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Sports marketing and sponsorship research is located at the intersection of behavioral and design research, which means that it analyzes the current world and shapes a future world. This dual focus poses challenges for formulating and testing theories of sports marketing.

This article develops criteria for categorizing theoretical concepts as either behavioral or formed as different ways of expressing ideas of sports marketing research. It emphasizes the need for clear concept categorization for proper operationalization and applies these criteria to selected theoretical concepts of sports marketing and sponsorship research.

The study defines three criteria to categorize theoretical concepts, namely (1) the guiding idea of research, (2) the role of observed variables, and (3) the relationship among observed variables. Applying these criteria to concepts of sports marketing research manifests the relevance of categorizing theoretical concepts as either behavioral or formed to operationalize concepts correctly.

This study is the first in sports marketing to clearly categorize theoretical concepts as either behavioral or formed, and to formulate guidelines on how to differentiate behavioral concepts from formed concepts.

The purpose of this study is threefold: (1) to propose partial least squares path modeling (PLS-PM) as a way to estimate models containing composites of composites and to compare the performance of the PLS-PM approaches in this context, (2) to provide and evaluate two testing procedures to assess the overall fit of such models and (3) to introduce user-friendly step-by-step guidelines.

A simulation is conducted to examine the PLS-PM approaches and the performance of the two proposed testing procedures.

The simulation results show that the two-stage approach, its combination with the repeated indicators approach and the extended repeated indicators approach perform similarly. However, only the former is Fisher consistent. Moreover, the simulation shows that guidelines neglecting model fit assessment miss an important opportunity to detect misspecified models. Finally, the results show that both testing procedures based on the two-stage approach allow for assessment of the model fit.

Analysts who estimate and assess models containing composites of composites should use the authors’ guidelines, since the majority of existing guidelines neglect model fit assessment and thus omit a crucial step of structural equation modeling.

This study contributes to the understanding of the discussed approaches. Moreover, it highlights the importance of overall model fit assessment and provides insights about testing the fit of models containing composites of composites. Based on these findings, step-by-step guidelines are introduced to estimate and assess models containing composites of composites.

People seem to function according to different models, which implies that in business and social sciences, heterogeneity is a rule rather than an exception. Researchers can investigate such heterogeneity through multigroup analysis (MGA). In the context of partial least squares path modeling (PLS-PM), MGA is currently applied to perform multiple comparisons of parameters across groups. However, this approach has significant drawbacks: first, the whole model is not considered when comparing groups, and second, the family-wise error rate is higher than the predefined significance level when the groups are indeed homogenous, leading to incorrect conclusions. Against this background, the purpose of this paper is to present and validate new MGA tests, which are applicable in the context of PLS-PM, and to compare their efficacy to existing approaches.

The authors propose two tests that adopt the squared Euclidean distance and the geodesic distance to compare the model-implied indicator correlation matrix across groups. The authors employ permutation to obtain the corresponding reference distribution to draw statistical inference about group differences. A Monte Carlo simulation provides insights into the sensitivity and specificity of both permutation tests and their performance, in comparison to existing approaches.

Both proposed tests provide a considerable degree of statistical power. However, the test based on the geodesic distance outperforms the test based on the squared Euclidean distance in this regard. Moreover, both proposed tests lead to rejection rates close to the predefined significance level in the case of no group differences. Hence, our proposed tests are more reliable than an uncontrolled repeated comparison approach.

Current guidelines on MGA in the context of PLS-PM should be extended by applying the proposed tests in an early phase of the analysis. Beyond our initial insights, more research is required to assess the performance of the proposed tests in different situations.

This paper contributes to the existing PLS-PM literature by proposing two new tests to assess multigroup differences. For the first time, this allows researchers to statistically compare a whole model across groups by applying a single statistical test.

One popular method to assess discriminant validity in structural equation modeling is the heterotrait-monotrait ratio of correlations (HTMT). However, the HTMT assumes tau-equivalent measurement models, which are unlikely to hold for most empirical studies. To relax this assumption, the authors modify the original HTMT and introduce a new consistent measure for congeneric measurement models: the HTMT2.

The HTMT2 is designed in analogy to the HTMT but relies on the geometric mean instead of the arithmetic mean. A Monte Carlo simulation compares the performance of the HTMT and the HTMT2. In the simulation, several design factors are varied such as loading patterns, sample sizes and inter-construct correlations in order to compare the estimation bias of the two criteria.

The HTMT2 provides less biased estimations of the correlations among the latent variables compared to the HTMT, in particular if indicators loading patterns are heterogeneous. Consequently, the HTMT2 should be preferred over the HTMT to assess discriminant validity in case of congeneric measurement models.

However, the HTMT2 can only be determined if all correlations between involved observable variables are positive.

This paper introduces the HTMT2 as an improved version of the traditional HTMT. Compared to other approaches assessing discriminant validity, the HTMT2 provides two advantages: (1) the ease of its computation, since HTMT2 is only based on the indicator correlations, and (2) the relaxed assumption of tau-equivalence. The authors highly recommend the HTMT2 criterion over the traditional HTMT for assessing discriminant validity in empirical studies.

This study aims to examine the role of an overall model fit assessment in the context of partial least squares path modeling (PLS-PM). In doing so, it will explain when it is important to assess the overall model fit and provides ways of assessing the fit of composite models. Moreover, it will resolve major concerns about model fit assessment that have been raised in the literature on PLS-PM.

This paper explains when and how to assess the fit of PLS path models. Furthermore, it discusses the concerns raised in the PLS-PM literature about the overall model fit assessment and provides concise guidelines on assessing the overall fit of composite models.

