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Nonlinear structural equation model with one latent criterion , two latent predictors 1 and 2 ,a latent interaction term 1 2 , and two latent quadratic terms 1 2 and
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The analyses of latent quadratic effects are as important as the analyses of latent interaction effects in structural equation modeling. However, while the latter has received considerable attention in the methodological literature, relatively few studies have been conducted that analyze both nonlinear effects simultaneously in a polynomial structu...
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... methods aim at providing unbiased and efficient parameter estimates for the nonlinear effects. A nonlinear SEM with three nonlinear terms, one interaction term and two quadratic terms, is depicted in Figure 3. ...
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... and Judd (1984) suggested using all possible manifest product variables as indicators of the latent interaction term 1 2 . Using the constrained approach for the example depicted in Figure 3 this would require the forming of 9 product indicators for the latent interaction term, X 1 X 4 , X 1 X 5 , X 1 X 6 , X 2 X 4 , X 2 X 5 , X 2 X 6 , X 3 X 4 , X 3 X 5 , and X 3 X 6 . ...
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... a measurement model for all latent nonlinear terms that includes all possible manifest products would require many measurement equations (e.g., nine equations when two linear latent predictors are each measured by three indicators) with overlapping information, Marsh et al. (2004) suggested to use the matched-pair strategy: All indicators of the linear terms 1 and 2 should be used in the formation of the indicators of each latent nonlinear term, but each of the multiple indicators should be used only once for each nonlinear term. For our example depicted in Figure 3 this means that only three indicators for each nonlinear factor are needed: X 1 X 4 , X 2 X 5 , X 3 X 6 for the latent interaction term 1 2 , X 1 2 , X 2 2 , X 3 2 for the latent quadratic term 1 2 , and X 4 2 , X 5 2 , X 6 2 for the latent quadratic term 2 2 . A further revision of the constrained approach was done by Algina and Moulder (2001). ...
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... 11 = 22 = 1.00. According to Figure 3, the predictor variables 1 , 2 , and the criterion variable 1 were each measured by three indicator variables with a reliability of .80. The given selection of nonlinear effects results in a model in which 4% (5%) of the variance of 1 is explained by the interaction effect and 2% by each quadratic effect, while the linear effects each explain 10% of the variance of 1 . ...
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... Cross-validated redundancy measure is recommended to examine the predictive relevance of one's theoretical/structural model (Chin, 1998). The blindfolding procedure is used to assess the cross-validated redundancy of constructs (Moosbrugger, Schermelleh-Engel, Kelava, & Klein, 2009). This study has got a Q 2 value of 0.405 for brand image variable which is greater than zero and indicates the predictive relevance of the model (Moosbrugger et al., 2009). ...
... The blindfolding procedure is used to assess the cross-validated redundancy of constructs (Moosbrugger, Schermelleh-Engel, Kelava, & Klein, 2009). This study has got a Q 2 value of 0.405 for brand image variable which is greater than zero and indicates the predictive relevance of the model (Moosbrugger et al., 2009). ...
... The present study has got a R 2 value of 0.745 which indicates that the dependent variable is influenced by the independent variables by 74.50%. As a rule of thumb, a R 2 values of 0.75, 0.50, or 0.25 for endogenous latent variables can be respectively described as substantial, moderate, or weak (Hair, Ringle, & Sarstedt, 2011;Moosbrugger et al., 2009). The present study has got a R 2 value of 0.745 which is very close to substantial effect. ...
Strong brand image is an invaluable asset and organizations are giving continuous endeavor to build strong image for their goods and services. Likewise, marketing researchers are focusing on researches to find out ways to enhance brand image. In this study, Aaker’s Customer-Based Brand Equity Framework-1996, Keller’s Customer-Based Brand Equity Pyramid-2003 and Baker’s Corporate Social Responsibility Model-2001 have been taken into consideration for identifying the pertinent factors relating to brand image of hotel brands. Subsequently a number of variables have been extracted through extensive literature review to investigate their influence on building brand image for branded hotels in the context of Bangladesh. The variables include brand awareness, brand association, brand superiority, brand affection, brand resonance and corporate social responsibility which are deemed to have a direct influence on brand image while tourism management and advertisement have been used as the moderators in the relationship between these six IVs and brand image. Data were collected from the customers of some selected 4 star and 5 star hotels in Bangladesh using multi-stage sampling procedure. The Partial Least Square Structural Equation Modeling (PLS-SEM) was used to test the hypotheses of this study. It was found that brand awareness, brand association, brand superiority, brand resonance and corporate social responsibility were significant factors influencing brand image of branded hotels. Among these five determinants, corporate social responsibility was found to be the most significant followed by brand superiority, brand association, brand awareness and brand resonance. In the moderating effect test of tourism management, it was found that the relationship between brand superiority and brand image was moderated by tourism management; the relationship between brand resonance and brand image was also found to be moderated by tourism management. On the other hand, advertisement was found to be a moderator in the relationship between brand awareness and brand image; brand association and brand image, and Corporate Social Responsibility (CSR) and brand image. Based on the findings, this study proposes a new model named “SAARCAT” to measure brand image of branded hotels. The current study gathers opinions from the diverse group of participants on the factors influencing the hotel brand image. Thus it supplements empirical evidence to address the research gaps and responds to the calls for examining the brand image of branded hotels within hotel industry. In this way it adds some new insights into the customer based brand equity models as proposed by Aker’s (1996), Keller’s (2003) and Baker’s (2001). The results derived from this research provide several practical implications for hotel managers and policy makers specifically, in terms of how to evaluate, build and improve the hotel brand image.
