seem to be wrongly specified as reflective rather than as formative measurements. Finally, the sample size also calls for a more explorative approach. Based on a power analysis, the necessary sample size for the model is 85, which is less than the sample size of 134 that the authors use in the study. Thus, the authors are not in danger of overlooking relevant effects when using PLS-SEM, which is also important for explorative research and hence to further theory development (Willaby et al., 2015). In line with Shields (2015) statement, the model developed by Hartmann and Maas (2011) could be further tested, e.g., across countries, to increase the study’s reliability and validity. Furthermore, different types of constructs could also be included in the future to test a more comprehensive model, for example, by including the variables involved and an independent controller as concurrent explanations (Sathe, 1982). Overall, the study by Hartmann and Maas (2011) provides a very good example for how PLS-SEM can be useful tool for theory development through its explorative characteristics. Their use of PLS-SEM perfectly matches the above-described characteristics of PLS-SEM regarding the approach used, the use of newly developed constructs, and the sample size (Table 2). 3.2. Data characteristics in management accounting research The most prominent argument for choosing PLS-SEM in management accounting is to accommodate small sample sizes. The sample size is crucial for management accounting research when the focus is on theory development; hence, it is important not to eliminate true effects from further analysis too early (Willaby et al., 2015). Using a simulation study, Reinartz et al. (2009) show that PLS-SEM is often more appropriate than CB-SEM when the sample size is smaller than 250. For empirical management accounting research using survey studies, the mean sample size is 239 and the median is 125 (Van der Stede et al., 2005), thus indicating that small sample sizes are a relevant argument for the use of SEM in Table 2 Reasons for Using PLS-SEM in Management Accounting.a

Total Mentioning Small Sample Size Non-Normal Data Distribution Simultaneous Estimation Exploratory Objective Formative Measurements Model Complexity Prediction Target a

N

Percentage

33 29 25 9 8 6 5 1

89.2% 78.4% 67.6% 24.3% 21.6% 16.2% 13.5% 2.7%

The sum of the percentages exceed 100 percent because multiple reasons mentioned.

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C. Nitzl / Journal of Accounting Literature 37 (2016) 19–35 Table 3 Sampling Characteristics.

Sample Size Ø Ten Times Rule of Thumb not Met Less than the Necessary Sample Size for Detecting Medium Effect Sizes Nonresponse Bias Tested Common Method Variance Missing Values Reported Treatment of Outliers Power Analysis Non-Normality Tested