This study explains that the model fit assessment is as important for composite models as it is for common factor models. To assess the overall fit of composite models, researchers can use a statistical test and several fit indices known through structural equation modeling (SEM) with latent variables.

Researchers who use PLS-PM to assess composite models that aim to understand the mechanism of an underlying population and draw statistical inferences should take the concept of the overall model fit seriously.

To facilitate the overall fit assessment of composite models, this study presents a two-step procedure adopted from the literature on SEM with latent variables.

This paper clarifies that the necessity to assess model fit is not a question of which estimator will be used (PLS-PM, maximum likelihood, etc). but of the purpose of statistical modeling. Whereas, the model fit assessment is paramount in explanatory modeling, it is not imperative in predictive modeling.

In their paper titled “A Miracle of Measurement or Accidental Constructivism? How PLS Subverts the Realist Search for Truth,” Cadogan and Lee (2022) cast serious doubt on PLS’s suitability for scientific studies. The purpose of this commentary is to discuss the claims of Cadogan and Lee, correct some inaccuracies, and derive recommendations for researchers using structural equation models.

This paper uses scenario analysis to show which estimators are appropriate for reflective measurement models and composite models, and formulates the statistical model that underlies PLS Mode A. It also contrasts two different perspectives: PLS as an estimator for structural equation models vs. PLS-SEM as an overarching framework with a sui generis logic.

There are different variants of PLS, which include PLS, consistent PLS, PLSe1, PLSe2, proposed ordinal PLS and robust PLS, each of which serves a particular purpose. All of these are appropriate for scientific inquiry if applied properly. It is not PLS that subverts the realist search for truth, but some proponents of a framework called “PLS-SEM.” These proponents redefine the term “reflective measurement,” argue against the assessment of model fit and suggest that researchers could obtain “confirmation” for their model.

Researchers should be more conscious, open and respectful regarding different research paradigms.

Researchers should select a statistical model that adequately represents their theory, not necessarily a common factor model, and formulate their model explicitly. Particularly for instrumentalists, pragmatists and constructivists, the composite model appears promising. Researchers should be concerned about their estimator’s properties, not about whether it is called “PLS.” Further, researchers should critically evaluate their model, not seek confirmation or blindly believe in its value.

This paper critically appraises Cadogan and Lee (2022) and reminds researchers who wish to use structural equation modeling, particularly PLS, for their statistical analysis, of some important scientific principles.

As technology in tourism and hospitality (TTH) develops technical artifacts according to visitors’ demands, it must deal with both behavioral and design constructs in the context of structural equation modeling (SEM). While behavioral constructs are typically modeled as common factors, the study at hand introduces the composite into TTH to model artifacts. To deal with both kinds of constructs, this paper aims to exploit partial least squares path modeling (PLS-PM) as a confirmatory approach to estimate models containing common factors and composites.

The study at hand presents PLS-PM in its current form, i.e. as a full-fledged approach for confirmatory purposes. By introducing the composite to model artifacts, TTH scholars can use PLS-PM to answer research questions of the type “Is artifact xyz useful?”, contributing to a further understanding of TTH. To demonstrate the composite model, an empirical example is used.

PLS-PM is a promising approach when the model contains both common factors and composites. By applying the test for overall model fit, empirical evidence can be obtained for latent variables and artifacts. In doing so, researchers can statistically test whether a developed artifact is useful.

To the best of the authors’ knowledge, this is the first study to discuss the practical application of composite and common factor models in TTH research. Besides introducing the composite to model artifacts, the study at hand also guides scholars in the assessment of PLS-PM results.

因为旅游酒店科技（TTH）根据游客需求而定制科技产品, TTH必须在结构方程模型（SEM）下结合游客行为和设计等变量。一般行为变量在模型中是常见因子, 本研究将这些变量编入TTH结构成为模块。本研究采用PLS-PM方法来预估含有隐性变量和模块的模型。.

本研究设计PLS-PM模式, 即确定性全变量方法。TTH学者们通过引进结构形成模型模块, 使用PLS-PM研究方法, 以回答研究问题“模块xyz有用吗？”, 因此对TTH进一步理解。为了展示复合模型, 本论文采用实际验证。.

PLS-PM在面对模块内存在常见因子和复合模块的结构时是有力方法。实际验证结果通过整体最佳模型参数, 得到隐性变量和模块。为此, 研究者们能够在统计方法上测量是否开发的模型模块是否有用。.

据作者所知, 本论文是首个研究在TTH领域上应用模块和常见因子模型。本研究引进显性变量在模型模块中, 以指导学者评估PLS-PM结果报告。.

The purpose of this paper is to enhance consistent partial least squares (PLSc) to yield consistent parameter estimates for population models whose indicator blocks contain a subset of correlated measurement errors.

Correction for attenuation as originally applied by PLSc is modified to include a priori assumptions on the structure of the measurement error correlations within blocks of indicators. To assess the efficacy of the modification, a Monte Carlo simulation is conducted.

In the presence of population measurement error correlation, estimated parameter bias is generally small for original and modified PLSc, with the latter outperforming the former for large sample sizes. In terms of the root mean squared error, the results are virtually identical for both original and modified PLSc. Only for relatively large sample sizes, high population measurement error correlation, and low population composite reliability are the increased standard errors associated with the modification outweighed by a smaller bias. These findings are regarded as initial evidence that original PLSc is comparatively robust with respect to misspecification of the structure of measurement error correlations within blocks of indicators.

Introducing and investigating a new approach to address measurement error correlation within blocks of indicators in PLSc, this paper contributes to the ongoing development and assessment of recent advancements in partial least squares path modeling.