... The latent moderated SEM method employed to estimate multiple latent interactions considers the non-normality explicitly caused by latent non-linear terms and measurement errors (Asparouhov & Muthén, 2021;Moosbrugger, Schermelleh-Engel, Kelava, & Klein, 2009). This method enables testing of interactions by controlling for possible correlations between the items that measure the factors involved in the interaction term. ...
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... According to it, a new moderation construct loading QtdProdInnov was created by multiplying all factors of the construct APD by the variable AC and decreasing the resulting variables by their means. The quadratic relationship between APD and product innovation was represented similarly by adding another construct formed by the squared proxies of the first, following Moosbrugger et al. (2009). ...
Most authors agree that alliance portfolio diversity (APD) has an inverted U-shaped influence on innovation performance and is particularly important for firms with a high absorptive capacity (AC), which moderates this relationship positively. However, the reality of developing countries with weaker national innovation systems (NIS) and firms with lower AC may influence these relationships. To test these hypotheses in such a context, we tested a longitudinal structural model in a sample of 1,237 Colombian manufacturing firms. The results indicated that, in a developing country context, APD at the appropriate level is especially relevant for firms with low AC, even the letter maintaining the positive moderation effect on the inverted U-shaped relationship of the former with innovation. Besides, the longitudinal structural equation modelling (SEM) chosen to conduct the analysis mitigates endogeneity issues presented in more commonly used cross-section analyses.
... For examining the influence of the different precursors on reading development, regressions were estimated from the intercept and slope of decoding abilities and text comprehension to IQ (K1), RAN, phonological awareness, letter knowledge, and language abilities (all K3). To estimate interactions and curvilinear effects, the latent moderated SEM approach was used (XWITH command in Mplus; Maslowsky et al., 2015;Moosbrugger et al., 2009). ...
Purpose: The transition to school and the first years of elementary school education are very sensitive phases for reading development. Reading researchers have established key precursors and developmental steps in these phases. However, how these components interact and affect growth is not well understood yet. The current study from Germany replicates established findings and explores how curvilinear effects can add informa- tion to our understanding of reading development.
Method: 525 German-speaking children were followed during a 5-year period from kindergarten to fourth Grade. Phonological awareness (PA), letter knowledge (LK), rapid naming (RAN) and language skills (LS) were assessed in kindergarten, decoding and reading comprehension in elemen- tary school. Analysis was based on latent growth models with curvilinear (quadratic) effects.
Results: The results indicate that PA and LK are of importance for early reading, RAN was additionally revealed to be of importance for further growth in decoding. Language skills and decoding, together with their interaction, explain variation in reading comprehension skills. A curvilinear effect was found for decoding on reading comprehension growth only. Conclusion: Our study shows which precursors predict growth in reading development in a transparent orthography and expands our understanding of how language and decoding affect the development of reading comprehension.
... To test the hypothesised quadratic effects and latent interactions, we used the latent moderated structural equation (LMS) approach (Klein & Moosbrugger, 2000;Moosbrugger et al., 2009). Researchers using CBSEM face difficulties in performing interactions between latent variables (Ping, 1996). ...
... The LMS approach for modelling the interactions of latent factors properly accounts for the non-normality of factors that are inherent in latent interaction models, and its maximum likelihood estimators exhibit desirable asymptotic and finite-sample statistical properties (Klein & Moosbrugger, 2000;Moosbrugger et al., 1997). The LMS method has been shown to do well in simulations (Little & Rubin, 2002;Marsh et al., 2004), generally outperforming alternative approaches for addressing interactions among latent variables (Klein & Moosbrugger, 2000;Marsh et al., 2006;Moosbrugger et al., 2009;Schermelleh-Engel et al., 1998Wen et al., 2003) and is regarded as 'the most efficient maximum likelihood method' (Dijkstra, 2014, p. 149). It uses maximum likelihood estimation with robust standard errors (henceforth MLR). ...
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... One reason is that the PI approach involves the specification of nonlinear parameter constraints that are difficult for researchers to implement (Kelava et al., 2011). To overcome the problem of PI, several other models (e.g., unconstrained approach, extended unconstrained approach), which freely estimate factor loadings, measurement error variances, as well as the variance of the latent nonlinear effect, have been considered (Kelava, 2009;Kelava & Brandt, 2009;Marsh et al., 2004Marsh et al., , 2006Moosbrugger et al., 2009). However, these traditional product indicator approaches still suffer from the violated assumption of multivariate normally distributed variables. ...