N

Percentage

138 4 15 19 4 4 4 4 2

10.8% 40.5% 51.4% 10.8% 10.8% 10.8% 10.8% 5.4%

management accounting (Smith & Langfield-Smith, 2004). As shown in Table 3, the average sample size in the review was 138 (median = 105). This average sample size is considerably lower than 292, which was reported for 41 management accounting studies using CB-SEM in the time period from 1980 to 2005 (Henri, 2007). In the present survey, the smallest sample size used was 18 (Anderson, Hesford, & Young, 2002) and the largest was 359 (Dowling, 2009). Although 19 studies (51.4%) addressed non-response bias, only four studies (10.8%) reported the important subject of detecting influential observations (outliers) and their treatment. Moreover, only four studies (10.8%) reported the exact treatment of missing values or the steps taken to control for common bias variance. Because one of the most cited reasons for PLS-SEM in management accounting research is that it can handle non-normally distributed data, it is somewhat surprising that only two studies (5.4%) reported the indicator data for a normal distribution (e.g., skewness and kurtosis). The often-cited sample size rationale for using PLS-SEM in management accounting has been intensely debated for many years (e.g., Henseler et al., 2014; Marcoulides & Chin, 2013; Rönkko & Evermann, 2013; Smith & Langfield-Smith, 2004), and it is also one of the most misused arguments (Goodhue et al., 2012; Marcoulides & Saunders, 2006). However, some contradictions should be resolved when considering that the meaning of sample size in SEM is important in two different ways. First, PLS-SEM shows better convergence characteristics than CB-SEM for small sample sizes (Henseler, 2010). Chin and Newsted (1999) show that PLS-SEM can deliver initial interpretable results starting with a sample size of 20 observations. PLS-SEM can even be used if the number of observations is smaller than the number of manifest or latent variables (Henseler et al., 2014). Therefore, PLS-SEM can often be applied when other methods fail due to a small sample size. This characteristic supports the exploratory nature of PLS-SEM (Henseler et al., 2014). The second issue relevant to the sample size argument is the role of inference statistics to increase the statistical power. In contrast to CB-SEM, PLS-SEM has a tendency to underestimate inner model relationships (Bentler & Huang, 2014; Dijkstra, 1983, 2014). Therefore, researchers often prefer CB-SEM over PLS-SEM (cf. Smith, 2011). Nevertheless, the results of the path coefficients in PLS-SEM become more accurate as the sample size grows (Hui & Wold, 1982; Reinartz et al., 2009). A management accounting researcher should always be aware that PLS-SEM estimations accompanying a questionably small sample size may deliver unstable estimations that cannot be used for valid practical conclusions. According to the rule of thumb of 10 cases per indicator provided by Barclay, Higgins, and Thompson (1995), only four studies (10.8%) in this review did not meet the minimum required sample size. However, the often-cited generic rule of thumb of 10 is not a reliable rule for determining a necessary sample size for PLS-SEM (Marcoulides & Chin, 2013). Because PLS-SEM essentially builds on OLS regressions, researchers can revert to statistical power analyses for multiple regression models (Cohen, 1992) to derive a satisfactory sample size. Statistical power is the probability of accepting an alternative Table 4 Sample Size for a Statistical Power of 0.80. Effect Size

Number of Predictors

1 2 3 4 5 6 7 8 9 10

0.02

0.15

0.35

(weak)

(medium)

(strong)

Significance Level

Significance Level

Significance Level

0.01

0.05

0.10

0.01

0.05

0.10

0.01

0.05

0.10

588 699 779 845 902 953 999 1042 1083 1121

395 485 550 602 647 688 725 759 791 822

311 388 444 489 527 562 594 623 651 677

82 98 109 114 127 135 142 148 154 160

55 68 77 85 92 98 103 109 114 118

43 54 62 69 75 80 85 90 94 98

37 45 51 55 59 63 67 70 73 76

25 31 36 40 43 46 49 52 54 57

20 25 29 32 35 38 41 43 45 47


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Table 5 Model Characteristics. N Number of latent variables Ø Number of inner model path Relations Ø Outer Model Specification Only reflective measurements Only formative measurements Reflective and formative measurements Indicators per reflective construct Ø Indicators per formative construct Ø Models with single items

