Limits...
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.


Simple slopes for female (black lines) and male students (gray lines) based on a standardization using the pooled variances. The relationship for online activities and reading skills were estimated for low, average, and high reading attitudes.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4663265&req=5

Figure 4: Simple slopes for female (black lines) and male students (gray lines) based on a standardization using the pooled variances. The relationship for online activities and reading skills were estimated for low, average, and high reading attitudes.

Mentions: Figure 4 illustrates the relationships between the variables using simple slopes based on standardized effects using the pooled means and variances.


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)

Simple slopes for female (black lines) and male students (gray lines) based on a standardization using the pooled variances. The relationship for online activities and reading skills were estimated for low, average, and high reading attitudes.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 4: Simple slopes for female (black lines) and male students (gray lines) based on a standardization using the pooled variances. The relationship for online activities and reading skills were estimated for low, average, and high reading attitudes.
Mentions: Figure 4 illustrates the relationships between the variables using simple slopes based on standardized effects using the pooled means and variances.

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.