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forest algorithm for missing data under various reserach conditions. The design of the simulation study included random and non-random missingness (i.e., MCAR, MAR, and MNAR), small samples, and different levels of missing rates. All statistical inferences were investigated using latent variable interaction modeling. Consistent with the missing data literature, the combined effects of small sample sizes, higher missing rates, and non-ignorable missingness along with complicated modeling structure adversely affected the accuracy of statistical inferences. Although there is a possibility for overparameterization, it is a good way to select MI when convergence is concerned. If the primary goal of research is to investigate the relationship between variables as in many studies, ML would be attractive. MF presented similar performance compared to MI and ML across all research conditions and outperformed when estimating the variability of parameter estimates. Other practical issues pertaining to the missing data methods were also discussed.
... Several methods have been developed to compute interaction effects in structural equation models (Kenny & Judd, 1984;Klein & Moosbrugger, 2000;Klein & Muthén, 2007;Little et al., 2006;Marsh, Wen, & Hau, 2004;Marsh et al., 2007;Moosbrugger, Schermelleh-Engel, Kelava, & Klein, 2009) and, over the years, have become increasingly accessible and easier to use by researchers in the social science field (Girard & Béland, 2017;Girard et al., 2020;Lorah & Wong, 2018;Maslowsky et al., 2015). As depicted in Figure 2, these methods can be categorized into two approaches: product indicator and distribution analytic (Marsh et al.,Figure 2 Overview of latent interaction methods in SEM and advantages of the LMS method. ...
Structural equation modeling involving latent interaction has garnered much attention from researchers in many disciplines. Interestingly, Becher & Trowler (2001) described academics as living in a tribe sharing a common set of practices and led by a stable elite. To provide an overview of psychological and educational studies using the latent moderated structural equations approach (LMS), we produced a scoping review from three databases (ERIC, PsychInfo, and Érudit) and selected 78 articles. The goal of this study is to examine the nature and extent of practices regarding the use of the LMS method in order to recommend good practices. Our results show that there are some discrepancies in the way researchers analyze data using LMS.
... However, over the years, it has been developed in some methods for the use of SEM in nonlinear situations. Moosbrugger, Schermelleh-Engel [44] and Lodder, Denollet [45] mentioned Latent Moderated Structural Equations, LMS [46] in their work. In addition, Quasi-Maximum Likelihood, QML, [47] and Extended Constrained Approach [48] laid by Kenny and Judd [49] are among the methods that can be used. ...
SEM is multivariate statistical analysis. In addition to its advantageous aspects, it needs to cope with many assumptions. The ANN methods developed in recent years have advantages both in themselves and in the black box section, but there are cases when they cannot explain or fall short. In this study, we aimed to show that the two methods can be used together as a hybrid model and can support each other. In the study, we aimed to show the perceived brand personality and satisfaction about the city in Van province as a data set and to examine its effects on behavioral intentions. SEM-ANN, the Hybrid method, has been shown to be a supportive analysis method.
In the research, the survey technique was used as a data collection tool. In this study, SPSS 22.0 was used for confirmatory factor analysis and ANN analysis, and R program was used for SEM analysis within the scope of the reliability and validity studies for the scales.
... To do so, the latent moderated structural equation approach (LMS; Klein & Moosbrugger, 2000) was used. This approach represents an extension to the conventional SEM framework, as it takes the non-normality of the latent interaction of the predictor and the moderator variable into account (Moosbrugger, Schermelleh-Engel, Kelava, & Klein, 2009). The LMS approach was further extended to include a multigroup design. ...
Background. Based on learned helplessness theory and conservation of resources theory, the present study explores the role of schools’ social environments (i.e., school belonging, school exclusion, and teacher–student relationships) as potential buffers and amplifiers in students’ development of learned helplessness during adolescence.
Aims. We examine whether school belonging, school exclusion, and teacher–student relationship moderate the longitudinal association of learned helplessness differently for students from low-track schools and high-track schools.
Sample. The study uses a sample of N = 1,088 (Mage = 13.70, SD = 0.53; 54% girls) adolescent students who participated in a two-wave longitudinal study.
Methods. We conducted latent moderated structural equation modelling to examine whether school belonging, school exclusion, and teacher–student relationship moderate the longitudinal association of learned helplessness differently for students from low- track schools and high-track schools.
Results. The moderation analyses revealed that students from both school tracks are differently affected by school belonging and school exclusion in their development of learned helplessness. Teacher–student relationship did not moderate the association.
Conclusion. Our findings underline the important role of the social environment in students’ development of learned helplessness. Particularly, the differential effects found for the different educational tracks highlight the necessary awareness of educators to interindividual differences of their students.