Percentage

6.16 11.43 29 0 8 3.83 4.44 12

78.9% 0.00% 21.6%

32.4%

hypothesis when the alternative hypothesis is true. In other words, it is the ability of a test to detect an effect if an effect actually exists. This characteristic is how researchers gain insight into the true state of affairs. The statistical power is a function of the effect size (f2), the sample size (n), the number of predictors and the significance level (a) (Faul, Erdfelder, Lang, & Buchner, 2007). To determine the necessary sample size for PLS-SEM, a management accounting researcher should initially determine the statistical power. For business studies, a statistical power of at least 0.8 at an a level of 0.05 is considered acceptable (Cohen, 1988; Hair et al., 2010). Furthermore, management accounting researchers must decide how strong the relative effects are that they aim to detect. For example, to detect weak relative effects, much larger sample sizes are needed. The strength is measured using the effect size (f2), where values of 0.02, 0.15 and 0.35 indicate whether an exogenous variable has a relatively small, medium or large influence, respectively (Cohen, 1988). To calculate the necessary sample size, a PLS-SEM researcher also needs to determine the largest regression in the iteration process (Chin & Newsted, 1999). To do so, he must identify the variable with the greatest number of predictors, which is the variable in the inner structural model or in the outer measurement model (formative) with the most incoming arrows. Table 4, which follows, shows how the sample size depends on the number of predictors, the effect size, and the significance level for the statistical power of 0.80.2 To detect a medium effect size of 0.15 with five predictors (the median value of predictors in this review), a necessary sample size of 92 at a significance level of 0.05 is required. Because the average sample size in the review was 138, there appears to be no problem with respect to the necessary sample size. However, at the level of the individual studies, 15 (40.5%) did not exhibit the necessary sample size for detecting at least medium effects (a = 0.05). Furthermore, Table 4 shows that the necessary sample size is very high for detecting small effects (f2 = 0.02). No study in the review had the necessary sample size for detecting small effects. Nevertheless, management accounting researchers should bear in mind that small effects only explain, at best, 2% of the variance of a variable and therefore have only minor practical relevance. Hence, it seems quite reasonable for management accounting research to proceed from the minimum sample size for detecting medium effects in PLS-SEM. Additionally, common method variance (CMV) is an important issue. CMV is the variance that must be ascribed to the measurement method rather than to the theoretical relationships between constructs (Podsakoff, MacKenzie, Lee, & Podsakoff, 2003). If researchers do not control for CMV, the overall correlation between items might be inflated, therefore showing a greater relationship between constructs while at the same time reducing the discriminant validity between constructs (Straub, Boudreau, & Gefen, 2004). CMV is one of the main reasons why management accounting researchers are often very critical of survey-based research (cf. Van der Stede et al., 2005). Current studies show that the methods frequently used to detect and control for CMV do not work in PLS-SEM, for example, the partialling out of a general factor score to control CMV (Chin, Thatcher, & Wright, 2012; Liang, Saraf, Hu, & Xue, 2007; Rönkkö & Ylitalo, 2011). Nevertheless, Chin, Thatcher, Wright, and Steel (2013) are able to remove 72% of the variance caused by CMV in a simulation study through the inclusion of a four-item marker variable. Such marker variables must be independent of the theoretical question (uncorrelated) that is expected to be answered by the specific PLS-SEM (Williams, Hartman, & Cavazotte, 2010). In the management accounting context, Mahama and Cheng (2013) use a separately measured marker variable in their PLS-SEM, although without providing detailed information on their approach. Typical marker variables are social desirability (Podsakoff, MacKenzie, Lee et al., 2003) or bureaucracy (Rafferty & Griffin, 2006). In contrast, in a study where attitude scales were mainly used, a question about work experience in years is not a good marker variable because it is not subject to the same measurement effects (Elbashir, Collier, & Sutton, 2011; Lindell & Whitney, 2001; Rönkkö & Ylitalo, 2011). 3.3. Model characteristics in management accounting research Table 5 provides an overview of the model characteristics in the survey. On average, the number of latent variables was 6.16, which is lower than 7.94, the amount that was reported for PLS-SEM in marketing (Hair, Sarstedt, Ringle et al., 2012).

2 The necessary sample size was calculated using the free download (http://www.gpower.hhu.de/) of the program G*Power 3.1.9.2 (Faul, Erdfelder, Buchner, & Lang, 2009; Faul et al., 2007). The following settings for the calculation were used: "F test" (test family), "Linear multiple regression: Fixed model, R2 deviation from zero" (statistical test) and "A priori: Compute required sample sizes – given a, power, and effect size" (type of power analysis).

