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The Standardization of Linear and Nonlinear Effects in Direct and Indirect Applications of Structural Equation Mixture Models for Normal and Nonnormal Data.

Brandt H, Umbach N, Kelava A - Front Psychol (2015)

Bottom Line: The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Jedidi et al., 1997b; Bauer, 2005; Muthén and Asparouhov, 2009; Wall et al., 2012; Kelava and Brandt, 2014; Muthén and Asparouhov, 2014).Here, we provide a general standardization procedure for linear and nonlinear interaction and quadratic effects in mixture models.The procedure can also be applied to multiple group models or to single class models with nonlinear effects like LMS (Klein and Moosbrugger, 2000).

View Article: PubMed Central - PubMed

Affiliation: Hector Research Institute of Education Sciences and Psychology, Eberhard Karls Universität Tübingen Tübingen, Germany.

ABSTRACT
The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Jedidi et al., 1997b; Bauer, 2005; Muthén and Asparouhov, 2009; Wall et al., 2012; Kelava and Brandt, 2014; Muthén and Asparouhov, 2014). The advantage of mixture models is that unobserved subgroups with class-specific relationships can be extracted (direct application), or that the mixtures can be used as a statistical tool to approximate nonnormal (latent) distributions (indirect application). Here, we provide a general standardization procedure for linear and nonlinear interaction and quadratic effects in mixture models. The procedure can also be applied to multiple group models or to single class models with nonlinear effects like LMS (Klein and Moosbrugger, 2000). We show that it is necessary to take nonnormality of the data into account for a correct standardization. We present an empirical example from education science applying the proposed procedure.

No MeSH data available.


Standardized multivariate relationship between reading attitude, online activities and reading skills.
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Figure 2: Standardized multivariate relationship between reading attitude, online activities and reading skills.

Mentions: The results for the two class solution of Model (b), which is the indirect application of a mixture model with (non)-linear effects, are presented in Table 3. In this model, the online activities had a significant negative quadratic effect on reading skills with an effect size of . The standardized linear effect for reading attitude was strong with . This effect can be interpreted as the effect for subjects with an average level of reading attitude. The standardized multivariate relationship between reading attitude, online activities, and reading skills are illustrated in Figure 2. The nonlinear relationship between online activities and reading skills modeled a saturation effect; that is, for subjects with standardized online activities between –3 and 0, a positive relation with reading skills was observed. For subjects with standardized online activities between 0 and 3, the reading skills only changed marginally. The explained variance in the model was 35% (1 − 0.647).


The Standardization of Linear and Nonlinear Effects in Direct and Indirect Applications of Structural Equation Mixture Models for Normal and Nonnormal Data.

Brandt H, Umbach N, Kelava A - Front Psychol (2015)

Standardized multivariate relationship between reading attitude, online activities and reading skills.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4663265&req=5

Figure 2: Standardized multivariate relationship between reading attitude, online activities and reading skills.
Mentions: The results for the two class solution of Model (b), which is the indirect application of a mixture model with (non)-linear effects, are presented in Table 3. In this model, the online activities had a significant negative quadratic effect on reading skills with an effect size of . The standardized linear effect for reading attitude was strong with . This effect can be interpreted as the effect for subjects with an average level of reading attitude. The standardized multivariate relationship between reading attitude, online activities, and reading skills are illustrated in Figure 2. The nonlinear relationship between online activities and reading skills modeled a saturation effect; that is, for subjects with standardized online activities between –3 and 0, a positive relation with reading skills was observed. For subjects with standardized online activities between 0 and 3, the reading skills only changed marginally. The explained variance in the model was 35% (1 − 0.647).

Bottom Line: The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Jedidi et al., 1997b; Bauer, 2005; Muthén and Asparouhov, 2009; Wall et al., 2012; Kelava and Brandt, 2014; Muthén and Asparouhov, 2014).Here, we provide a general standardization procedure for linear and nonlinear interaction and quadratic effects in mixture models.The procedure can also be applied to multiple group models or to single class models with nonlinear effects like LMS (Klein and Moosbrugger, 2000).

View Article: PubMed Central - PubMed

Affiliation: Hector Research Institute of Education Sciences and Psychology, Eberhard Karls Universität Tübingen Tübingen, Germany.

ABSTRACT
The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Jedidi et al., 1997b; Bauer, 2005; Muthén and Asparouhov, 2009; Wall et al., 2012; Kelava and Brandt, 2014; Muthén and Asparouhov, 2014). The advantage of mixture models is that unobserved subgroups with class-specific relationships can be extracted (direct application), or that the mixtures can be used as a statistical tool to approximate nonnormal (latent) distributions (indirect application). Here, we provide a general standardization procedure for linear and nonlinear interaction and quadratic effects in mixture models. The procedure can also be applied to multiple group models or to single class models with nonlinear effects like LMS (Klein and Moosbrugger, 2000). We show that it is necessary to take nonnormality of the data into account for a correct standardization. We present an empirical example from education science applying the proposed procedure.

No MeSH data available.