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However, the number of inner path relationships was 11.43, which is higher than the reported number of path relationships in marketing, with 10.56 (Hair, Sarstedt, Ringle et al., 2012). These findings mean that latent variables tend to be more frequently connected using PLS-SEM in management accounting research than in marketing research, which also indicates the more explorative state of management accounting research. However, the complexity of the tested models in general is somewhat low due to the relatively small set of latent constructs used (cf. Marcoulides & Chin, 2013). In addition, a higher number of factors would often better capture the complex interrelationships in the current explorative stage of many management accounting research areas. The vast majority of articles in management accounting research (78.38%) used the reflective measurement approach for measuring latent constructs. Eight models (21.62%) used both reflective and formative measures. In comparison with the PLS-SEM reviews noted above, formative measurement models have been used less in management accounting research than in any other research field. This result is surprising because, as already discussed, using formative measurements can be highly beneficial to management accounting research as practical-orientated research area. Rodgers and Guiral (2011) show that 79% of the studies that use SEM in general accounting journals potentially suffer from problems of measurement misspecification. Formative measurements are often defined as reflective measurements, which can lead to invalid inner model estimation. Additionally, in management accounting research, a high degree of measurement misspecification can be assumed (Bisbe et al., 2007). The best way to avoid such misspecifications are a priori techniques such as Diamantopoulos and Winklhofer (2001) approach to index construction, the examination of qualitative decision rules discussed by Jarvis et al. (2003), or the C-OAR-SE procedure described by Rossiter (2002). After a survey, a confirmatory tetrad analysis (CTA) can be applied to distinguish formative from reflective measurements (Gudergan, 2005; Gudergan, Ringle, Wende, & Will, 2008). The correct measurement specification is of crucial relevance in management accounting, where weak theoretical or conceptual grounds are often the basis of models, and possible misspecification can highly bias the results of path estimations (cf. Bisbe et al., 2007; Chenhall, 2012). Furthermore, management accounting researchers often need to develop entirely new constructs, which also increases the likelihood of unreliable measurements because such constructs have not been widely tested before (e.g., Bisbe & Malagueño, 2015; Chapman & Kihn, 2009; Chenhall, 2004, 2005; Naranjo-Gil & Hartmann, 2006; Rodgers & Guiral, 2011). As Churchill (1979) shows, the development process involves multiple rounds of data collection, testing, and refinement. Bagozzi (2011) shows that strong theories are necessary for model specification but also for the development and evaluation of indicators, which is not regularly the case in management accounting. Management accounting researchers have to use new constructs in a rather explorative way based on often weak theory bases. Furthermore, management accounting researchers often use archival data that are typically found in corporate databases, not characteristics that are created and refined to fulfil certain statistical requirements of CBSEM. However, that approach also means that a precondition of using CB-SEM in management accounting is often not fulfilled, whereas PLS-SEM may perform quite well (Gefen et al., 2011). The average number of indicators was 3.83 for reflective constructs and 4.44 for formative constructs. These results show that management accounting researchers do not fully take advantage of the capabilities of PLS-SEM by estimating more complex models with formative measurements and a large number of constructs. PLS-SEM allows the unrestricted use of single items. In this survey, nearly one out of every three contributions (12 studies; 32.43%) used single items for construct measurement in the models. However, management accounting researchers should pay close attention when using a single item for construct measurements because, in most cases, single items do not perform as well as multi-item measurements (Diamantopoulos, Sarstedt, Fuchs, Kaiser, & Wilczynski, 2012; Sarstedt & Wilczynski, 2009). Due to the “consistency at large” characteristic, five to six items per construct should be the goal in PLS-SEM (Lohmöller, 1989; Reinartz et al., 2009). Due to the higher consistency of the estimations, a more valid development of management accounting theory is possible in the future. Moreover, focusing on the predictive function of PLS-SEM also means that a higher number of observed variables for each conceptual construct is useful because a higher number of observed variables also improves the accuracy of forecasts (Rigdon, 2014). Furthermore, management accounting researchers should be careful when using categorical (binary) data. One study in the survey used a single binary indicator to measure a choice situation with an endogenous construct. However, due to the basic premise of the OLS algorithm, the use of categorical variables as endogenous variables is not possible under a standard

Table 6 Outer model evaluation.

Reflective

Quality criterion

Test criterion

N

Percentage

Indicator reliability Internal consistency reliability

Indicator loadings Composite reliability Cronbach's Alpha Average Variance Explained Fornell-Larcker criterion Cross-loadings

28 32 18 31 33 21

75.68% 86.49% 48.65% 83.78% 89.19% 56.76%

Indicator weights Significance levels VIF/tolerance

5 6 5

62.50% 75.00% 62.50%

Convergent validity Discriminant validity

Formative

Indicators absolute contribution Significance of weights Multicollinearity


29

implementation of PLS algorithms (Jakobowicz & Derquenne, 2007; Lohmöller, 1989). Binary variables should only be used as exogenous measurements. 3.4. Model evaluation in management accounting research The reliable and valid measurement of latent constructs is a prerequisite for accurately estimating an inner model in SEM. The inclusion of behavioural aspects and decision-making has become increasingly important over the last decades in management accounting and require the inclusion of latent psychological variables in research models (Trotman, Tan, & Ang, 2011). Such constructs often have to be measured using multi-item constructs that can be directly incorporated in PLS-SEM, in contrast to regression analyses. In accordance with Bisbe et al. (2007), a sound conceptualization of the measurement constructs in management accounting is crucial. For model measurement evaluation, researchers first need to distinguish between reflective and formative measurements (Podsakoff, MacKenzie, Lee et al., 2003; Podsakoff, MacKenzie, Podsakoff, & Lee, 2003). The typically used, internally consistent view of reflective measurements cannot be applied to formative measurements. Lee et al. (2011) provide a guideline for the evaluation of outer models in PLS-SEM. Table 6 shows the findings from the reviewed management accounting journals. From the total set of articles analysed, 28 studies (75.7%) reported the loadings for their reflective measurements, which represent the bivariate correlations between the indicators and their latent constructs. A total of 32 studies (86.5%) reported the composite reliability, and 18 studies (48.7%) reported the Cronbach’s alpha (Cronbach, 1951). This latter statistic is the most commonly used measure of internal consistency in the CB-SEM context (Davcik, 2014; Henri, 2007). However, because Cronbach’s alpha assumes that all indicators are equally reliable, it generally underestimates internal consistency reliability in PLS-SEM. Therefore, composite reliability provides a more appropriate measure in a PLS-SEM context (Werts, Linn, & Jöreskog, 1974). Following this reasoning, it should be critically noted that five studies relied on Cronbach’s alpha alone (13.5%) for the evaluation of internal consistency reliability. Some researchers interpret Cronbach’s alpha as a lower bound of reliability because of this tendency towards underestimation. However, this approach is only proper under certain conditions, e.g., with uncorrelated error terms (Raykov, 2001). Therefore, Cronbach’s alpha should not be considered a reliable criterion in PLS-SEM (Marcoulides & Chin, 2013). Convergent validity was assessed using the average variance extracted (AVE) value in 31 studies (83.8%). Moreover, discriminant validity was tested using either the Fornell-Larcker criterion (Fornell & Larcker, 1981a) in 33 studies (89.1%) or more liberal criteria with the help of cross-loadings in 21 studies (58.33%). However, these widely accepted discriminant validity assessments often fail to detect a lack of discriminant validity (Henseler, Ringle, & Sarstedt, 2015). Therefore, Henseler et al. (2015) propose a more reliable criterion to assess discriminant validity in PLS-SEM: the heterotrait-monotrait ratio of correlations (HTMT). For example, a value of HTMT above 0.85 indicates a lack of discriminant validity. In future management accounting studies, the more reliable HTMT should also be used for the assessment of discriminant validity. Despite the clear advantage of PLS-SEM when conducting formative measurements, only eight studies (21.6%) incorporated the formative measurement of at least one latent construct. The principles underlying formative measurements are fundamentally different from reflective measurements; therefore, their assessment process is also different (Petter, Straub, & Rai, 2007). The most common statistics used to assess formative measurements are indicator weights, which were reported in five studies (62.50%). A formative indicator’s weight represents the relative contribution of the indicator in forming the latent construct when the influences of all other indicators are controlled (Cenfetelli & Bassellier, 2009). A total of six out of eight studies (75.00%) reported the significance of the weights (t-values or p-values). As with multiple regression (Hair et al., 2010), high collinearity between formative indicators can bias the significance of weights because it increases the standard errors (Cenfetelli & Bassellier, 2009). Five studies (62.50%) assessed multicollinearity using the variance inflation factor (VIF). After the reliability and validity of the measurements have been ensured, an evaluation of the inner model is possible. PLS-SEM uses sample data to obtain parameters that minimize the variance (prediction orientation). In contrast, CB-SEM uses sample data to estimate parameters that minimize the difference between the empirical covariance matrix and the

Table 7 Inner model evaluation. Quality criterion/Additional Analyses

Test criterion

N

Percentage

Explained variance Effect size Predictive relevance Relative predicted relevance Path coefficients Significance of path coefficients Mediator Analysis Moderation Analysis Continuous Categorical

R2 f2 Cross-validated redundancy Q2 q2 Absolute values Statistical significance

35 3 4 0 37 37 12 9 3 6

95.0% 8.1% 10.8% 0.0% 100.0% 100.0% 32.4% 24.3% 8.1% 16.2%

30


covariance matrix estimated by the model (Hair et al., 2016). An SEM can yield a very good global-fit-index, but at same time, the coefficient of determination (R2) can be extremely low. Classical goodness-of-fit statistics are often inappropriate for overall model fit evaluation in PLS-SEM (Henseler & Sarstedt, 2013). A promising goodness-of-fit statistic for use in future model evaluation could be the standardized root mean square residual (SRMR) (Henseler et al., 2014). SRMR is the root mean square discrepancy between the observed correlations and the model-implied correlations and should be below 0.08 (Hu & Bentler, 1998). With SRMR, PLS-SEM can also be used in a more confirmatory management accounting theory approach. In the past, however, researchers have relied on variancebased, distribution-free evaluation criteria models that reflect the predictive capabilities of PLS-SEM (Table 7). The coefficient of determination (R2) measures predictive accuracy. Hence, it is the central criterion for judging the quality of PLS-SEM. As mentioned above, the focus of theory development in management accounting should also be on prediction (Malmi & Granlund, 2009; Merchant, 2012). Against this background, the average degree of explanation of the main focal variables of 33% seems somewhat low. Of all of the studies investigated, a total of 35 studies (94.6%) in management accounting research reported the R2. In contrast, only 43.9% of the management accounting studies using CBSEM reported the R2 (Henri, 2007). A second important criterion for the evaluation of a model is the effect size (f2), which was reported in only three studies (8.3%). In addition, the cross-validated redundancy measure Q2 can be used to assess predictive relevance (Wold, 1982). To calculate Q2, a PLS-SEM model must be repeatedly re-estimated while systematically excluding data points from the target construct (Rigdon, 2013). Although Q2 is an appropriate criterion for the prediction-oriented PLSSEM (Sarstedt et al., 2014), only four studies in management accounting (10.8%) reported the Q2. In line with f2, q2 also assesses the relative impact of a certain exogenous latent variable on an endogenous latent variable using the changes in the Q2 (Chin, 1998b). However, none of the reviewed studies reported the q2. To test the predictive orientation of a measurement model in PLS-SEM, management accounting researchers should use additional statistical criteria, such as f2, q2 and Q2, because valid overall fit criteria do not exist. In addition to assessing the predictive quality of PLS-SEM, evaluating the standardized path coefficients is important when deciding whether the hypothesized relationship can be found in the data. All of the reviewed studies reported the absolute values and the significance levels (t-values or p-values) of the path relationships. However, management accounting researchers have relied too heavily on the statistical level and have paid insufficient attention to the absolute size of a path relationship in their interpretations. Researchers should also consider the absolute size of a path coefficient because even when a relationship is significant, it might be too small to warrant managerial attention (cf. Hair, Sarstedt, Hopkins, & Kuppelwieser, 2014). Standardized paths connections should be higher than 0.2 to be considered relevant (Chin, 1998a). The analysis of inner models is not limited to direct relationships. Mediation and moderation effects become particularly relevant when models increase in complexity, as can be observed in management accounting research over the last several years (cf. Chenhall & Moers, 2007; Chenhall, 2012; Hartmann & Moers, 1999). In the review, twelve studies (32.4%) included an explicit mediator analysis. Furthermore, six studies conducted a moderation analysis with categorical variables (16.2%), and three conducted a moderation analysis with continuous variables (8.1%). Group comparisons infrequently include the necessary information for an assessment. For example, with respect to the often used Chin test (Chin, 2000), no study reported whether the variance was tested for equality (Henseler, Ringle, & Sarstedt, 2016; Sarstedt & Mooi, 2014) or addressed the issue of measurement invariance (cf. Eberl, 2010; Haenlein & Kaplan, 2011; Ringle, Sarstedt, & Zimmermann, 2011). Particularly in the areas of mediation and moderation, great potential for future research in management accounting exists (cf. Hartmann & Moers, 1999, 2003). However, especially for testing mediation and moderator effects, outdated methods are often used in management accounting. Guidelines for testing mediation can be found in Zhao et al. (2010) and for moderator effects in Henseler and Chin (2010). 3.5. Reporting in management accounting research Reporting plays a central role in the communication of SEM results (Hoyle & Panter, 1995). Shields (2015) views the relatively small number of studies reporting on the same set of variables as an important obstacle to theory development in management accounting research. The reproduction of studies with modifications is crucial for further theory development in management accounting, as illustrated above in the development of an organizational incentive system theory (Malmi & Granlund, 2009). Clear reporting is essential for a study’s reproducibility and provides researchers the opportunity to test alternative models. Therefore, such reporting is vital for the process of knowledge accumulation and theory development in a research area (Henri, 2007). Chin (2010) notes that, in addition to information on the population and sample structure, the distribution of the data, the theoretical model, and the statistical results, information on the specific details related to the software, the computational choices, and the parameter settings is also important in PLS-SEM reporting (cf. Smith & Langfield-Smith, 2004). Whereas nearly all of the studies in management accounting reported information about the sample structure (100.0%), the model structure (100.0%), and the measurements used (94.44%), little information was provided on computational and parameter settings. A total of 25 out of 37 studies (67.6%) reported the software package that was used for the estimations. Of the studies providing this information, 15 used PLS Graph (Chin, 2003), and the remaining ten studies used SmartPLS (Ringle, Wende, & Will, 2005). Because these programs rely on default settings, reporting which software package was used automatically provides additional information regarding the initial values used for the outer model relationships, parameter settings, computational options, and the maximum number of iterations of the stop criterion.


31

In addition to information regarding which software package was used, future management accounting studies should pay additional attention to some other reporting areas. The first area is reporting the computational options that are used in estimating the inner model. There are three main schemes (centroid, factor weighting, and path weighting) used for the calculation of inner weights in PLS-SEM (Henseler et al., 2009; Tenenhaus, Esposito Vinzi, Chatelin, & Lauro, 2005). None of the reviewed studies in management accounting provided information about the weighting scheme used. Moreover, not every weighting scheme is appropriate in every situation. For example, the path-weighting scheme is the standard weighting scheme and provides the highest R2 values for endogenous variables, whereas the factor scheme offers some advantages when multicollinearity is a critical factor (Hair et al., 2016). In the case of higher-order models in PLS-SEM, the centroid scheme should not be used. Additionally, with respect to statistical reporting in management accounting research, more technical details concerning resampling procedures are necessary. Because PLS-SEM is not built on the assumption of normally distributed data, it relies on a nonparametric bootstrap procedure to test coefficients for their significance (Hair et al., 2016). Of the 37 studies analysed, a total of 30 studies (81.1%) noted the use of bootstrapping (29 studies) or jack-knifing (one study), which surpassed the 66.2% rate found in marketing research (Hair, Sarstedt, Ringle et al., 2012). However, most studies in management accounting that used PLS-SEM typically only reported the number of bootstrapped subsamples (e.g., 500) but not precisely which resampling procedure was used. Additional reporting is necessary, for example, because the sign change option recommended by Henseler et al. (2009) is more likely to indicate a significant path when the path coefficient is close to zero compared with the no sign change option (Hair, Sarstedt, Pieper, & Ringle, 2012). Furthermore, reporting the sample number of bootstraps is important because using a smaller number than the original sample size considerably deflates standard errors (Chernick, 2011). 4. Conclusion PLS-SEM could be a very useful analysis tool for future theory development in management accounting, especially based on its suitability for exploratory research questions. Indeed, management accounting research frequently has exploratory elements because the theoretical basis is often weak. Therefore, researchers are habitually confronted with uncertainty about the correctness of their model, thus leaving their dependent variable unexplained. Given that management accounting researchers are often forced to use newly developed variables in SEMs, their findings are likely to be unreliable because such constructs have not yet been tested widely, or they use after-the-fact structural modelling of secondary data such as transactional data or data from financial statements. Moreover, accounting studies are frequently characterized by small sample sizes – a problem that can be tackled by PLS-SEM better than by CB-SEM. In an exploratory stage of research, it is important not to reject certain effects because of low power too early. The reviewed studies meet many of the requirements for PLS-SEM analysis; nonetheless, there are important areas for improvement. The aim of citing concrete publications was only to illustrate how scholars can improve their research. There was no intention to criticize how PLS-SEM was used in certain publications in the past. Based on the review, management accountants should pay more attention to the following topics. (1) They should concentrate more intensely on the predictive orientation as a reason for using PLS-SEM as a component-based method (including the use of formative measurements). (2) The necessary sample size for a specific PLS-SEM should be checked by means of a power analysis to detect at least mediumsized effects. (3) Multiple items should be used for construct measurement whenever possible, whereas binary-coded items should be used very carefully (e.g., not used as dependent variables). (4) Pursuant to the goal of prediction, additional criteria for inner model evaluation (e.g., predictive relevance and effect size) should be used. (5) Reporting the technical and computational options used for estimations in PLS-SEM (e.g., the bootstrapping procedure and the weighting scheme) should not be neglected. Additionally, there are a variety of new developments in the field of PLS-SEM that should not be neglected by management accounting researchers in the future. (1) The new PLSc-SEM delivers similar results to the CB-SEM and retains many of the advantages of the traditional PLS-SEM. (2) Controlling for CMV by means of marker variables should be employed. (3) After a survey, a CTA can be conducted to distinguish between formative and reflective measurements when there is doubt about the measurement specification. (4) The HTMT should also be used as a criterion to assess discriminant validity. (5) SRMR can be used for evaluating the global fit of a research model in a PLS-SEM. As with every analytical method, PLS-SEM also has certain constraints, and it should not be used thoughtlessly. There are two sides to every coin: on one side, PLS-SEM delivers a high degree of freedom; on the other side, a researcher must use it meticulously in a highly responsible manner. If the several choices involved in performing PLS-SEM are made incorrectly, the model will negatively influence the reliability and validity of the results and can possibly harm future theory development in management accounting. In recent years, the use of PLS-SEM has become more sophisticated; therefore, management accounting researchers must improve their knowledge of PLS-SEM (cf. Chenhall & Smith, 2011; Chenhall, 2012). Hence, this article presents a review of PLS-SEM usage in management accounting research and provides guidelines and recommendations for applying PLS-SEM that may be important for maintaining the rigor of research and publication practices in management accounting research.

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Acknowledgements The author would like to thank Marko Sarstedt, Roland Speklé, Jörg Henseler, Christian Ringle, Bernhard Hirsch, Matthias Sohn and Nicole Schulte for their valuable comments on an earlier version of the manuscript. I further wish to express my gratitude to the reviewers and participants at the 2015 International Symposium on Partial Least Squares Path Modeling in Seville (Spain), the 2015 Annual Meeting of the VHB in Vienna (Austria), the 2015 AAA Management Accounting Section Research Conference in Newport Beach (USA) as well as the 2014 Empirical Research in Management Accounting & Control Conference in Vienna (Austria) – their feedback and remarks helped me to improve the paper. I also thank Christian Daumoser and Vanessa Tews for their help in reviewing the management accounting journals. References Abernethy, M. A., Bouwens, J., & van Lent, L. (2010). Leadership and control system design. Management Accounting Research, 21(1), 2–16. Abernethy, M. 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